a wide range of real - world data takes the format of _ matrices _ and _ tensors _ , e.g. , recommendation , video sequences , climates , genomes , and neuro - imaging .a naive way to learn from such matrix and tensor data is to vectorize them and apply ordinary regression or classification methods designed for vectorial data .however , such a vectorization approach would lead to loss in structural information of matrices and tensors such as _ low - rankness_.  the objective of this paper is to investigate regression and classification methods that directly handle tensor data without vectorization .low - rank structure of _ data _ has been successfully utilized in various applications such as missing data imputation , robust principal component analysis , and subspace clustering . in this paper , instead of low - rankness of data itself , we consider its dual_learning coefficients _ of a regressor and a classifier .low - rankness in learning coefficients means that only a subspace of feature space is used for regression and classification.  for matrices , regression and classification has been studied in and in the context of eeg data analysis .it was experimentally demonstrated that directly learning matrix data by low - rank regularization can significantly improve the performance compared to learning after vectorization .another advantage of using low - rank regularization in the context of eeg data analysis is that analyzing _singular value spectra _ of learning coefficients is useful in understanding activities of brain regions .more recently , an inductive learning method for tensors has been explored .compared to the matrix case , learning with tensors is inherently more complex .for example , the _ multilinear _ ranks of tensors make it more complicated to find a proper low - rankness of a tensor compared to matrices which has only one rank .so far , several tensor norms such as the _ overlapped trace norm _ or the _ tensor nuclear norm _ , the _ latent trace norm _ , and the _ scaled latent trace norm _ have been proposed and demonstrated to perform well for various tensor structures .however , theoretical analysis of tensor learning in inductive learning settings has not been much investigated yet .another challenge in inductive tensor learning is efficient optimization strategies , since tensor data often has much higher dimensionalities than matrix and vector data .  in this paper, we theoretically and experimentally investigate tensor - based regression and classification with regularization by the overlapped trace norm , the latent trace norm , and the scaled latent trace norm .we first provide their dual formulations and propose optimization procedures using the _ alternating direction method of multipliers _ , which is computationally efficient when the number of data samples is moderate .we then derive an excess risk bound for each tensor regularization , which allows us to theoretically understand the behavior of tensor norm regularization .more specifically , we elucidate that the excess risk of the overlapped trace norm is bounded with the average multilinear ranks of each mode , that of the latent trace norm is bounded with the minimum multilinear rank among all modes , and that of the scaled latent trace norm is bounded with the minimum ratio between multilinear ranks and mode dimensions .finally , for simulated and real tensor data , we experimentally investigate the behavior of tensor - based regression and classification methods .the experimental results are in concordance with our theoretical findings , and tensor - based learning methods compare favorably with vector- and matrix - based methods .the remainder of the paper is organized as follows . in section 2, we formulate the problem of tensor - based supervised learning and review the overlapped trace norm , the latent trace norm , and the scaled latent trace norm . in section 3 , we derive dual optimization algorithms based on the alternating direction method of multipliers . in section 4 , we theoretically give an excess risk bound for each tensor norm . in section 5 ,we give experimental results on both artificial and real - world data and illustrate the advantage of tensor - based learning methods .finally , in section 6 , we conclude this paper .   throughout the paper ,we use standard tensor notation following .we represent a -way tensor as that consists of elements .a mode- fiber of is an -dimensional vector which can be obtained by fixing all except the index .the mode- unfolding of tensor is represented as which is obtained by concatenating all the mode- fibers along its columns .the spectral norm of a matrix is denoted by which is the maximum singular value of .the operator is the sum of element - wise multiplications of and , i.e. , .the frobenius norm of a tensor is defined as .in this section , we put forward inductive tensor learning models with tensor regularization and review different tensor norms used for low - rank regularization .our focus in this paper is regression and classification of tensor data .let us consider a data set , where is a covariate tensor and is a target . for regression , while for classification .we consider the following learning model for a tensor norm : where is the loss function : the squared loss , is used for regression , and the logistic loss , is used for classification . is the bias term and is the regularization parameter . if or , then the above problem is equivalent to ordinary vector - based - or -regularization .  to understand the effect of tensor - based regularization , it is important to investigate the low - rankness of tensors . when considering a matrix , its _ trace norm _is defined as where is the singular value and is the number of non - zero singular values ( ) .a matrix is called _ law rank _if . the matrix trace norm is a convex envelop to the matrix rank and it is commonly used in matrix low - rank approximation .  as in matrices ,the rank property is also available for tensors , but it is more complicated due to its multidimensional structure .the mode- rank of a tensor is defined as the rank of mode- unfolding and the multilinear rank of is given as .the mode- of a tensor is called low rank if .one of the earliest definitions of a tensor norm is the _ tensor nuclear norm _ or the _ overlapped trace norm _ , which can be represented for a tensor as the overlapped trace norm can be viewed as a direct extension of the matrix trace norm since it unfolds a tensor on each of its mode and computes the sum of trace norms of the unfolded matrices .regularization with the overlapped trace norm can also be seen as an overlapped group regularization due to the fact that the same tensor is unfolded over different modes and regularized with the trace norm .one of the popular applications of the overlapped trace norm is _ tensor completion _ , where missing entries of a tensor are imputed .another application is _ multilinear multitask learning _ , where multiple vector - based linear learning tasks with a common feature space are arranged as a tensor feature structure and the multiple tasks are solved together with constraints to minimize the multilinear ranks of the tensor feature .theoretical analyses on the overlapped norm have been carried out for both tensor completion and multilinear multitask learning ; they have shown that the prediction error of overlapped trace norm regularization is bounded by the average mode- ranks which can be large if some modes are close to full rank even if there are low - rank modes .thus , these studies imply that the overlapped trace norm performs well when the multilinear ranks have small variations , and it may result in a poor performance when the multilinear ranks have high variations .  to overcome the weakness of the overlapped trace norm , recent research in tensor norms has led to new norms such as the _ latent trace norm _ and the _ scaled latent trace norm _ . proposed the latent trace norm as the latent trace norm takes a mixture of latent tensors which is equal to the number of modes , and regularizes each of them separately .in contrast to the overlapped trace norm , the latent tensor trace norm regularizes different latent tensors for each unfolded mode and this gives the tendency that the latent tensor trace norm picks the latent tensor with the lowest rank .in general , the latent trace norm results in a mixture of latent tensors and the content of each latent tensor would depend on the rank of its unfolding . in an extreme case , for a tensor with all its modes full except one mode , regularization with the latent tensor trace norm would result in making the latent tensor withthe lowest mode become prominent while others become zero .recently , proposed the scaled latent trace norm as an extension of the latent trace norm : compared to the latent trace norm , the scaled latent trace norm takes the rank relative to the mode dimension .a major drawback of the latent trace norm is its inability to identify the rank of a mode relative to its dimension .if a tensor has a mode where its dimension is smaller than other modes yet its relative rank with respect to its mode dimension is high compared to other modes , the latent trace norm could incorrectly pick the smallest mode .the scaled latent norm has the ability to overcome this problem by its scaling with the mode dimensions such that it is able to work with the relative ranks of the tensor . in the context of multilinear multitask learning, it has been shown that the scaled latent trace norm works well for tensors with high variations in multilinear ranks and mode dimensions compared to the overlapped trace norm and the latent trace norm .the inductive learning setting mentioned in with the overlapped trace norm has been studied previously in . however, theoretical analysis and performance comparison with other tensor norms have not been conducted yet . similarly to tensor decomposition and multilinear multitask learning , tensor - based regression and classificationmay also be improved by regularization methods that can work with high variations in multilinear ranks and mode dimensions .  in the following sections , to make tensor - based learning more practical and to improve the performance , we consider formulation with the overlapped trace norm , the latent trace norm , and the scaled latent trace norm , and give computationally efficient optimization algorithms and excess risk bounds .in this section , we consider the dual formulation for and propose computationally efficient optimization algorithms . since optimization of with regularization using the overlapped trace norm has already been studied in , we do not discuss it again here .our main focus in this section is optimization of with regularization using the latent trace norm and the scaled latent trace norm .let us consider the formulation for a data set with latent and scaled latent trace norm regularization as follows : where , for and for any given regularization parameter , in the case of the latent trace norm and in the case of the scaled latent trace norm , respectively . is the unfolding of on its mode .it is worth noticing that the application of the latent and scaled latent trace norms requires optimizing over latent tensors which contain variables in total . for large and ,solving the primal problem can be computationally expensive especially in non - linear problems such as logistic regression , since they require computationally expensive optimization methods such as gradient descent or the newton method .if the number of training samples is , solving the dual problem of could be computationally more efficient .for this reason , we focus on optimization in the dual below .  the dual formulation of can be written as follows ( its detailed derivation is given in appendix a ) :  where are dual variables corresponding to the training data set , is the _ conjugate loss function _ defined as in the case of regression with the squared loss , and with constraint in the case of classification with the logistic loss . is the indicator function defined as if and otherwise .the constraint is due to the bias term . here , the auxiliary variables are introduced to remove the coupling between the indicator functions in the objective function ( see appendix a for details ) .the _ alternating direction method of multipliers _ ( admm ) has been previously used to solve primal problems of tensor decomposition and multilinear multi - task learning with the overlapped trace norm regularization .optimization in the dual for tensor decomposition problems with the latent and scaled latent trace norm regularization has been solved using admm in . here, we also adopt admm to solve , and describe the formulation and the optimization steps in detail .  with introduction of dual variables ( corresponding to the primal variables of ) , , and parameter , the augmented lagrangian function for is defined as follows : this admm formulation is solved for variables , , , and by considering sub - problems for each variable .below , we give the solution for each variable at iterative step .the first sub - problem to solve is for at step : where , and are the solutions obtained at step .depending on the conjugate loss , the solution for differs . in the case of regression with the squared loss, the augmented lagrangian can be minimized with respect to by solving the following linear equation : where \in \mathbb{r}^{m \times n}$ ] , , , , and is the -dimensional vector of all ones .note that , in the above system of equations , coefficient matrix multiplied with does not change during optimization .thus , it can be efficiently solved at each iteration by precomputing the cholesky factorization of the matrix .  for classification with the logistic loss, the newton method is used to find the solution for , which requires the gradient and the hessian of : k\beta  \langle \mathcal{x}_{i } ,  \mathcal{x}_{j } \rangle + \beta & ( i\neq j ) .\end{cases}\end{aligned}\ ] ]  next , we update at step by solving the following sub - problem : where and .finally , we update the dual variables and at step as note that step and step can be combined as where and .this allows us to avoid computing singular values and the associated singular vectors that are smaller than the threshold in .   as a stopping condition , we use the _ relative duality gap _ , which can be expressed as where is the primal solution at step of and is a predefined tolerance value is the dual solution at step of with obtained by multiplying with , where and is the largest singular value of .in this section , we theoretically analyze the excess risk for regularization with the overlapped trace norm , the latent trace norm , and the scaled latent trace norm .we consider a loss function which is lipshitz continuous with constant .note that this condition is true for both the squared loss and logistic loss functions .let the training data set be given as , where for regression and for classification . in our theoretical analysis, we assume that elements of independently follow the standard gaussian distribution .  as the standard formulation , the empirical risk without the bias term is defined as and the expected risk is defined as where is the probability distribution from which are sampled .  the optimal that minimizes the expected risk is given as where is either the overlapped trace norm , the latent trace norm , or the scaled latent trace norm .the optimal that minimizes the empirical risk is denoted as   the next lemma provides an upper bound of the excess risk for tensor - based learning problems ( see appendix b for its proof ) , where is the dual norm of for :  for a given -lipchitz continuous loss function and for any such that for problems , the excess risk for a given training data set is bounded with probability at least as where and are rademacher random variables .the next theorem gives an excess risk bound for overlapped trace norm regularization ( its proof is also included in appendix b ) , which is based on the inequality given in :  with probability at least , the excess risk of learning using the overlapped trace norm regularization for any with , multilinear ranks , and estimator with is bounded as where and and are constants .  in the next theorem, we give an excess risk bound for the latent trace norm ( its proof is also included in appendix b ) , which uses the inequality given in :  with probability at least , the excess risk of learning using the latent norm regularization for any with , multilinear ranks , and estimator with is bounded as where and , , and are constants .the above theorem shows that the excess risk for the latent trace norm is bounded by the minimum multilinear rank .if , the latent trace norm is always better then the overlapped trace norm in terms of the excess risk bounds because .if the dimensions are not the same , the overlapped trace norm could be better .  finally , we bound the excess risk for the scaled latent trace norm based on the inequality given in :  with probability at least , the excess risk of learning using the scaled latent trace norm regularization for any with , multilinear ranks , and estimator with is bounded as where , , and are constants .  note that when and the multilinear ranks are different , the bounds in theorem 2 and theorem 3 are the same .theorem 3 shows that the excess risk for regularization with the scaled latent trace norm is bounded with the minimum of multilinear ranks relative to their mode dimensions .similarly to the latent trace norm , the scaled latent trace norm would also perform better than the overlapped norm when the multilinear ranks have large variations .if we consider a `` flat '' tensor , the modes with small dimensions may have ranks comparable to their dimensions .although these modes have the lowest mode- rank , they do not impose a low - rank structure .in such cases , our theory predicts that the scaled latent trace norm performs better because it is sensitive to the mode- rank relative to its dimension .  as a variation, we can also consider a mode - wise `` scaled '' version of the overlapped trace norm defined as .it can be easily seen that holds and with the same conditions as in theorem 1 , we can upper - bound the excess risk for the scaled overlapped trace norm regularization as note that when all modes have the same dimensions , coincides with . compared with bound , the scaled latent norm would perform better than the scaled overlapped norm regularization since .we conducted several experiments using simulated and real - world data to evaluate the performance of tensor - based regression and classification methods with regularizations using different tensor norms .we discuss simulations for tensor - based regression in section 5.1 , experiments with real - world data for tensor classification in section 5.2 . for all experiments, we use a matlab environment on a 2.10 ghz ( 2 cores ) intel xeon e5 - 2450 server machine with 128 gb memory .we report the results of artificial data experiments on tensor - based regression .we generated three different -mode tensors as weight tensors with different multilinear ranks and mode dimensions .we created two homogenous tensors with equal mode dimensions of with different multilinear ranks and .the third weight tensor is an inhomogenous case with mode dimensions of , and multilinear ranks . to generate these weight tensors, we use the _ tucker decomposition _ of a tensor as , where is the core tensor and are component matrices .we sample elements of the core tensor from a standard gaussian distribution , choose component matrices to be orthogonal matrices , and generate by mode - wise multiplication of the core tensor and component matrices . to create training samples , we first create the random tensors generated with each element independently sampled from the standard gaussian distribution and obtain , where is noise drawn from the gaussian distribution with mean zero and variance . in our experiments we use cross validation to select the regularization parameter from range at intervals of . for the purpose of comparison , we have also simulated matrix regularized regressions for each mode unfolding . also , we experimented with cross validation among matrix regularization on each unfolded matrix to understand whether it can find the correct mode for regularization .as the baseline vector - based learning method , we use _ ridge regression _( i.e. , -regularized least - squares ) .figure 1 shows the performance of homogenous tensors with equal mode dimensions and equal multilinear ranks  .we see that the overlapped norm performs the best , while both latent norms perform equally ( since mode dimensions are equal ) but inferior to the overlapped norm .also , the regression results from all matrix regularizations with individual modes perform better than the latent and the scaled latent norm regularized regression models . due to the equal multilinear ranks and equal mode dimensions, it results in equal performance with cross validation among each mode - wise unfolded matrix regularization .figure 2 shows the performances of homogenous tensors with equal mode dimensions and unequal multilinear ranks . in this case, both the latent and the scaled latent norms also perform equally since tensor dimensions are the same .the mode- regularized regression models give the best performance since it has the lowest rank and regularization with the latent and scaled latent norms gives the next best performance .the mode - wise cross validation correctly coincides with the mode- regularization .the overlapped norm performs poorly compared to the latent and the scaled latent trace norms .figure 3 shows the performance of inhomogenous tensors with mode dimensions , and multilinear ranks . in this case, we can see that the scaled latent trace norm outperforms all other tensor norms .the latent trace norm performs poorly since it fails to find the mode with the lowest rank. this well agrees with our theoretical analysis : as shown in , the excess risk of the latent trace norm is bounded with the minimum of multilinear ranks , which is on the first mode in the current setup and it is high ranked .the scaled latent trace norm is able to find the mode with the lowest rank since it takes the relative rank with respect to the mode dimension as in .if we look at the individual mode regularizations , we see that the best performance is given with the second mode , which has the lowest rank with respect to the mode dimension , and the worst performance is given with the first mode , which is high ranked compared to other modes . here , the mode - wise cross validation is again as good as mode- regularization .   and unequal multilinear rank ,title="fig : " ] [ fig:1 ]   and unequal multilinear rank ,title="fig : " ] [ fig:2 ]  , and multilinear rank  , title="fig : " ] [ fig:3 ]  , and multilinear rank  , title="fig : " ] [ fig:5 ]  it is also worth noticing in all above experiments that ridge regression performed worse than all the tensor regularized learning models .this highlights the necessity of employing low - rank inducing norms for learning with tensor data without vectorization to get the best performance .figure 4 shows the computation time for the toy regression experiment with inhomogenous tensors with mode dimensions , and multilinear ranks  ( computation time for other setups showed similar tendency and thus we omit the results ) . for each dataset , we measured the computation time of training regression models , cross validation for model selection , and predicting output values for test data .we can see that methods based on tensor norms and matrix norms are computationally much more expensive compared to ridge regression .however , as we saw above , they achieves higher accuracy than ridge regression .it is worth noticing that mode - wise cross validation is computationally more expensive compared to the scaled latent trace norm and other tensor norms .this computational advantage and comparable performance with respect to the best mode - wise regularization makes the scaled latent trace norm a useful regularization method for tensor - based regression especially for tensors with high variations in its multilinear ranks .next , we report the results of experiments on tensor classification with the _ cambridge hand gesture data set _ .the cambridge hand gesture data set contains image sequences from 9 gesture classes .these gesture classes include 3 primitive hand shapes of flats , spread , and v - shape , and 3 different hand motions of rightward , leftward , and contrast .each class has 100 image sequences with different illumination conditions and arbitrary motions of two people .previously , the _ tensor canonical correlation _ has been used to classify these hand gestures .  to apply tensor classification ,first we build action sequences as tensor data by sampling images with equal time intervals from each sequence .this makes each sequence a tensor of , where the first two modes are down - sampled images as in and is the number of sampled images . in our experiments , we set at or .we consider binary classification and we have chosen visually similar sequences of left / flat and left / spread ( figure 5 ) , which we found to be difficult to classify .we apply standardization of data by mean removal and variance normalization .we randomly sample data into a training set of data elements , use a validation set of data elements to select the optimal regularization parameter , and finally use a test set of elements to evaluate the learned classifier .in addition to the tensor regularized learning models , we also trained classifiers with matrix regularization with unfolding on each mode separately .as a baseline vector - based learning method , we have used the -regularized logistic regression .we also trained mode - wise cross validation with individual mode regularization ( mode - wise cv ) .we repeated the learning procedure for sample sets for each classifier and the results are shown in table 1 .[ fig:4 ]  .classification error of experiments with the hand gesture data set .the boldfaced figures indicate comparable accuracies among classifiers after a t - test with significance of . [cols="^,^,^ " , ]   the results of the experiment are given in table [ t:2 ] , which strongly indicate that vector - based logistic regression is clearly outperformed by the overlapped and scaled latent trace norms . also , in most cases , the averaged matrix method performs poorly compared to the optimal tensor structured regularization methods .mode-1 regularization performs poorly since mode-1 was high ranked compared to the other modes .similarly , the latent trace norm gives poor performance since it can not properly regularize since it does not consider the rank relative to the mode dimension .for all subjects , mode-2 and mode-3 unfolded regularizations result in the same performance due to the symmetry of each resulting in same rank along mode-2 and mode-3 unfoldings . for subject _ aa _ , the scaled latent norm , mode-1 , mode-2 , and mode - wise cross validation give the best or comparable performance .in subject _al _ , all classifiers except the latent norm and mode-1 regularization gives comparable performance .for all other subjects except for _ aa _ and _ al _ , the overlapped trace norm gives the best performance .in contrast to the computation time for regression experiments , in this experiment , we see that the computation time for tensor trace norm regularizations are more expensive compared to the mode - wise regularization . also , the mode - wise cross validation is computationally less expensive than the scaled latent trace norm and other tensor trace norms .this is a slight drawback with the tensor norms , though they tend to have higher classification accuracy .in this paper , we have studied tensor - based regression and classification with regularization using the overlapped trace norm , the latent trace norm , and the scaled latent trace norm .we have provided dual optimization methods , theoretical analysis and experimental evaluations to understand tensor - based inductive learning .our theoretical analysis on excess risk bounds showed the relationship of excess risks with the multilinear ranks and dimensions of the weight tensor .our experimental results on both simulated and real data sets further confirmed the validity of our theoretical analyses . from the theoretical and empirical results, we can conclude that the performance of regularization with tensor norms depends on the multilinear ranks and mode dimensions , where the latent and scaled latent norms are more robust in tensors with large variations of multilinear ranks .our research opens up many future research directions .for example , an important direction is on improvement of optimization methods .optimization over the latent tensors that results in the use of the latent trace norm and the scaled latent trace norm increases the computational cost compared to the vectorized methods .also , computing multiple singular value decompositions and solving newton optimization sub - problems ( for logistic regression ) at each iterative step are computationally expensive .this is evident from our experimental results on computation time for regression and classification. it would be an important direction to develop computationally more efficient methods for learning with tensor data to make it more practical .regularization with a mixture of norms is common in both vector - based ( e.g. , the _ elastic net _ ) and matrix - based regularizations .it would be an interesting research direction to combine sparse regularization ( the -norm ) to existing tensor norms .there is also a recent research direction to develop new composite norms such the -trace norm .development of composite tensor norms can be useful for inductive tensor learning to obtain sparse and low - rank solutions .kw acknowledges the monbukagakusho mext scholarship and kakenhi 23120004 , rt acknowledges xxxxxx , and ms acknowledges the jst crest program .in this appendix , we derive the dual formulation of the latent trace norms .let us consider a training data set , where . to derive the dual for the latent trace norms , we rewrite the primal for the regression of as  its lagrangiancan be written by introducing variables as let us introduce auxiliary variables to remove the coupling between the indicator functions .then the above dual solutions can be restated as  similarly , we can derive the dual formulation for logistic regression .in this appendix , we prove the theoretical results in section 4 .  _ proof of lemma 1 _ : by using the same approach as the one given in , we rewrite + [ \hat{r}(\mathcal{\hat{w } } ) - \hat{r}(\mathcal{w}^{0 } ) ]  + [ \hat{r}(\mathcal{w}^{0 } ) - r(\mathcal{w}^{0})].\end{gathered}\ ] ] the second term is always negative and based on hoeffding s inequality , with probability , the third term can be bounded as : further applying mcdiarmid s inequality , with probability at least , we get the following following rademacher complexity : where are rademacher variables which leads to   _ proof of theorem 1 _ : first we bound the data - dependent component of . for this, we use the following duality relationship borrowed from : since we can take any to equal , the above norm can be upper bounded as furthermore , the expectation of the minimum of can be upper - bounded by the minimum of the expectation : let be fixed rademacher variables . since each contains elements following the standard gaussian distribution , it makes each element in a sample from .based on the standard methods used in , we can express as using gordan s theorem as in , we have next taking the expectation over , we have combining and with results in finally , the excess loss can be written as   _ proof of theorem 2 _ : to bound the data - dependent component , we use the duality result given in : since consists of elements following the standard gaussian distribution , for each mode unfolding , we can write a tail bound as using a union bound , we have and this results in where is a constant .similarly to , taking the expectation over , we arrive at where is constant .finally , the excess risk is given as   _ proof of theorem 3 _ : from , we have using a similar approach to the latent trace norm with the additional scaling of , we arrive at the following excess bound for the scaled latent trace norm :           ganesh , a. , lin , z. , wright , j. , wu , l. , chen , m. , and ma , y. ( 2009 ) .fast convex optimization algorithms for exact recovery of a corrupted low - rank matrix . in _ proceedings of 3rd ieee international workshop on computational advances in multi - sensor adaptive processing _ ,pages 213216 .karatzoglou , a. , amatriain , x. , baltrunas , l. , and oliver , n. ( 2010 ) .multiverse recommendation : n - dimensional tensor factorization for context - aware collaborative filtering . in _ proceedings of the fourth acm conference on recommender systems _ ,pages 7986 .kim , t .- k . , wong , s .- f . , and cipolla , r. ( 2007 ) .tensor canonical correlation analysis for action classification . in _ proceedings of the ieee conference on computer vision and pattern recognition _ , pages 18 .liu , j. , musialski , p. , wonka , p. , and ye , j. ( 2009 ) .tensor completion for estimating missing values in visual data . in _ proceedings of the ieee international conference on computer vision _ ,pages 21142121 .sankaranarayanan , p. , schomay , t. e. , aiello , k. a. , and alter , o. ( 2015 ) .tensor gsvd of patient- and platform - matched tumor and normal dna copy - number profiles uncovers chromosome arm - wide patterns of tumor - exclusive platform - consistent alterations encoding for cell transformation and predicting ovarian cancer survival ., 10(4):e0121396 .wimalawarne , k. , sugiyama , m. , and tomioka , r. ( 2014 ) .multitask learning meets tensor factorization : task imputation via convex optimization . in _ advances in neural information processing systems 27_ , pages 28252833 .

Abstract: we theoretically and experimentally investigate tensor - based regression and classification . our focus is regularization with various tensor norms , including the _ overlapped trace norm _ , the _ latent trace norm _ , and the _ scaled latent trace norm_. we first give dual optimization methods using the _ alternating direction method of multipliers _ , which is computationally efficient when the number of training samples is moderate . we then theoretically derive an excess risk bound for each tensor norm and clarify their behavior . finally , we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor - based learning methods over vector- and matrix - based learning methods .


one of the most important tasks of data mining is the search for partial dependencies in data .a partial dependency between attributes means that some values occur together more often than expected , if the attributes were independent .when two attribute sets and are partially dependent , the dependency can be expressed as a rule , for the given value combinations and .if the rule is common and strong enough , it is called an _ association rule _ .  the commonness and strength of rule measured by frequency + and confidence .it is required that and for some user - defined thresholds and .the problem of traditional association rules is that they do not reflect the statistical significance of partial dependencies .statistically , the significance of an association rule is defined by the probability that it has occurred by chance . in practice ,the statistical significance depends on two things : frequency , , and the degree of dependence , .the stronger the dependence , the smaller the frequency can be , and vice versa .this means that no absolute values can be given for the minimum frequency and minimum confidence .this problem is well - known , and especially webb has criticized the frequency - confidence framework . he has shown that in the worst case , all discovered rules are spurious ( statistically insignificant ) .berzal et al . and aggarwal and yu have shown that the frequency - confidence framework is problematic , even if the absolute threshold values are not used .still the mainstream has ignored the problem , because the efficiency of the search algorithms lies on the frequency - based pruning .nearly all search algorithms utilize the antimonotonicity of the frequency : if set is not frequent ( given some ) , then none of its supersets can be frequent .if the minimum frequency is set too high , several significant rules can be missed . on the other hand ,if the minimum frequency is too low , a large number of spurious rules is accepted and the problem becomes computationally intractable . in statistics ,these two error types accepting spurious patterns and rejecting true patterns are known as _ type 1 _ and _ type 2 errors_.  as a solution , statistical or other objective measures have been used to rank the discovered rules or to guide the search ( e.g.  ) .these measures have generally two problems : either they are designed to assess dependencies between attributes ( not attribute values ) and can miss significant association rules , or they are statistically unsound .  in this paper, we examine how well the common interestingness measures and search heuristics capture significant association rules . for each method, we analyze whether it can make type 1 or type 2 error and the conditions under the errors they occur .we give several important results which can be used to select the most suitable search heuristics for the given mining task . on the other hand, the new theoretical results can give an insight for developing new , statistically sound search methods for partial dependencies .the paper is structured as follows : in section 2 the problem of finding statistically significant association rules is formalized .the basic definitions of full and partial dependencies , association rules , and statistical significance are given .the effect of commonly used interest measures and search heuristics to the statistical significance is analyzed in sections 35 . in section 3, we analyze how well the basic measures of association rules , frequency , confidence , and the degree of dependency , indicate the statistical significance . in section 4 ,we proceed into more complex measures : , correlation coefficient , and -measure .the effect of common redundancy reduction techniques is analyzed in section 5 .the final conclusions are drawn in section [ concl ] .we begin by formalizing the problem and give exact definitions for full and partial dependencies , association rules , and statistical significance .the basic notations are defined in table [ reldb ] .when it is clear from the context , we use abbreviations and for single attribute values and , and or for assignment .  [ reldb ]   statistical dependence is classically defined through statistical independence ( see e.g.  ) . in the following ,we will concentrate on _ two - way dependencies _ , i.e. dependencies between two attribute sets or events .let and be sets of binary attributes .  events and , , , are _ mutually independent _, if .attribute sets and are mutually independent , if for all value combinations and .if the events or attribute sets are not independent , they are _the following example demonstrates that attribute sets can be dependent , even if some events are independent :  let be a set of binary attributes , where attribute depends on attribute set .still it is possible that events and are mutually independent .table [ probesim ] gives an example of such a probability assignment ..a probability assignment , where attribute depends on set , but event is independent. . [ cols="<,<",options="header " , ]a common goal in association rule discovery is to find the most general rules ( containing the minimal number of attributes ) which satisfy the given search criteria .there is no sense to output complex rules , if their generalizations , are at least equally significant .generally , the goal is to find _ minimal _ ( or most general ) _ interesting rules _ , and prune out _ redundant rules _ .   generally , redundancy can be defined as follows :  given some interestingness measure , rule is a minimal rule , if there does not exist any rule such that , and .if the rule is not minimal , then it is redundant .measure can be -measure , -measure , -measure , or any function which increases with the interestingness . in the traditional frequency - confidence - framework with minimum frequency and confidence thresholds, can be defined as   the motivation for the redundancy reduction is two - fold : first , a smaller set of general rules is easier to interpret than a large set of complex and often overlapping rules .second , the problem complexity is reduced , because it is enough to find a small subset of all interesting rules .thus , it is possible at least in principle to perform the search more efficiently .  in the previous research, redundancy has been defined in various ways .an important distinction is whether the redundancy refers to the _ interestingness _ of a rule or the _ representation _ of rules . in the first case ,a rule is considered redundant , if there are more general rules which are at least equally interesting .such a redundant rule contains no new information and it can be pruned out . in the second case ,even an interesting rule is considered redundant , if it ( or its frequency and confidence ) can be derived from the other rules in the representation .now the rule is not pruned out , but it is not represented explicitly .examples of such _ condensed representations _ are closed , free , and non - derivable sets .we will briefly analyze the effect of two common pruning techniques on discovering statistically significant rules .the important question is , whether a statistically significant rule can be pruned out as `` redundant '' causing type 2 error .   according to a classical definition( e.g.  ) , rule is redundant , if there exists such that .the aim of this definition is to achieve a compact representation of all frequent and strong association rules .the justification is sensible in the traditional frequency - confidence - framework with fixed thresholds and : if rule is frequent and strong enough , then all its specializations with are also frequent and strong .  however , this definition is not adequate , if the goal is to find the most significant rules .in fact , it causes always type 2 error ( rejects the most significant rules ) , unless .if , then rule has higher confidence and is more significant than :  if for some , then  * , and * only if .let redundant , i.e.  such that .let , and . according to the redundancy condition .now  because . iff .  type 1 error ( accepting spurious rules ) is also likely , because the least significant rules are output .so , in the worst case all significant rules are pruned and only spurious rules are presented .  in the context of closed sets ,the definition of redundancy is similar ( e.g.  ) .however , now it is required that there exists more general rule , and , such that and .this means that and have the same frequency and confidence .still it is possible that ( i.e.  ) and the more significant rule is pruned .   according to another common interpretation ,rule is considered redundant or uninteresting , if there exists more general rule , , such that . following we call these rules _ non - productive_. if for all , rule is _productive_. the aim of this definition is to prune out rules which are less interesting than their generalizations .the heuristic works correctly and avoids type 2 error . for non - productive rule , .in addition , we know that and can not be more significant than . in practice , this means that contains some attributes which are either independent from or negatively correlated with .generally , it is required that the improvement of rule is sufficient : in practice , each rule is compared only to its immediate generalizations ( ) . if equation ( [ imp ] ) does not hold for some , then rule and all its specializations are pruned .the problem is that now there could be such that and which is statistically more significant than .this rule is not discovered , because the whole branch was pruned .thus , the pruning condition should not be used to restrict the search space .  instead, the pruning condition can be used in the post - processing phase , where a rule is compared to all its generalizations .we will show that requirement is a necessary but not sufficient condition for the superiority of over .this means that type 2 error does not occur , but type 1 error ( accepting spurious rules ) is possible .however , when , also type 2 error is possible , and non - redundant significant rules can be missed .the following theorem gives a necessary and sufficient condition for the superiority of :  let for some .rule is more significant than , if and only if        since it follows that  if , then and .now we can give a better pruning condition than equation ( [ imp ] ) :  if then .the condition can be expressed equivalently as    this pruning condition is more efficient than , but still it does not prune out any non - redundant significant rules . generally , the correct threshold depends on the rules considered and , and no absolute thresholds ( other than ) can be used .in this paper , we have formalized an important problem : how to find statistically significant association rules .we have inspected the most common interest measures and search techniques from the statistical point of view .for all methods , we have analyzed , whether they can cause type 1 error ( accept spurious rules ) or type 2 error ( reject significant rules ) and the conditions under which the errors can occur .the conclusions are the following : the traditional frequency - confidence framework should be abandoned , because it can cause both type 1 and type 2 errors .the simplest correction is to adopt the so called frequency - dependence framework , where the degree of dependence is used instead of confidence .if the minimum frequency is set carefully ( theorem [ safeminfr ] ) , no significant rules are missed . on the other hand ,all insignificant rules with the desired level of significance can be pruned , using the -measure .the -measure works correctly only if all significant partial dependencies in the data are actually full dependencies .when it is used to asses association rules , several spurious rules can be accepted ( type 1 error ) .type 2 error does not occur , if the partial dependencies are sufficiently significant , but the ranking order of association rules can be incorrect .pearson correlation coefficient is not recommendable for assessing association rules .it can easily cause both type 1 and type 2 errors .-measure can also cause both error types , although type 1 error ( accepting spurious rules ) is more likely .both and omit the data size , , and it can be hard to decide proper cut - off values for significant dependencies .  finally , we analyzed two common redundancy reduction techniques , which compare rule to its generalizations , . we showed that the minimum improvement condition , , works correctly , if .however , it can not be used to restrict the search space , but only for post - processing . if , significant rules can be missed .we gave also a more efficient pruning condition , which can be used to prune redundant rules without type 2 error .in the future research , these new insights should be utilized in the search algorithms for discovering the statistically most significant rules .the computational efficiency of such algorithms is a potential bottle - neck , but the starting point looks promising : while the small increases the number of frequent sets , we can use -based pruning to restrict the search space , and the effects may compensate each other .aggarwal , c. , yu , p. : a new framework for itemset generation . in : proceedings of the seventeenth acm sigact - sigmod - sigart symposium on principles of database systems ( pods 1998 ) , pp .acm press , new york , usa ( 1998 )  agrawal , r. , imielinski , t. , swami , a. : mining association rules between sets of items in large databases . in : p.buneman , s. jajodia ( eds . ) proceedings of the 1993 acm sigmod international conference on management of data , pp .washington , d.c .( 1993 )  bastide , y. , pasquier , n. , taouil , r. , stumme , g. , lakhal , l. : mining minimal non - redundant association rules using frequent closed itemsets . in : proceedings of the first international conference on computational logic ( cl00 ) , _ lecture notes in computer science _ , vol .1861 , pp .springer - verlag , london , uk ( 2000 )  berzal , f. , blanco , i. , snchez , d. , miranda , m.a.v . : a new framework to assess association rules . in : proceedings of the 4th international conference on advances in intelligent data analysis ( ida01 ) , _ lecture notes in computer science _ , vol . 2189 , pp .springer - verlag , london , uk ( 2001 )  blanchard , j. , guillet , f. , gras , r. , briand , h. : using information - theoretic measures to assess association rule interestingness . in : proceedings of the fifth ieee international conference on data mining ( icdm05 ) , pp .ieee computer society , washington , usa ( 2005 )  boulicaut , j.f . , bykowski , a. , rigotti , c. : approximation of frequency queris by means of free - sets . in : proceedings of the 4th european conference principles of data mining and knowledge discovery ( pkdd00 ) , _ lecture notes in computer science _1910 , pp .springer - verlag ( 2000 )  brin , s. , motwani , r. , silverstein , c. : beyond market baskets : generalizing association rules to correlations . in : j. peckham ( ed . ) proceedings acmsigmod international conference on management of data , pp . 265276 .acm press ( 1997 )  calders , t. , goethals , b. : mining all non - derivable frequent itemsets . in : proceedings of the 6th european conference on principles of data mining and knowledge discovery ( pkdd02 ) , _ lecture notes in computer science _ ,vol . 2431 , pp .springer - verlag , london , uk ( 2002 )  casas - garriga , g. : statistical strategies for pruning all the uninteresting association rules . in : r.l .de mntaras , l. saitta ( eds . ) proceedings of the 16th eureopean conference on artificial intelligence ( ecai2004 ) , pp .ios press ( 2004 )  dong , x. , sun , f. , han , x. , hou , r. : study of positive and negative association rules based on multi - confidence and chi - squared test . in : x.li , o. zaane , z. li ( eds . ) proceedings of the second international conference on advanced data mining and applications ( adma ) , _ lecture notes in computer science _ , vol . 4093 , pp .springer - verlag , berlin / heidelberg ( 2006 )  jaroszewicz , s. , simovici , d.a . : a general measure of rule interestingness . in : proceedings of 5th european conference on principles of data mining and knowledge discovery ( pkdd 2001 ) ,_ lecture notes in computer science _ , vol .2168 , pp .springer ( 2001 )    liu , b. , hsu , w. , ma , y. : pruning and summarizing the discovered associations . in: proceedings of the fifth acm sigkdd international conference on knowledge discovery and data mining ( kdd99 ) , pp .acm press , new york , usa ( 1999 )  mannila , h. , toivonen , h. : multiple uses of frequent sets and condensed representations ( extended abstract ) . in : proceedings of the second international confrerence on knowledge discovery and data mining ( kdd96 ) , pp .189194 ( 1996 )    morishita , s. , nakaya , a. : parallel branch - and - bound graph search for correlated association rules . in : m. zaki , c.t .ho ( eds . )revised papers from large - scale parallel data mining , workshop on large - scale parallel kdd systems , sigkdd , _ lecture notes in computer science _, vol . 1759 , pp .springer - verlag , london , uk ( 2000 )  morishita , s. , sese , j. : transversing itemset lattices with statistical metric pruning . in : proceedings of the nineteenth acm sigmod - sigact - sigart symposium on principles of database systems ( pods00 ) , pp .acm press , new york , usa ( 2000 )  pasquier , n. , bastide , y. , taouil , r. , lakhal , l. : discovering frequent closed itemsets for association rules . in : proceedings of the 7th international conference on database theory ( icdt99 ) , _ lecture notes in computer science _ ,vol . 1540 , pp .springer - verlag ( 1999 )       tan , p. , kumar , v. : interestingness measures for association patterns : a perspective .tech . rep . tr00 - 036 , department of computer science , university of minnesota ( 2000 ) .citeseer.ist.psu.edu/tan00interestingness.html  tan , p.n . ,kumar , v. , srivastava , j. : selecting the right interestingness measure for association patterns . in : proceedings of the eighth acmsigkdd international conference on knowledge discovery and data mining ( kdd02 ) , pp .acm press , new york , usa ( 2002 )  vilalta , r. , oblinger , d. : a quantification of distance bias between evaluation metrics in classification . in : proceedings of the seventeenth international conference on machine learning ( icml00 ) , pp .morgan kaufmann publishers inc ., san francisco , usa ( 2000 )     yao , y. , zhong , n. : an analysis of quantitative measures associated with rules . in : proceedings of the third pacific - asia conference on methodologies for knowledge discovery and data mining ( pakdd99 ) , pp .springer - verlag , london , uk ( 1999 )  zaki , m. : generating non - redundant association rules . in : proceedings ofthe sixth acm sigkdd international conference on knowledge discovery and data mining ( kdd00 ) , pp .acm , new york , usa ( 2000 )

Abstract: an association rule is statistically significant , if it has a small probability to occur by chance . it is well - known that the traditional frequency - confidence framework does not produce statistically significant rules . it can both accept spurious rules ( type 1 error ) and reject significant rules ( type 2 error ) . the same problem concerns other commonly used interestingness measures and pruning heuristics .  in this paper , we inspect the most common measure functions frequency , confidence , degree of dependence , , correlation coefficient , and -measure and redundancy reduction techniques . for each technique , we analyze whether it can make type 1 or type 2 error and the conditions under which the error occurs . in addition , we give new theoretical results which can be use to guide the search for statistically significant association rules .


monolithic cmos pixel sensors open new perspectives in fast nano - imaging through single electron direct detection in transmission electron microscopy ( tem ) .high - voltage electron microscopy , developed and used for high resolution imaging in the late 1970s  produced advances in spatial resolution , but was abandoned due to the severe displacement damage of the sample .as the displacement damage threshold is proportional to , there is now much interest in tem of organic samples with energies of 80 - 100 kev , where recent advances in electron optics ensure deep sub - angstrom spatial resolution  .for example , the maximum energy transferred by an 80 kev electron to a carbon atom is 15.6 ev , which is below the threshold for knock - on damage .this makes low energy tem necessary for atomic resolution studies of samples such as single atomic layers of carbon in graphene or carbon nanotubes  and in biology .there are two main issues to be considered for imaging with low energy electrons .the first is the large fluctuations in the energy deposition .the second is the degradation of the point spread function ( psf ) due to the increase of the electron multiple scattering in the detector .  in an earlier paper , we presented the design of a radiation tolerant cmos pixel cell and investigated the response of 10  m and 20  m pixels to electrons in the energy range 120 kev up to 300 kev for tem . in this letterwe extend that study to lower energies , by investigating the response to 80 kev and 100 kev electrons .we perform a detailed simulation of the charge deposition and signal formation in the cmos pixel sensor based on the geant-4 program  using the low energy electromagnetic physics models  .the cmos sensor is modelled according to the detailed geometric structure of oxide , metal interconnect and silicon layers , as specified by the foundry .electrons are incident perpendicular to the detector plane and tracked through the sensor . for each interaction within the epitaxial layer ,the ionisation point position and the amount of energy released are recorded .charge collection in the sensor is simulated with pixelsim , a dedicated digitisation module  , developed in the marlin c++ reconstruction framework  , originally deployed for the international linear collider particle physics project .the processor starts from the ionisation points generated along the particle trajectory by geant-4 and stored in lcio format  .the pixelsim simulation models diffusion of charge carriers from their production point in the epitaxial layer to the collection diode .this provides us with full simulation of the response of each individual pixels in the detector matrix , including sensor geometry and electronics noise effects , which can be processed through the same analysis chain as the experimental data .the simulation has a single free parameter , the diffusion parameter , used to determine the width of the charge carrier cloud .its value is extracted from data by a fit to the pixel multiplicity in the clusters of 1.5 gev electrons since , at this energy , the multiple scattering contribution to the charge distribution is negligible .we find = ( 16.3 1.4 )  m , which agrees well with the diffusion length estimated from the doping in the epitaxial layer and the charge collection time  .the detector charge - to - voltage conversion is 0.98 kev / adc count or 26.7 /adc count at 6.25 mhz readout frequency , obtained by recording the position of the 5.9 kev full energy peak of a collimated 2.2 mci source .we use the titan test column at the national center for electron microscopy ( ncem ) to characterise the detector response to 80 kev and 100 kev electrons and validate the simulation . the signal pulse height in a 3 matrix around each seedpixel having a signal - to - noise in excess of 4.5 is shown in figure [ fig : landau ] for data and simulation .the broadening of the energy distribution compared to electrons of higher energy is evident , however the ratio of the landau width to the landau most probable value does not increase significantly compared to that for electrons of higher energy .we estimate the uncertainty on the number of electrons per pixel that can be reconstructed from the measured pulse height in a single pixel . we simulate a flat field illumination by generating multiple electrons hitting each pixel and reconstruct the pixel pulse height .this accounts for cross - feed between neighbouring pixels due to charge diffusion and multiple scattering .we determine the number of electrons on each pixel by dividing the simulated pixel pulse height by the average pulse height induced by a single electron and study the distribution of the reconstructed number of electrons as a function of that simulated .we find that the relative uncertainties on this number scale from 0.17 ( 0.14 ) for 10 /pixel to 0.12 ( 0.10 ) for 20 /pixel and to 0.08 ( 0.06 ) for 50 /pixel at 80 kev ( 100 kev ) , respectively .these results are comparable to relative uncertainties of 0.15 , 0.11 , 0.07 obtained for 200 kev electrons .  [ cols="^,^ " , ]   [ tab : psfsim ]  we describe the measured pulse height on the pixel rows across the image projected by the wire with a box function having the same width as the measured wire diameter smeared by a gaussian term , which describes the point spread function .the contrast factor , i.e. the ratio of maximum to minimum pulse height levels , for the pixels away from the wire shadow and for those exactly below the wire centre , respectively , are set to those observed in data and we perform a simple 1-parameter fit to extract the gaussian width term , which gives the estimation of the psf .results are given in table [ tab : psfsim ] .a good agreement is found between the measurement and the prediction from simulation .these results are compared with those obtained at higher energies , presented in  .it is interesting to observe how the degradation of the psf at decreasing energies , caused by multiple scattering , reaches a plateau around 120 kev .this is due to the decrease of the electron range with the particle energy , which limits the distance over which charge can be spread .in fact , we measure a point spread function value for 80 and 100 kev electrons which is compatible with that measured at higher energies , as predicted by the simulation .this result is quite encouraging for extending the application of cmos pixel sensors to fast tem imaging of organic and biological samples with low energy electrons .we wish to thank thomas duden , rolf erni and zhongoon lee .this work was supported by the director , office of science , of the u.s .department of energy under contract no .de - ac02 - 05ch11231 .m. battaglia _ et al ._ , nucl .instrum .a * 598 * ( 2009 ) 642 [ arxiv:0811.2833 [ physics.ins-det ] . s. agostinelli _ et al ._ , nucl .instrum .a * 506 * ( 2003 ) 250 .s. chauvie , g. depaola , v. ivanchenko , f. longo , p. nieminen and m. g. pia , _ prepared for chep01 : computing in high - energy physics and nuclear , beijing , china , 3 - 7 sep 2001 _  m. battaglia , nucl . instrum .a * 572 * ( 2007 ) 274 .f. gaede , nucl .instrum .meth . a * 559 * ( 2006 ) 177 .f. gaede , t. behnke , n. graf and t. johnson , in the _ proc . of 2003 conf . for computing in high - energy and nuclear physics _( chep 03 ) , la jolla , california , 24 - 28 mar 2003 , pp tukt001 , [ arxiv : physics/0306114 ] .

Abstract: this letter presents the results of a study of the response of a test cmos sensor with a radiation tolerant pixel cell design to 80 kev and 100 kev electrons . the point spread function is measured to be ( 13.0 1.7 )  m at 100 kev and ( 12.1 1.6 )  m at 80 kev , for 20  m pixels . results agree well with values predicted by a geant-4 and dedicated charge collection simulation .  ,  ,  ,  ,  monolithic active pixel sensor , transmission electron microscopy ;


hundreds to thousands of stars can be formed in aggregates from one single molecular clouds ( shu et al . , meyer et al . , lada et al . ) .if we assume that the progenitor cloud was chemically well - mixed ( feng et al . ) , then we expect to observe homogeneous chemical composition in the stars formed from this cloud as already confirmed by de silva et al .( , and ) .since each molecular cloud has its own history of pollution by ejecta from core - collapse supernovae ( i.e. type ii , ib and ic supernovae where most of the -element are produced ) , type ia supernovae ( sne ia where most iron peak elements are created ) and asymptotic giant branch stars ( agb where a s - process takes place ) , we expect different open clusters to have different chemical patterns . with this information, we could use the method of chemical tagging to track individual stars back to their common formation sites as proposed by freeman & bland - hawthorn ( ) .the majority of the stars formed in clusters in our galaxy have already been dispersed into the field , but a few of them managed to stay gravitationally bound . old and intermediate - age open clusters ( age myr ) represent a fantastic laboratory to investigate if we can distinguish between stars born from different molecular clouds .  in this study , we collected high - resolution spectra of open clusters stars observed by different instruments , we implemented a completely automatic process to derive atmospheric parameters and chemical abundances , and we used machine learning algorithms to try to recover the original clusters from the homogeneously derived chemical abundances .we compiled more than 400 high - resolution spectra of which 20% come from the narval instrument ( aurire ) , 40% from harps ( mayor et al . ) and 40% from uves( dekker et al .we mainly looked for clusters discussed on paunzen et al .( ) and heiter et al . ( ) , although we did not strictly limit the selection to these . to match the setup in the gaia eso survey ( gilmore et al . ) , we chose to limit the spectral analysis to the range between 480 and 680 nm and we considered only spectra with a resolution of at least 47,000 .an automatic computational process was developed to derive atmospheric parameters and chemical abundances .the process is based on the integrated spectroscopic framework named ispec ( blanco - cuaresma et al . ) and it was calibrated using the library of gaia fgk benchmark stars ( blanco - cuaresma et al . ) .the atomic data was kindly provided by the ges line - list sub - working group prior to publication ( heiter et al ., in prep . ) .the line - list covers our wavelength range of interest and it also provides a selection of high quality lines ( based on the reliability of the oscillator strength and the blend level ) , which are ideal for the determination of chemical abundances . as model atmosphere we used marcs ( gustafsson et al . ) with the solar abundances from grevesse et al .( ) .  after filtering non cluster members ( validated by radial velocity ) , chemically peculiar and non - fgk stars , we were left with a dataset of more than 200 stars covering 32 open clusters with abundances for 17 species corresponding to 14 different elements ( fig .[ fig : abundances ] ) .to evaluate if we can distinguish stars born from different molecular clouds , we designed a blind experiment where we try to recover the original clusters using only the stellar chemical abundances .the stars were separated per evolutionary stage ( i.e. dwarfs and giants ) to reduce the impact of nlte effects and the physical atomic diffusion process .we compressed the 17 abundances into two dimensions using the principal components analysis ( pca ) , and we executed a k - means clustering algorithm in order to form groups of stars chemically similar ( fig .[ fig : pca ] ) . even if the conditions of the experiment were extremely favorable ( i.e. separation per evolutionary stage , filtered chemically peculiar stars ) , we were not able to recover the original clusters because of their high degree of overlapping in the chemical space .given the set of elements used in this study , we found that some open clusters have very similar chemical signature ( such as the clusters shown in fig .[ fig : abundances ] ) .our blind experiment was not able to successful recover the original clusters using only the chemical abundances .nevertheless , there are elements that seem to have a better discriminatory power such as the heavy n - capture element ba . for future analysis, it would be interesting to include other elements such as la , nd and eu that are formed through similar processes that produce ba ( slow and rapid n - capture processes in low mass agb , brusso et al . ; and core - collapse supernovae , kratz et al . ) .99 shu , f. h.  1987 , a&a , 25 , 23 - 81 meyer , m. r.  2000 , protostars and planets iv proceeding lada , c. j. 2003 , a&a , 41 , 57 - 115 feng , y. 2014 , nature , 2014 , 513 , 523 - 525 de silva , g. m. 2006 , aj , 131 , 455 - 460 de silva , g. m. 2007 , aj , 133 , 1161 - 1175 de silva , g. m. 2009 , proc ., 26 , 11 - 16 freeman & bland - hawthorn , 2002 , ara&a , 40 , 487 - 537 aurire , m. 2003 , eas publications series , 9 , 105 mayor , m. 2003 , the messenger , 114 , 20 - 24 dekker , h. 2000 , society of photo - optical instrumentation engineers ( spie ) conference series , 4008 , 534 - 545 paunzen , e. 2010 , apj , 517 heiter , u. 2014 , a&a , 561 gilmore , g. 2012 , the messenger , 147 blanco - cuaresma , s. 2014 , a&a , 569 blanco - cuaresma , s. 2014 , a&a , 566 gustafsson , b. 2008 , a&a , 486 grevesse , n. 2007 , space sci ., 130 , 105 - 114 busso , m. 2001 , apj , 557 , 802 - 821 kratz , k .-2007 , apj , 662 , 39 - 52

Abstract: past studies have already shown that stars in open clusters are chemically homogeneous ( e.g. de silva et al . 2006 , 2007 and 2009 ) . these results support the idea that stars born from the same giant molecular cloud should have the same chemical composition . in this context , the chemical tagging technique was proposed by freeman & bland - hawthorn 2002 . the principle is to recover disrupted stellar clusters by looking only to the stellar chemical composition . in order to evaluate the feasibility of this approach , it is necessary to test if we can distinguish between stars born from different molecular clouds . for this purpose , we studied the chemical composition of stars in 32 old and intermediate - age open clusters , and we applied machine learning algorithms to recover the original cluster by only considering the chemical signatures .


most computer simulations on biological ageing use the penna model .this model , motivated by the accumulation mutation hypothesis , provides a population of bit - strings that exhibits many features known for real senescence .recently stauffer in a general review of the penna model has suggested a simpler alternative with less parameters .this new attempt is based on the postulate of a minimum reproduction age and a maximal genetic lifespan .only these two numbers are transmitted from generation to generation , with certain mutations , by asexual reproduction .this simple model shows the basic features required for senescence .the age distribution shows an increase of mortality with age .the model reproduces successfully the catastrophic senescence of salmon and some specific human aspects like the social structures of technological societies or a transition between extinction and survival if a minimal population for survival is required .  in the following we examine the other modification to the basic model .the privilege conditions are introduced to earlier and then to late reproduction . by doing this , in case of late reproduction, we achieve the exponential growth of mortality in agreement with the gompertz law .the increase of fertility with age exists in nature .some fish , lobsters and trees share this feature and therefore this life strategy has been considered by the penna model also .the population consists of individuals  initially .each individual is characterized by three integers : its age , its minimum reproduction age and its maximal genetic lifespan with .the maximal lifetime is restricted to 32 time units ( called years ) , the minimum reproduction age may be chosen between zero and . within these constraintsthe values of and are randomly mutated for an offspring by , away from the maternal values , and for each child separately .after an individual has reached its minimum reproduction age , it gives birth to one offspring with probability , chosen as thus during its whole mature life any individual gives one offspring at the cumulated probability equal to 1 .independently of the genetic death , which happens automatically and unavoidably if , at each time interval an individual can also die `` accidentally '' , with the verhulst probability . is called the carrying capacity to account for the fact that any given environment can only support populations up to some maximal size .otherwise the individuals die because of food and space limitations .  in this paper differently than in the standard model we consider populations in which the cumulated birth rate is not uniformly distributed among years of reproduction : .instead we propose to consider :  1 .privilege to younger third part of a reproduction period : 2 .privilege to older third part of a reproduction period :   in the following figures we present characteristics of populations developed when three ways of reproduction are considered : standard , ( a ) and ( b ) models . to avoid possible divergencewe follow the stauffer recipe and shift the birth rate accordingly : with . in figure 1we show the population volumes in percentage of the capacity .the population where the reproduction of older individuals is privileged , i.e. , model ( b ) , is the smallest one and varies in time by .figures 2 , 3 compare the distribution of the minimal reproduction age and the maximal genetic lifespan , respectively , in the three models considered . a significant change in the length of life of individualsis observed when the reproduction at old age is favorable , see figure 4 for the distribution of age in a stationary population .finally figure 5 shows the mortality in the populations simulated .the mortality is calculated according to the formula and plotted on log - scale to extract the gompertz law .in stauffer s new proposition of a model for biological ageing , by considering the privilege conditions for time of reproduction we can easily manipulate the mortality in a population .when reproduction at old age is preferred then the model provides the mortality in agreement with the gompertz law .  in the simple ageing model discussed here the maximal genetic lifespan for each individual is limited to 32 yearsthis limitation was introduced to the model to make results better comparable with many penna model results .but one could ask if discarding this assumption would help in getting a nice gompertz law within the standard model .this useful suggestion pointed out to us by the referee has motivated us for investigations on the simple ageing model .specially we were interested in where the model ( b ) would drive a population .preliminary studies show that this model simulated without the limitation for the maximal genetic lifespan leads to the stationary state such that the distribution of is concentrated around age of 50 .the mortality in this population is presented in figure 6 .one can notice that the gompertz law of the exponential increase of mortality holds for adult individuals at age lower than about 35 .m. argollo de menezes , a. racco and t. j. p. penna , physica a * 233 * 221 ( 1996 ) ; + m. argollo de menezes , a. racco and t. j. p. penna , int. j. mod .c * 9 * 787 ( 1998 ) ; + t. j. p. penna , a. racco and a. o. sousa , physica a * 295 * 31 ( 2001 )

Abstract: it is shown that if the computer model of biological ageing proposed by stauffer is modified such that the late reproduction is privileged then the gompertz law of exponential increase of mortality can be retrieved .  * keywords * : population dynamics , ageing , stauffer s model , monte carlo simulations