Abstract This paper introduces SensoGraph, a novel approach for fast sensory evaluation using two-dimensional geometric techniques. In the tasting sessions, the assessors follow their own criteria to place samples on a tablecloth, according to the similarity between samples. In order to analyse the data collected, first a geometric clustering is performed to each tablecloth, extracting connections between the samples. Then, these connections are used to construct a global similarity matrix. Finally, a graph drawing algorithm is used to obtain a 2D consensus graphic, which reflects the global opinion of the panel by (1) positioning closer those samples that have been globally perceived as similar and (2) showing the strength of the connections between samples. The proposal is validated by performing four tasting sessions, with three types of panels tasting different wines, and by developing a new software to implement the proposed techniques. The results obtained show that the graphics provide similar positionings of the samples as the consensus maps obtained by multiple factor analysis (MFA), further providing extra information about connections between samples, not present in any previous method. The main conclusion is that the use of geometric techniques provides information complementary to MFA, and of a different type. Finally, the method proposed is computationally able to manage a significantly larger number of assessors than MFA, which can be useful for the comparison of pictures by a huge number of consumers, via the Internet.
Thus, several alternative methods have arisen in the last years , aiming to provide a fast sensory positioning of a set of products by assessors who are not necessarily trained. Skipping the need to train the panellists allows to elude the need of waiting a long time before obtaining results, as well as the need of agreeing on particular attributes, which may become difficult when working with experts like wine professionals or chefs . Introduced by @cite_2 @cite_10 , Projective Mapping asks the assessors to position the presented samples on a two-dimensional space, usually a blank sheet of paper as tablecloth, following their own criteria: The more similar they perceive two samples, the closer they should position them, and vice versa . In those seminal works, the data were analysed by generalized procrustes analysis (GPA) and principal component analysis (PCA) , using the RV coefficient to compare the method with conventional profiling.
@cite_10 @cite_2
1979883873 2065540379
Abstract Studies have indicated that profiling and (dis)similarity scaling yield different perceptual product maps. Conceptually, these two procedures are different. This paper looks at a third and alternative method of producing a two-dimensional, perceptual map utilizing a projective-type method whereby individual assessors themselves are required to place products on the space according to the similarities and differences they perceive. However, visual comparison of the final results provided by each assessor is difficult and, hence, generalized Procrustes analysis is applied to compare each assessor's map for similarity with the others. In this study it was found that the perceptual map derived from projective mapping was as similar to the map derived from profiling as from dissimilarity scaling. However, consistency over repeated trials was greater for projective mapping than for the other two methods. It is suggested that projective mapping could be a potentially useful technique for linking sensory analysis and consumer research data. Abstract This paper deals with the method of projective mapping and its use in sensory analysis. Projective mapping is a method which allows naive consumers to map products on a two dimension space, based on similarities and differences in the products. An experiment was carried out on seven blueberry soups, whereby sensory profiling was undertaken using a trained panel and projective mapping. Preference assessment was undertaken using a small group of consumers. Results indicated that the three replicates of the mapping exercise produced visually very similar maps, at least on the first two dimensions. However, it was found that consumers perceived the samples in somewhat different ways as high-lighted by RV coefficients. The consensus mapping dimensions were compared to those from the profile data, and it was apparent that the best similarity was found when comparing the first dimension, thus suggesting good agreement on the obvious aspects of the product. The internal preference map also revealed major product contrasts along this dimension with some weak evidence of segmentation. The overall conclusion of this paper raises further fundamental questions about consensus spaces with consumers, and the question of dimensionality of consumer perception as compared to trained panels. We introduce kernel entropy component analysis (kernel ECA) as a new method for data transformation and dimensionality reduction. Kernel ECA reveals structure relating to the Renyi entropy of the input space data set, estimated via a kernel matrix using Parzen windowing. This is achieved by projections onto a subset of entropy preserving kernel principal component analysis (kernel PCA) axes. This subset does not need, in general, to correspond to the top eigenvalues of the kernel matrix, in contrast to the dimensionality reduction using kernel PCA. We show that kernel ECA may produce strikingly different transformed data sets compared to kernel PCA, with a distinct angle-based structure. A new spectral clustering algorithm utilizing this structure is developed with positive results. Furthermore, kernel ECA is shown to be an useful alternative for pattern denoising. How do we find patterns in author-keyword associations, evolving over time? Or in Data Cubes, with product-branch-customer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule identification in numerous settings like streaming data, text, graphs, social networks and many more. However, they have only two orders, like author and keyword, in the above example.We propose to envision such higher order data as tensors,and tap the vast literature on the topic. However, these methods do not necessarily scale up, let alone operate on semi-infinite streams. Thus, we introduce the dynamic tensor analysis (DTA) method, and its variants. DTA provides a compact summary for high-order and high-dimensional data, and it also reveals the hidden correlations. Algorithmically, we designed DTA very carefully so that it is (a) scalable, (b) space efficient (it does not need to store the past) and (c) fully automatic with no need for user defined parameters. Moreover, we propose STA, a streaming tensor analysis method, which provides a fast, streaming approximation to DTA.We implemented all our methods, and applied them in two real settings, namely, anomaly detection and multi-way latent semantic indexing. We used two real, large datasets, one on network flow data (100GB over 1 month) and one from DBLP (200MB over 25 years). Our experiments show that our methods are fast, accurate and that they find interesting patterns and outliers on the real datasets. Data sets are often modeled as samples from a probability distribution in RD, for D large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a d-dimensional manifold M, with d much smaller than D. When M is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of d vectors in RD (for example found by SVD), at a cost (n+D)d for n data points. When M is nonlinear, there are no “explicit” and algorithmically efficient constructions of dictionaries that achieve a similar efficiency: typically one uses either random dictionaries, or dictionaries obtained by black-box global optimization. In this paper we construct data-dependent multi-scale dictionaries that aim at efficiently encoding and manipulating the data. Their construction is fast, and so are the algorithms that map data points to dictionary coefficients and vice versa, in contrast with L1-type sparsity-seeking algorithms, but like adaptive nonlinear approximation in classical multi-scale analysis. In addition, data points are guaranteed to have a compressible representation in terms of the dictionary, depending on the assumptions on the geometry of the underlying probability distribution. We study the problem of multimodal dimensionality reduction assuming that data samples can be missing at training time, and not all data modalities may be present at application time. Maximum covariance analysis, as a generalization of PCA, has many desirable properties, but its application to practical problems is limited by its need for perfectly paired data. We overcome this limitation by a latent variable approach that allows working with weakly paired data and is still able to efficiently process large datasets using standard numerical routines. The resulting weakly paired maximum covariance analysis often finds better representations than alternative methods, as we show in two exemplary tasks: texture discrimination and transfer learning. A new formulation for multiway spectral clustering is proposed. This method corresponds to a weighted kernel principal component analysis (PCA) approach based on primal-dual least-squares support vector machine (LS-SVM) formulations. The formulation allows the extension to out-of-sample points. In this way, the proposed clustering model can be trained, validated, and tested. The clustering information is contained on the eigendecomposition of a modified similarity matrix derived from the data. This eigenvalue problem corresponds to the dual solution of a primal optimization problem formulated in a high-dimensional feature space. A model selection criterion called the balanced line fit (BLF) is also proposed. This criterion is based on the out-of-sample extension and exploits the structure of the eigenvectors and the corresponding projections when the clusters are well formed. The BLF criterion can be used to obtain clustering parameters in a learning framework. Experimental results with difficult toy problems and image segmentation show improved performance in terms of generalization to new samples and computation times. In this letter, an ensemble learning approach, Rotation Forest, has been applied to hyperspectral remote sensing image classification for the first time. The framework of Rotation Forest is to project the original data into a new feature space using transformation methods for each base classifier (decision tree), then the base classifier can train in different new spaces for the purpose of encouraging both individual accuracy and diversity within the ensemble simultaneously. Principal component analysis (PCA), maximum noise fraction, independent component analysis, and local Fisher discriminant analysis are introduced as feature transformation algorithms in the original Rotation Forest. The performance of Rotation Forest was evaluated based on several criteria: different data sets, sensitivity to the number of training samples, ensemble size and the number of features in a subset. Experimental results revealed that Rotation Forest, especially with PCA transformation, could produce more accurate results than bagging, AdaBoost, and Random Forest. They indicate that Rotation Forests are promising approaches for generating classifier ensemble of hyperspectral remote sensing. Nonlinear principal component analysis is a novel technique for multivariate data analysis, similar to the well-known method of principal component analysis. NLPCA, like PCA, is used to identify and remove correlations among problem variables as an aid to dimensionality reduction, visualization, and exploratory data analysis. While PCA identifies only linear correlations between variables, NLPCA uncovers both linear and nonlinear correlations, without restriction on the character of the nonlinearities present in the data. NLPCA operates by training a feedforward neural network to perform the identity mapping, where the network inputs are reproduced at the output layer. The network contains an internal “bottleneck” layer (containing fewer nodes than input or output layers), which forces the network to develop a compact representation of the input data, and two additional hidden layers. The NLPCA method is demonstrated using time-dependent, simulated batch reaction data. Results show that NLPCA successfully reduces dimensionality and produces a feature space map resembling the actual distribution of the underlying system parameters. This paper provides the first comprehensive analysis of Uber's driver-partners, based on both survey data and anonymized, aggregated administrative data. Uber has grown at an exponential rate over the last few years, and drivers who partner with Uber appear to be attracted to the platform in large part because of the flexibility it offers, the level of compensation, and the fact that earnings per hour do not vary much with hours worked, which facilitates part-time and variable hours. Uber's driver-partners are more similar in terms of their age and education to the general workforce than to taxi drivers and chauffeurs. Uber may serve as a bridge for many seeking other employment opportunities, and it may attract well-qualified individuals because, with Uber's star rating system, driver-partners' reputations are explicitly shared with potential customers. Most of Uber's driver-partners had full- or part-time employment prior to joining Uber, and many continued in those positions after starting to drive with the Uber platform, which makes the flexibility to set their own hours all the more valuable. Uber's driver-partners also often cited the desire to smooth fluctuations in their income as a reason for partnering with Uber. Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets. Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified principal components with sparse loadings. We first show that PCA can be formulated as a regression-type optimization problem; sparse loadings are then obtained by imposing the lasso (elastic net) constraint on the regression coefficients. Efficient algorithms are proposed to fit our SPCA models for both regular multivariate data and gene expression arrays. We also give a new formula to compute the total variance of modified principal components. As illustrations, SPCA is applied to real and simulated data with encouraging results. Matching 3D point clouds, a critical operation in map building and localization, is difficult with Velodyne-type sensors due to the sparse and non-uniform point clouds that they produce. Standard methods from dense 3D point clouds are generally not effective. In this paper, we describe a feature-based approach using Principal Components Analysis (PCA) of neighborhoods of points, which results in mathematically principled line and plane features. The key contribution in this work is to show how this type of feature extraction can be done efficiently and robustly even on non-uniformly sampled point clouds. The resulting detector runs in real-time and can be easily tuned to have a low false positive rate, simplifying data association. We evaluate the performance of our algorithm on an autonomous car at the MCity Test Facility using a Velodyne HDL-32E, and we compare our results against the state-of-the-art NARF keypoint detector. Previous research indicates that during the past 20 years, the highest-quality work has been published in an increasingly diverse and larger group of journals. In this article, we examine whether this diversification has also affected the handful of elite journals that are traditionally considered to be the best. We examine citation patterns during the past 40 years of seven long-standing traditionally elite journals and six journals that have been increasing in importance during the past 20 years. To be among the top 5 or 1 cited papers, papers now need about twice as many citations as they did 40 years ago. Since the late 1980s and early 1990s, elite journals have been publishing a decreasing proportion of these top-cited papers. This also applies to the two journals that are typically considered as the top venues and often used as bibliometric indicators of "excellence": Science and Nature. On the other hand, several new and established journals are publishing an increasing proportion of the most-cited papers. These changes bring new challenges and opportunities for all parties. Journals can enact policies to increase or maintain their relative position in the journal hierarchy. Researchers now have the option to publish in more diverse venues knowing that their work can still reach the same audiences. Finally, evaluators and administrators need to know that although there will always be a certain prestige associated with publishing in "elite" journals, journal hierarchies are in constant flux. In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data samples to optimize over this subspace. As with the Hessian Free (HF) method of Martens (2010), the Hessian matrix is never explicitly constructed, and is computed using a subset of data. In practice, as in HF, we typically use a positive definite substitute for the Hessian matrix such as the Gauss-Newton matrix. We investigate the effectiveness of our proposed method on deep neural networks, and compare its performance to widely used methods such as stochastic gradient descent, conjugate gradient descent and L-BFGS, and also to HF. Our method leads to faster convergence than either L-BFGS or HF, and generally performs better than either of them in cross-validation accuracy. It is also simpler and more general than HF, as it does not require a positive semidefinite approximation of the Hessian matrix to work well nor the setting of a damping parameter. The chief drawback versus HF is the need for memory to store a basis for the Krylov subspace. Kernel functions have become an extremely popular tool in machine learning, with an attractive theory as well. This theory views a kernel as implicitly mapping data points into a possibly very high dimensional space, and describes a kernel function as being good for a given learning problem if data is separable by a large margin in that implicit space. However, while quite elegant, this theory does not directly correspond to one's intuition of a good kernel as a good similarity function. Furthermore, it may be difficult for a domain expert to use the theory to help design an appropriate kernel for the learning task at hand since the implicit mapping may not be easy to calculate. Finally, the requirement of positive semi-definiteness may rule out the most natural pairwise similarity functions for the given problem domain.In this work we develop an alternative, more general theory of learning with similarity functions (i.e., sufficient conditions for a similarity function to allow one to learn well) that does not require reference to implicit spaces, and does not require the function to be positive semi-definite (or even symmetric). Our results also generalize the standard theory in the sense that any good kernel function under the usual definition can be shown to also be a good similarity function under our definition (though with some loss in the parameters). In this way, we provide the first steps towards a theory of kernels that describes the effectiveness of a given kernel function in terms of natural similarity-based properties. Collaborative Filtering (CF) is the most successful approach to Recommender Systems (RS). In this paper, we suggest methods for global and personalized visualization of CF data. Users and items are first embedded into a high-dimensional latent feature space according to a predictor function particularly designated to conform with visualization requirements. The data is then projected into 2-dimensional space by Principal Component Analysis (PCA) and Curvilinear Component Analysis (CCA). Each projection technique targets a di fferent application, and has its own advantages. PCA places all items on a Global Item Map (GIM) such that the correlation between their latent features is revealed optimally. CCA draws personalized Item Maps (PIMs) representing a small subset of items to a specifi c user. Unlike in GIM, a user is present in PIM and items are placed closer or further to her based on their predicted ratings. The intra-item semantic correlations are inherited from the high-dimensional space as much as possible. The algorithms are tested on three versions of the MovieLens dataset and the Netflix dataset to show they combine good accuracy with satisfactory visual properties. We rely on a few examples to argue our methods can reveal links which are hard to be extracted, even if explicit item features are available. This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case where the tensor in question is super-symmetric with an even degree. In that case, the tensor can be embedded into a symmetric matrix. We prove that if the tensor is rank-one, then the embedded matrix must be rank-one too, and vice versa. The tensor PCA problem can thus be solved by means of matrix optimization under a rank-one constraint, for which we propose two solution methods: (1) imposing a nuclear norm penalty in the objective to enforce a low-rank solution; (2) relaxing the rank-one constraint by semidefinite programming. Interestingly, our experiments show that both methods can yield a rank-one solution for almost all the randomly generated instances, in which case solving the original tensor PCA problem to optimality. To further cope with the size of the resulting convex optimization models, we propose to use the alternating direction method of multipliers, which reduces significantly the computational efforts. Various extensions of the model are considered as well. Standard group analyses of fMRI data rely on spatial and temporal averaging of individuals. This averaging operation is only sensible when the mean is a good representation of the group. This is not the case if subjects are not homogeneous, and it is therefore a major concern in fMRI studies to assess this group homogeneity. We present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects. The method allows a multivariate comparison between data sets of several subjects in the time or in the space domain. These analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects, at the population level. We adapt the RV coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject's position with respect to other subjects in the group. We also provide a measure for detecting subjects that may be outliers. Results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns, and that, despite the apparent loss of information, restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fMRI analyses. Most of the existing methods for pedestrian detection work well, only when the following assumption is satisfied: the features extracted from the training dataset and the testing dataset have very similar distributions in the feature space. However, in practice, this assumption does not hold because of the scene complexity and variation. In this paper, a new method is proposed for detecting pedestrians in various scenes based on the transfer learning technique. Our proposed method employs the following two strategies for improving the pedestrian detection performance. First, a new sample screening method based on manifold learning is proposed. The basic idea is to choose samples from the training set, which may be similar to the samples from the unseen scene, and then merge the selected samples into the unseen set. Second, a new classification model based on transfer learning is proposed. The advantage of the classification model is that only a small number of samples need to be used from the unseen scenes. Most of the training samples are still obtained from the training scene, which take up to 90 of the entire training samples. Compared to the traditional pedestrian detection methods, the proposed algorithm can adapt to different scenes for detecting pedestrians. Experiments on two pedestrian detection benchmark datasets, DC and NICTA, showed that the method can obtain better performance as compared to other previous methods.