Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. However, the performance of RP is usually lower. We attempt to improve classification accuracy of RP through combining other reduction dimension methods such as Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Feature Selection (FS). We compared classification accuracy and running time of different combination methods on three microarray datasets and a simulation dataset. Experimental results show a remarkable improvement of 14.77 in classification accuracy of FS followed by RP compared to RP on BC-TCGA dataset. LDA followed by RP also helps RP to yield a more discriminative subspace with an increase of 13.65 on classification accuracy on the same dataset. FS followed by RP outperforms other combination methods in classification accuracy on most of the datasets.
There are several statistical tests to select features @cite_21 , such as rank sum test @cite_22 , t-test @cite_29 and so on. In the paper these methods are called feature selection methods. Here we take t-test as a representative to study the performance of FS methods derived from statistical test. The t-test assesses whether the means of two groups are statistically different from each other. Normalized distance between two classes of samples can be obtained using the sample mean values: @math , @math and the sample variances @math and @math :
@cite_29 @cite_21 @cite_22
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Given samples from distributions p and q, a two-sample test determines whether to reject the null hypothesis that p = q, based on the value of a test statistic measuring the distance between the samples. One choice of test statistic is the maximum mean discrepancy (MMD), which is a distance between embeddings of the probability distributions in a reproducing kernel Hilbert space. The kernel used in obtaining these embeddings is critical in ensuring the test has high power, and correctly distinguishes unlike distributions with high probability. A means of parameter selection for the two-sample test based on the MMD is proposed. For a given test level (an upper bound on the probability of making a Type I error), the kernel is chosen so as to maximize the test power, and minimize the probability of making a Type II error. The test statistic, test threshold, and optimization over the kernel parameters are obtained with cost linear in the sample size. These properties make the kernel selection and test procedures suited to data streams, where the observations cannot all be stored in memory. In experiments, the new kernel selection approach yields a more powerful test than earlier kernel selection heuristics. Feature selection with specific multivariate performance measures is the key to the success of many applications such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple-instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real-world datasets show that the proposed method outperforms l1-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVMperl in terms of F1-score. Two important problems which can affect the performance of classification models are high-dimensionality (an overabundance of independent features in the dataset) and imbalanced data (a skewed class distribution which creates at least one class with many fewer instances than other classes). To resolve these problems concurrently, we propose an iterative feature selection approach, which repeated applies data sampling (in order to address class imbalance) followed by feature selection (in order to address high-dimensionality), and finally we perform an aggregation step which combines the ranked feature lists from the separate iterations of sampling. This approach is designed to find a ranked feature list which is particularly effective on the more balanced dataset resulting from sampling while minimizing the risk of losing data through the sampling step and missing important features. To demonstrate this technique, we employ 18 different feature selection algorithms and Random Undersampling with two post-sampling class distributions. We also investigate the use of sampling and feature selection without the iterative step (e.g., using the ranked list from a single iteration, rather than combining the lists from multiple iterations), and compare these results from the version which uses iteration. Our study is carried out using three groups of datasets with different levels of class balance, all of which were collected from a real-world software system. All of our experiments use four different learners and one feature subset size. We find that our proposed iterative feature selection approach outperforms the non-iterative approach. Comparing two sets of multivariate samples is a central problem in data analysis. From a statistical standpoint, the simplest way to perform such a comparison is to resort to a non-parametric two-sample test (TST), which checks whether the two sets can be seen as i.i.d. samples of an identical unknown distribution (the null hypothesis). If the null is rejected, one wishes to identify regions accounting for this difference. This paper presents a two-stage method providing feedback on this difference, based upon a combination of statistical learning (regression) and computational topology methods. Consider two populations, each given as a point cloud in Rd. In the first step, we assign a label to each set and we compute, for each sample point, a discrepancy measure based on comparing an estimate of the conditional probability distribution of the label given a position versus the global unconditional label distribution. In the second step, we study the height function defined at each point by the aforementioned estimated discrepancy. Topological persistence is used to identify persistent local minima of this height function, their basins defining regions of points with high discrepancy and in spatial proximity. Experiments are reported both on synthetic and real data (satellite images and handwritten digit images), ranging in dimension from d = 2 to d = 784, illustrating the ability of our method to localize discrepancies. On a general perspective, the ability to provide feedback downstream TST may prove of ubiquitous interest in exploratory statistics and data science. Feature selection (FS) is an important data preprocessing technique, which has two goals of minimising the classification error and minimising the number of features selected. Based on particle swarm optimisation (PSO), this paper proposes two multi-objective algorithms for selecting the Pareto front of non-dominated solutions (feature subsets) for classification. The first algorithm introduces the idea of non-dominated sorting based multi-objective genetic algorithm II into PSO for FS. In the second algorithm, multi-objective PSO uses the ideas of crowding, mutation and dominance to search for the Pareto front solutions. The two algorithms are compared with two single objective FS methods and a conventional FS method on nine datasets. Experimental results show that both proposed algorithms can automatically evolve a smaller number of features and achieve better classification performance than using all features and feature subsets obtained from the two single objective methods and the conventional method. Both the continuous and the binary versions of PSO are investigated in the two proposed algorithms and the results show that continuous version generally achieves better performance than the binary version. The second new algorithm outperforms the first algorithm in both continuous and binary versions. Feature selection is a preprocessing phase to machine learning, which leads to increase the classification accuracy and reduce its complexity. However, the increase of data dimensionality poses a challenge to many existing feature selection methods. This paper formulates and validates a method for selecting optimal feature subset based on the analysis of the Pearson correlation coefficients. We adopt the correlation analysis between two variables as a feature goodness measure. Where, a feature is good if it is highly correlated to the class and is low correlated to the other features. To evaluate the proposed Feature selection method, experiments are applied on NSL-KDD dataset. The experiments shows that, the number of features is reduced from 41 to 17 features, which leads to improve the classification accuracy to 99.1 . Also,The efficiency of the proposed linear correlation feature selection method is demonstrated through extensive comparisons with other well known feature selection methods. Nowadays, many disciplines have to deal with big datasets that additionally involve a high number of features. Feature selection methods aim at eliminating noisy, redundant, or irrelevant features that may deteriorate the classification performance. However, traditional methods lack enough scalability to cope with datasets of millions of instances and extract successful results in a delimited time. This paper presents a feature selection algorithm based on evolutionary computation that uses the MapReduce paradigm to obtain subsets of features from big datasets. The algorithm decomposes the original dataset in blocks of instances to learn from them in the map phase; then, the reduce phase merges the obtained partial results into a final vector of feature weights, which allows a flexible application of the feature selection procedure using a threshold to determine the selected subset of features. The feature selection method is evaluated by using three well-known classifiers (SVM, Logistic Regression, and Naive Bayes) implemented within the Spark framework to address big data problems. In the experiments, datasets up to 67 millions of instances and up to 2000 attributes have been managed, showing that this is a suitable framework to perform evolutionary feature selection, improving both the classification accuracy and its runtime when dealing with big data problems. With the advent of high dimensionality, adequate identification of relevant features of the data has become indispensable in real-world scenarios. In this context, the importance of feature selection is beyond doubt and different methods have been developed. However, with such a vast body of algorithms available, choosing the adequate feature selection method is not an easy-to-solve question and it is necessary to check their effectiveness on different situations. Nevertheless, the assessment of relevant features is difficult in real datasets and so an interesting option is to use artificial data. In this paper, several synthetic datasets are employed for this purpose, aiming at reviewing the performance of feature selection methods in the presence of a crescent number or irrelevant features, noise in the data, redundancy and interaction between attributes, as well as a small ratio between number of samples and number of features. Seven filters, two embedded methods, and two wrappers are applied over eleven synthetic datasets, tested by four classifiers, so as to be able to choose a robust method, paving the way for its application to real datasets. We propose two test statistics for use in inverse regression problems "Y"e"K""t"p"e", where "K" is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations "Y" for the function "t" are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data-driven Neyman smooth test. We also introduce two model selection criteria which extend the classical Akaike information criterion and Bayes information criterion to inverse regression problems. In a simulation study we show that the inverse order selection and Neyman smooth tests outperform their direct counterparts in many cases. The theory is motivated by data arising in confocal fluorescence microscopy. Here, images are observed with blurring, modelled as convolution, and stochastic error at subsequent times. The aim is then to reduce the signal-to-noise ratio by averaging over the distinct images. In this context it is relevant to decide whether the images are still equal, or have changed by outside influences such as moving of the object table. Copyright (c) 2009 Royal Statistical Society. Summary. Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, accuracy of estimation and computational cost are two top concerns. Recently, Candes and Tao have proposed the Dantzig selector using L1‐regularization and showed that it achieves the ideal risk up to a logarithmic factor log (p). Their innovative procedure and remarkable result are challenged when the dimensionality is ultrahigh as the factor log (p) can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method that is based on correlation learning, called sure independence screening, to reduce dimensionality from high to a moderate scale that is below the sample size. In a fairly general asymptotic framework, correlation learning is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, iterative sure independence screening is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be accomplished by a well‐developed method such as smoothly clipped absolute deviation, the Dantzig selector, lasso or adaptive lasso. The connections between these penalized least squares methods are also elucidated. By removing the irrelevant and redundant features, feature selection aims to find a compact representation of the original feature with good generalization ability. With the prevalence of unlabeled data, unsupervised feature selection has shown to be effective in alleviating the curse of dimensionality, and is essential for comprehensive analysis and understanding of myriads of unlabeled high dimensional data. Motivated by the success of low-rank representation in subspace clustering, we propose a regularized self-representation (RSR) model for unsupervised feature selection, where each feature can be represented as the linear combination of its relevant features. By using L 2 , 1 -norm to characterize the representation coefficient matrix and the representation residual matrix, RSR is effective to select representative features and ensure the robustness to outliers. If a feature is important, then it will participate in the representation of most of other features, leading to a significant row of representation coefficients, and vice versa. Experimental analysis on synthetic and real-world data demonstrates that the proposed method can effectively identify the representative features, outperforming many state-of-the-art unsupervised feature selection methods in terms of clustering accuracy, redundancy reduction and classification accuracy. HighlightsA regularized self-representation (RSR) model is proposed for unsupervised feature selection.An iterative reweighted least-squares algorithm is proposed to solve the RSR model.The proposed method shows superior performance to state-of-the-art. ABSTRACTMultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this article, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list to increase the number of discoveries. Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR). Generalizing several existing methods, we develop a family of “accumulation tests” to choose a cutoff k that adapts to the amount of signal at the top of the ranked list. We introduce a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques. Our theoretical results prove that these metho... Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. Online selection of dynamic features has attracted intensive interest in recent years. However, existing online feature selection methods evaluate features individually and ignore the underlying structure of a feature stream. For instance, in image analysis, features are generated in groups which represent color, texture, and other visual information. Simply breaking the group structure in feature selection may degrade performance. Motivated by this observation, we formulate the problem as an online group feature selection. The problem assumes that features are generated individually but there are group structures in the feature stream. To the best of our knowledge, this is the first time that the correlation among streaming features has been considered in the online feature selection process. To solve this problem, we develop a novel online group feature selection method named OGFS. Our proposed approach consists of two stages: online intra-group selection and online inter-group selection. In the intra-group selection, we design a criterion based on spectral analysis to select discriminative features in each group. In the inter-group selection, we utilize a linear regression model to select an optimal subset. This two-stage procedure continues until there are no more features arriving or some predefined stopping conditions are met. Finally, we apply our method to multiple tasks including image classification and face verification. Extensive empirical studies performed on real-world and benchmark data sets demonstrate that our method outperforms other state-of-the-art online feature selection methods. We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distribution free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests. This article considers approaches which rerank the output of an existing probabilistic parser. The base parser produces a set of candidate parses for each input sentence, with associated probabilities that define an initial ranking of these parses. A second model then attempts to improve upon this initial ranking, using additional features of the tree as evidence. The strength of our approach is that it allows a tree to be represented as an arbitrary set of features, without concerns about how these features interact or overlap and without the need to define a derivation or a generative model which takes these features into account. We introduce a new method for the reranking task, based on the boosting approach to ranking problems described in (1998). We apply the boosting method to parsing the Wall Street Journal treebank. The method combined the log-likelihood under a baseline model (that of Collins [1999]) with evidence from an additional 500,000 features over parse trees that were not included in the original model. The new model achieved 89.75 F-measure, a 13 relative decrease in F measure error over the baseline model's score of 88.2 . The article also introduces a new algorithm for the boosting approach which takes advantage of the sparsity of the feature space in the parsing data. Experiments show significant efficiency gains for the new algorithm over the obvious implementation of the boosting approach. We argue that the method is an appealing alternative—in terms of both simplicity and efficiency—to work on feature selection methods within log-linear (maximum-entropy) models. Although the experiments in this article are on natural language parsing (NLP), the approach should be applicable to many other NLP problems which are naturally framed as ranking tasks, for example, speech recognition, machine translation, or natural language generation. A common problem in modern genetic research is that of comparing the mean vectors of two populations-typically in settings in which the data dimension is larger than the sample size-where Hotelling's test cannot be applied.Recently, a test using random subspaces was proposed, in which the data are randomly projected into several lower-dimensional subspaces, and Hotelling's test is well defined. Superior performance with competing tests was demonstrated when the variables were correlated.Following the research of random subspaces, a modified test was proposed that might make more efficient use of covariance structure at high dimension. Hierarchical clustering is performed first such that highly correlated variables are clustered together. Next, Hotelling's statistics are computed for every cluster-subspace and summed as the new test statistic. High performance was demonstrated via simulations and real data analysis. A two-sample test using hierarchical clustering was proposed.Hotelling's statistics are computed in cluster-subspaces and summed as the statistic.Highly correlated variables take priority for being processed.A cutoff distance is used to restrain the effect of statistical fluctuations.High performance was demonstrated in simulations and real data analysis. We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. The test statistic can be computed in O(m2) time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist. Feature selection is an effective technique in dealing with dimensionality reduction. For classification, it is used to find an "optimal" subset of relevant features such that the overall accuracy of classification is increased while the data size is reduced and the comprehensibility is improved. Feature selection methods contain two important aspects: evaluation of a candidate feature subset and search through the feature space. Existing algorithms adopt various measures to evaluate the goodness of feature subsets. This work focuses on inconsistency measure according to which a feature subset is inconsistent if there exist at least two instances with same feature values but with different class labels. We compare inconsistency measure with other measures and study different search strategies such as exhaustive, complete, heuristic and random search, that can be applied to this measure. We conduct an empirical study to examine the pros and cons of these search methods, give some guidelines on choosing a search method, and compare the classifier error rates before and after feature selection. The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the random material is chosen - the representative volume - and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well: For example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in material science, Le Bris, Legoll, and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably.