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Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 683 (17 self)
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This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higherorder extensions of the matrix singular value decompo
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rankone tensors, and the Tucker decomposition is a higherorder form of principal components analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The Nway Toolbox and Tensor Toolbox, both for MATLAB, and the Multilinear Engine are examples of software packages for working with tensors.
Evaluating the use of exploratory factor analysis in psychological research
 Psychological Methods
, 1999
"... Despite the widespread use of exploratory factor analysis in psychological research, researchers often make questionable decisions when conducting these analyses. This article reviews the major design and analytical decisions that must be made when conducting a factor analysis and notes that each of ..."
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Cited by 292 (4 self)
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Despite the widespread use of exploratory factor analysis in psychological research, researchers often make questionable decisions when conducting these analyses. This article reviews the major design and analytical decisions that must be made when conducting a factor analysis and notes that each of these decisions has important consequences for the obtained results. Recommendations that have been made in the methodological literature are discussed. Analyses of 3 existing empirical data sets are used to illustrate how questionable decisions in conducting factor analyses can yield problematic results. The article presents a survey of 2 prominent journals that suggests that researchers routinely conduct analyses using such questionable methods. The implications of these practices for psychological research are discussed, and the reasons for current practices are reviewed. Since its initial development nearly a century ago (Spearman, 1904, 1927), exploratory factor analysis (EFA) has been one of the most widely used statistical procedures in psychological research. Despite this
Principal Component Analysis
 (IN PRESS, 2010). WILEY INTERDISCIPLINARY REVIEWS: COMPUTATIONAL STATISTICS, 2
, 2010
"... Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal var ..."
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Cited by 107 (6 self)
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Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the pca model can be evaluated using crossvalidation techniques such as the bootstrap and the jackknife. Pca can be generalized as correspondence analysis (ca) in order to handle qualitative variables and as multiple factor analysis (mfa) in order to handle heterogenous sets of variables. Mathematically, pca depends upon the eigendecomposition of positive semidefinite matrices and upon the singular value decomposition (svd) of rectangular matrices.
Optimal Solutions for Sparse Principal Component Analysis
"... Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applica ..."
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Cited by 95 (13 self)
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Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n 3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n 3) per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.
Sensitivity of pca for traffic anomaly detection
, 2007
"... Detecting anomalous traffic is a crucial part of managing IP networks. In recent years, networkwide anomaly detection based on Principal Component Analysis (PCA) has emerged as a powerful method for detecting a wide variety of anomalies. We show that tuning PCA to operate effectively in practice ..."
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Cited by 62 (3 self)
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Detecting anomalous traffic is a crucial part of managing IP networks. In recent years, networkwide anomaly detection based on Principal Component Analysis (PCA) has emerged as a powerful method for detecting a wide variety of anomalies. We show that tuning PCA to operate effectively in practice is difficult and requires more robust techniques than have been presented thus far. We analyze a week of networkwide traffic measurements from two IP backbones (Abilene and Geant) across three different traffic aggregations (ingress routers, OD flows, and input links), and conduct a detailed inspection of the feature time series for each suspected anomaly. Our study identifies and evaluates four main challenges of using PCA to detect traffic anomalies: (i) the false positive rate is very sensitive to small differences in the number of principal components in the normal subspace, (ii) the effectiveness of PCA is sensitive to the level of aggregation of the traffic measurements, (iii) a large anomaly may inadvertently pollute the normal subspace, (iv) correctly identifying which flow triggered the anomaly detector is an inherently challenging problem.
A review of dimension reduction techniques
, 1997
"... The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in highdimensional spaces and as a modelling tool for such data. It is defined as the search for a lowdimensional manifold that embeds the highdimensional data. A cl ..."
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Cited by 40 (4 self)
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The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in highdimensional spaces and as a modelling tool for such data. It is defined as the search for a lowdimensional manifold that embeds the highdimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.
Nonlinear multivariate and time series analysis by neural network methods
, 2003
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Measurement of Delusional Ideation in the Normal Population: Introducing the PDI (Peters et aL Delusions Inventory)
"... The Peters et al. Delusions Inventory (PDI) was designed to measure delusional ideation in the normal population, using the Present State Examination as a template. The multidimensionality of delusions was incorporated by assessing measures of distress, preoccupation, and conviction. Individual item ..."
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Cited by 31 (2 self)
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The Peters et al. Delusions Inventory (PDI) was designed to measure delusional ideation in the normal population, using the Present State Examination as a template. The multidimensionality of delusions was incorporated by assessing measures of distress, preoccupation, and conviction. Individual items were endorsed by one in four adults on average. No sex differences were found, and an inverse relationship with age was obtained. Good internal consistency was found, and its concurrent validity was confirmed by the percentages of common variance with three scales measuring schizotypy, magical ideation, and delusions. PDI scores up to 1 year later remained consistent, establishing its testretest reliability. Psychotic inpatients had significantly higher scores, establishing its criterion validity. The ranges of scores between the normal and deluded groups overlapped considerably, consistent with the continuity view of psychosis. The two samples were differentiated by their ratings on the distress, preoccupation, and conviction scales, confirming the necessity for a multidimensional analysis of delusional thinking. Possible avenues of research using this scale and its clinical utility are highlighted.
Temporal analysis of semantic graphs using ASALSAN
 SEVENTH IEEE INTERNATIONAL CONFERENCE ON DATA MINING
, 2007
"... ASALSAN is a new algorithm for computing threeway DEDICOM, which is a linear algebra model for analyzing intrinsically asymmetric relationships, such as trade among nations or the exchange of emails among individuals, that incorporates a third mode of the data, such as time. ASALSAN is unique beca ..."
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Cited by 23 (2 self)
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ASALSAN is a new algorithm for computing threeway DEDICOM, which is a linear algebra model for analyzing intrinsically asymmetric relationships, such as trade among nations or the exchange of emails among individuals, that incorporates a third mode of the data, such as time. ASALSAN is unique because it enables computing the threeway DEDICOM model on large, sparse data. A nonnegative version of ASALSAN is described as well. When we apply these techniques to adjacency arrays arising from directed graphs with edges labeled by time, we obtain a smaller graph on latent semantic dimensions and gain additional information about their changing relationships over time. We demonstrate these techniques on international trade data and the Enron email corpus to uncover latent components and their transient behavior. The mixture of roles assigned to individuals by ASALSAN showed strong correspondence with known job classifications and revealed the patterns of communication between these roles. Changes in the communication pattern over time, e.g., between top executives and the legal department, were also apparent in the solutions.