Results 1  10
of
14
LargeScale Sparse Principal Component Analysis with Application to Text Data
"... Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
(Show Context)
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact that sparse PCA can be easier than PCA in practice, and that it can be reliably applied to very large data sets. This comes from a rigorous feature elimination preprocessing result, coupled with the favorable fact that features in reallife data typically have exponentially decreasing variances, which allows for many features to be eliminated. We introduce a fast block coordinate ascent algorithm with much better computational complexity than the existing firstorder ones. We provide experimental results obtained on text corpora involving millions of documents and hundreds of thousands of features. These results illustrate how Sparse PCA can help organize a large corpus of text data in a userinterpretable way, providing an attractive alternative approach to topic models. 1
Sparse PCA through Lowrank Approximations
"... We introduce a novel algorithm that computes the ksparse principal component of a positive semidefinite matrix A. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a lowdimensional eigensubspace of A. We obtain provable approximation guarantees th ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We introduce a novel algorithm that computes the ksparse principal component of a positive semidefinite matrix A. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a lowdimensional eigensubspace of A. We obtain provable approximation guarantees that depend on the spectral profile of the matrix: the faster the eigenvalue decay, the better the quality of our approximation. For example, if the eigenvalues of A follow a powerlaw decay, we obtain a polynomialtime approximation algorithm for any desired accuracy. We implement our algorithm and test it on multiple artificial and real data sets. Due to a feature elimination step, it is possible to perform sparse PCA on data sets consisting of millions of entries in a few minutes. Our experimental evaluation shows that our scheme is nearly optimal while finding very sparse vectors. We compare to the prior state of the art and show that our scheme matches or outperforms previous algorithms in all tested data sets. 1.
SPARSE MACHINE LEARNING METHODS FOR UNDERSTANDING LARGE TEXT CORPORA
"... Abstract. Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. This paper posits that these methods can be extremely useful for understanding large collections of text documents, witho ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
Abstract. Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. This paper posits that these methods can be extremely useful for understanding large collections of text documents, without requiring user expertise in machine learning. Our approach relies on three main ingredients: (a) multidocument text summarization and (b) comparative summarization of two corpora, both using sparse regression or classification; (c) sparse principal components and sparse graphical models for unsupervised analysis and visualization of large text corpora. We validate our approach using a corpus of Aviation Safety Reporting System (ASRS) reports and demonstrate that the methods can reveal causal and contributing factors in runway incursions. Furthermore, we show that the methods automatically discover four main tasks that pilots perform during flight, which can aid in further understanding the causal and contributing factors to runway incursions and other drivers for aviation safety incidents. 1.
Sparse Principal Component Analysis with Constraints
 PROCEEDINGS OF THE TWENTYSIXTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2012
"... The sparse principal component analysis is a variant of the classical principal component analysis, which finds linear combinations of a small number of features that maximize variance across data. In this paper we propose a methodology for adding two general types of feature grouping constraints in ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
The sparse principal component analysis is a variant of the classical principal component analysis, which finds linear combinations of a small number of features that maximize variance across data. In this paper we propose a methodology for adding two general types of feature grouping constraints into the original sparse PCA optimization procedure. We derive convex relaxations of the considered constraints, ensuring the convexity of the resulting optimization problem. Empirical evaluation on three realworld problems, one in process monitoring sensor networks and two in social networks, serves to illustrate the usefulness of the proposed methodology.
Sparse principal component of a rankdeficient matrix
 in Proc. IEEE ISIT 2011, Saint
, 2011
"... Abstract—We consider the problem of identifying the sparse principal component of a rankdeficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate indexsets (that is, sets of indices to the nonzero elements of the vector argument) whose size is poly ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We consider the problem of identifying the sparse principal component of a rankdeficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate indexsets (that is, sets of indices to the nonzero elements of the vector argument) whose size is polynomially bounded, in terms of rank, and contains the optimal indexset, i.e. the indexset of the nonzero elements of the optimal solution. Finally, we develop an algorithm that computes the optimal sparse principal component in polynomial time for any sparsity degree. I.
Unsupervised subject detection via remote ppg
 Biomedical Engineering, IEEE Transactions on
, 2015
"... Abstract—Subject detection is a crucial task for camerabased remote healthcare monitoring. Most existing methods in subject detection rely on supervised learning of physical appearance features. However, their performances are highly restricted to the pretrained appearance model while still suffer ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract—Subject detection is a crucial task for camerabased remote healthcare monitoring. Most existing methods in subject detection rely on supervised learning of physical appearance features. However, their performances are highly restricted to the pretrained appearance model while still suffering from false detection of humansimilar objects. In this paper, we propose a novel unsupervised method to detect alive subject in a video using physiological features. Our basic idea originates from the observation that only living skin tissue of a human presents pulsesignals, which can be exploited as the feature to distinguish human skin from nonhuman surfaces in videos. The proposed VPS method, named VoxelPulseSpectral, consists of three steps: it (1) creates hierarchical voxels across the video for temporally parallel pulse extraction; (2) builds a similarity matrix for hierarchical pulsesignals based on their intrinsic properties; and (3) utilizes incremental sparse matrix decomposition with hierarchical fusion to robustly identify and combine the voxels that correspond to single/multiple subjects. Numerous experiments demonstrate the superior performance of VPS over a stateoftheart method. On average, VPS improves 82.2 % on the precision of skinregion detection; 595.5 % on the Pearson correlation and 542.2 % on BlandAltman agreement of instant pulserate. ANOVA shows that in allround evaluations, the improvements of VPS are significant. The proposed method is the first method that uses pulse to robustly detect alive subjects in realistic scenarios, which can be favorably applied for healthcare monitoring. Index Terms—Biomedical monitoring, remote sensing, photoplethysmography, face detection, object segmentation. I.
Transelliptical Component Analysis Fang
"... We propose a high dimensional semiparametric scaleinvariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution family includes many wellknown multivariate distributions ..."
Abstract
 Add to MetaCart
(Show Context)
We propose a high dimensional semiparametric scaleinvariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution family includes many wellknown multivariate distributions like multivariate Gaussian, t and logistic and it is extended to the metaelliptical by Fang et.al (2002) using the copula techniques. In this paper we extend the metaelliptical distribution family to a even larger family, called transelliptical. We prove that TCA can obtain a nearoptimal s √ log d/n estimation consistency rate in recovering the leading eigenvector of the latent generalized correlation matrix under the transelliptical distribution family, even if the distributions are very heavytailed, have infinite second moments, do not have densities and possess arbitrarily continuous marginal distributions. A feature selection result with explicit rate is also provided. TCA is further implemented in both numerical simulations and largescale stock data to illustrate its empirical usefulness. Both theories and experiments confirm that TCA can achieve model flexibility, estimation accuracy and robustness at almost no cost. 1
Coordinatedescent for learning orthogonal matrices through Givens rotations
"... Optimizing over the set of orthogonal matrices is a central component in problems like sparsePCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of ..."
Abstract
 Add to MetaCart
Optimizing over the set of orthogonal matrices is a central component in problems like sparsePCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinatedescent in Euclidean spaces. It is based on Givensrotations, a fasttocompute operation that affects a small number of entries in the learned matrix, and preserves orthogonality. We show two applications of this approach: an algorithm for tensor decompositions used in learning mixture models, and an algorithm for sparsePCA. We study the parameter regime where a Givens rotation approach converges faster and achieves a superior model on a genomewide brainwide mRNA expression dataset. 1.
Understanding Large Text Corpora via Sparse Machine Learning
, 2012
"... Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. The approach has been successfully used in many areas, such as signal and image processing. This paper posits that these methods ca ..."
Abstract
 Add to MetaCart
(Show Context)
Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. The approach has been successfully used in many areas, such as signal and image processing. This paper posits that these methods can be extremely useful in the analysis of large collections of text documents, without requiring user expertise in machine learning. Our approach relies on three main ingredients: (a) multidocument text summarization and (b) comparative summarization of two corpora, both using sparse regression or classification; (c) sparse principal components and sparse graphical models for unsupervised analysis and visualization of large text corpora. We validate our methods using a corpus of Aviation Safety Reporting System (ASRS) reports and demonstrate that the methods can reveal causal and contributing factors in runway incursions. Furthermore, we show that the methods automatically discover four main tasks that pilots perform during flight, which can aid in further understanding the causal and contributing factors to runway incursions and other drivers for aviation safety incidents. We also provide a comparative study involving other commonly used datasets, and report on the competitiveness of sparse machine learning compared to stateoftheart methods such as Latent Dirichlet Allocation (LDA).
Understanding Large Text Corpora via Sparse Machine Learning
, 2013
"... Abstract: Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. The approach has been successfully used in many areas, such as signal and image processing. This article posits that thes ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: Sparse machine learning has recently emerged as powerful tool to obtain models of highdimensional data with high degree of interpretability, at low computational cost. The approach has been successfully used in many areas, such as signal and image processing. This article posits that these methods can be extremely useful in the analysis of large collections of text documents, without requiring user expertise in machine learning. Our approach relies on three main ingredients: (i) multidocument text summarization; (ii) comparative summarization of two corpora, both using sparse regression or classification; (iii) sparse principal components and sparse graphical models for unsupervised analysis and visualization of large text corpora. We validate our methods using a corpus of Aviation Safety Reporting System (ASRS) reports and demonstrate that the methods can reveal causal and contributing factors in runway incursions. Furthermore, we show that the methods automatically discover four main tasks that pilots perform during flight, which can aid in further understanding the causal and contributing factors to runway incursions and other drivers for aviation safety incidents. We also provide a comparative study involving other commonly used datasets, and report on the competitiveness of sparse machine learning compared to stateoftheart methods such as latent