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Finding a Sparse Vector in a Subspace: Linear Sparsity Using Alternating Directions
2016
IEEE Transactions on Information Theory
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Is it possible to find the sparsest vector (direction) in a generic subspace S⊆R^p with dim(S)= n < p? ...
In this paper, we focus on a **planted sparse model** for the subspace: the target sparse vector is embedded in an otherwise random subspace. ...
Finding a sparse vector in a subspace: Linear sparsity using alternating directions. In Advances in Neural Information Processing Systems, 2014.[SQW14] Ju Sun, Qing Qu, and John Wright. ...
doi:10.1109/tit.2016.2601599
fatcat:s4xr2mmy2jcxnlfpi7u2dopqgy
Directing Power Towards Conic Parameter Subspaces
[article]
2019
arXiv
pre-print
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I illustrate the statistic on subspaces that consist of sparse or nearly-sparse vectors, for which the computation corresponds to ℓ_0- and ℓ_1-regularized regression, respectively. ...
I simultaneously address these two issues by proposing a novel test statistic that is large in a conic parameter subspace of interest. ...
This allows us to pick C in such a way that power is directed towards a specific alternative of interest. ...
arXiv:1907.05077v6
fatcat:jtnplgzbsrhmfizke2yifvcs3a
Kernel sparse subspace clustering
2014
2014 IEEE International Conference on Image Processing (ICIP)
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We show that the alternating direction method of multipliers can be used to efficiently find kernel sparse representations. ...
In this paper, we extend SSC to non-linear manifolds by using the kernel trick. ...
The above problems can be efficiently solved by using the classical alternating direction method of multipliers (ADMM) [16] . ...
doi:10.1109/icip.2014.7025576
dblp:conf/icip/PatelV14
fatcat:g5hpcmf6t5dyzi6znuvdvniegi
Sparse subspace clustering
2009
2009 IEEE Conference on Computer Vision and Pattern Recognition
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We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. ...
Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. ...
We have presented a novel approach to subspace clustering based on sparse representation. ...
doi:10.1109/cvprw.2009.5206547
fatcat:3yogs2jzirhl3npbdj4i2f7rmq
Sparse subspace clustering
2009
2009 IEEE Conference on Computer Vision and Pattern Recognition
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We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. ...
Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. ...
We have presented a novel approach to subspace clustering based on sparse representation. ...
doi:10.1109/cvpr.2009.5206547
dblp:conf/cvpr/ElhamifarV09
fatcat:wlbox6rlpfhrzobtdm6fekelwa
Face Subspace Learning
[chapter]
2011
Handbook of Face Recognition
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The earliest subspace method for face recognition is Eigenface [43] , which uses PCA [23] to select the most representative subspace for representing a set of face images. ...
By projecting face images onto the subspace spanned by Eigenface, classifiers can be used in the subspace for recognition. One main limitation of Eigenface is that the ...
There a query is projected onto a linear subspace spanned by a set of basis vectors, where the basis vectors can be any form from a subspace analysis or a set of local features, and the distance between ...
doi:10.1007/978-0-85729-932-1_3
fatcat:ot7fkakworamtavm4jwlp4sfjm
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
2018
IEEE Signal Processing Magazine
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2018 pre-print arXiv:1711.09492v3 fatcat:6c6egqu4rzhlrgdweasrnddovqOther Versions
The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions. ...
PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". ...
GOSUS (Grassmannian Online Subspace Updates with Structured-sparsity) [53] is another incremental algorithm that uses structured sparsity of the outlier terms in conjunction with a GRASTA-like (or ReProCS-like ...
doi:10.1109/msp.2018.2826566
fatcat:4fscwwy7rjbjrm3xoztm5api2i
Portfolio diversification using subspace factorizations
2008
2008 42nd Annual Conference on Information Sciences and Systems
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In this work we contribute a new approach to portfolio diversification by comparing a recently developed clustering technique, SemiNMF, with a new sparse low-rank approximate factorization technique, Sparse-semiNMF ...
We evaluate these techniques using a diffusion model based on the Black-Scholes options pricing model. ...
PCA algorithms only use second order statistics and give projections of the data in the direction of maximum variance in the remaining orthogonal subspaces. ...
doi:10.1109/ciss.2008.4558678
dblp:conf/ciss/FreinDR08
fatcat:tx67ojac4rb4tomn2promozmm4
5. Krylov Subspace Methods
[chapter]
2000
Trust Region Methods
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For large sparse symmetric linear systems arising in topology optimization, Krylov subspace methods are required. ...
Therefore, recycling a subspace of the Krylov subspace and using it to solve the next system can improve the convergence rate significantly. ...
For large sparse symmetric linear systems arising in topology optimization, Krylov subspace methods are required. ...
doi:10.1137/1.9780898719857.ch5
fatcat:thyxqdt2wrf5vnxclogpcsgg3a
A Fast deflation Method for Sparse Principal Component Analysis via Subspace Projections
[article]
2019
arXiv
pre-print
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In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. ...
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. ...
Given a data set, PCA aims at finding a sequence of orthogonal vectors that represent the directions of largest variance. ...
arXiv:1912.01449v2
fatcat:fiilhiasfzdzjnoigfky7nro4e
Tensor LRR and Sparse Coding-Based Subspace Clustering
2016
IEEE Transactions on Neural Networks and Learning Systems
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Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. ...
The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. ...
The general process of the BCD is shown in Algorithm 1. We use the linearized alternating direction method (LADM) [30] to solve the constrained optimization problem (15) . ...
doi:10.1109/tnnls.2016.2553155
pmid:27164609
fatcat:rdyohb5qybgxvipppbdv5wepyq
Robust Subspace Recovery via Bi-Sparsity Pursuit
[article]
2014
arXiv
pre-print
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In this paper, we propose a bi-sparse model as a framework to analyze this problem and provide a novel algorithm to recover the union of subspaces in presence of sparse corruptions. ...
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces ...
In this section, we leverage the successes of alternating direction method (ADM) [9] and linearized ADM (LADM) [10] in large scale sparse representation problem, and focus on designing an appropriate ...
arXiv:1403.8067v2
fatcat:zko7ckhw3rdbngpqo6pvzye73a
Efficient Solvers for Sparse Subspace Clustering
[article]
2020
arXiv
pre-print
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Using ℓ_1 regularization results in a convex problem but requires O(n^2) storage, and is typically solved by the alternating direction method of multipliers which takes O(n^3) flops. ...
Sparse subspace clustering (SSC) clusters n points that lie near a union of low-dimensional subspaces. ...
Sparse subspace clustering (SSC) approaches the problem of finding subspace-preserving coefficients by enforcing a sparsity prior on the columns of the matrix C. ...
arXiv:1804.06291v2
fatcat:pprn74ulyjfyhgarz262wxlix4
Latent Space Sparse Subspace Clustering
2013
2013 IEEE International Conference on Computer Vision
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We propose a novel algorithm called Latent Space Sparse Subspace Clustering for simultaneous dimensionality reduction and clustering of data lying in a union of subspaces. ...
Specifically, we describe a method that learns the projection of data and finds the sparse coefficients in the low-dimensional latent space. ...
alternating direction method of multipliers (ADMM) [6] . ...
doi:10.1109/iccv.2013.35
dblp:conf/iccv/PatelNV13
fatcat:lgxzosjv4rfgdkdtnwqcuulp24
Learning Document Representations Using Subspace Multinomial Model
2016
Interspeech 2016
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Subspace multinomial model (SMM) is a log-linear model and can be used for learning low dimensional continuous representation for discrete data. ...
In this paper, we propose a new variant of SMM that introduces sparsity and call the resulting model as 1 SMM. ...
In [11] , sparse log-linear models were used to learn a small and useful feature space for dialogue-act classification. ...
doi:10.21437/interspeech.2016-1634
dblp:conf/interspeech/KesirajuBSC16
fatcat:pjhvtk6khvb3zkaqup2vhsk7ie
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