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A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data [article]

Yining Wang, Yu-Xiang Wang, Aarti Singh
2016 arXiv   pre-print
In this paper, we study the theoretical properties of a popular subspace clustering algorithm named sparse subspace clustering (SSC) and establish formal success conditions of SSC on dimensionality-reduced  ...  Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace.  ...  The main contribution of this paper is a unified framework for analyzing sparse subspace clustering on dimensionality-reduced data.  ... 
arXiv:1610.07650v1 fatcat:2buszkthtngq5n6q5cfvln4msu

A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data

Yining Wang, Yu-Xiang Wang, Aarti Singh
2019 IEEE Transactions on Information Theory  
In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms  ...  Subspace clustering groups data into several lowrank subspaces.  ...  Clustering consistent sparse subspace clustering. arXiv:1504.01046, 2015. Wang, Yu-Xiang and Xu, Huan. Noisy sparse subspace clustering. arXiv:1309.1233, 2013.  ... 
doi:10.1109/tit.2018.2879912 fatcat:f5hlrhcsczhn3hyofxxtnxdsoe

Graph Connectivity in Noisy Sparse Subspace Clustering [article]

Yining Wang, Yu-Xiang Wang, Aarti Singh
2016 arXiv   pre-print
A line of recent work (4, 19, 24, 20) provided strong theoretical guarantee for sparse subspace clustering (4), the state-of-the-art algorithm for subspace clustering, on both noiseless and noisy data  ...  Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces.  ...  There is rich literature on algorithmic and theoretical analysis of subspace clustering [4, 12, 8, 17] .  ... 
arXiv:1504.01046v2 fatcat:hpxzkul3wfb4pp7kf6lzggxrlm

Exploiting low-dimensional structures to enhance DNN based acoustic modeling in speech recognition

Pranay Dighe, Gil Luyet, Afsaneh Asaei, Herve Bourlard
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional  ...  We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces.  ...  The proposed approach relies on the fact that a data point in a union of subspaces can be more efficiently reconstructed using a sparse combination of data points from its own subspace than data points  ... 
doi:10.1109/icassp.2016.7472767 dblp:conf/icassp/DigheLAB16 fatcat:jezw6rilvzf35fen5drjrxpe34

Study on the Optimization of Macroeconomics Teaching Model Based on Cluster Analysis in the Context of Data

Jinshun Wu, Muhammad Arif
2022 Security and Communication Networks  
We present an optimization approach for macroeconomics teaching mode based on cluster analysis in the context of data based on this.  ...  The method has certain feasibility and effectiveness, which lays a foundation for the optimization of macroeconomics teaching mode.  ...  Sparse subspace clustering is a clustering method based on sparse representation. e so-called sparse representation refers to the use of the sparsity of high-dimensional data in lowdimensional space to  ... 
doi:10.1155/2022/9091208 fatcat:jfyqgkbykja3pgk2cezpg3suki

Provable Subspace Clustering: When LRR meets SSC

Yu-Xiang Wang, Huan Xu, Chenlei Leng
2019 IEEE Transactions on Information Theory  
Because the representation matrix is often simultaneously sparse and low-rank, we propose a new algorithm, termed Low-Rank Sparse Subspace Clustering (LRSSC), by combining SSC and LRR, and develops theoretical  ...  Sparse Subspace Clustering (SSC) and Low-Rank Representation (LRR) are both considered as the state-of-the-art methods for subspace clustering.  ...  Xu is partially supported by the Ministry of Education of Singapore through AcRF Tier Two grant R-265-000-443-112 and NUS startup grant R-265-000-384-133.  ... 
doi:10.1109/tit.2019.2915593 fatcat:qgpar2nwtbaovp6rwjdycrm5hy

Hippocampus Segmentation Method Based on Subspace Patch-Sparsity Clustering in Noisy Brain MRI

Xiaogang Ren, Yue Wu, Zhiying Cao, Gu Xiaoqing
2021 Journal of Healthcare Engineering  
Since the hippocampus is of small size, low contrast, and irregular shape, a novel hippocampus segmentation method based on subspace patch-sparsity clustering in brain MRI is proposed to improve the segmentation  ...  The experimental results show that our proposed method is effective in the noisy brain MRI data, which can well deal with hippocampus segmentation problem.  ...  In other words, the representation coefficient of these data in other subspaces is zero. erefore, as for high-dimensional data, the representation coefficients of data in low-dimensional subspace are sparse  ... 
doi:10.1155/2021/3937222 pmid:34608408 pmcid:PMC8487389 fatcat:o5uylb3ndbexhlkd33ipfotuja

Sparse Subspace Clustering via Diffusion Process [article]

Qilin Li, Ling Li, Wanquan Liu
2016 arXiv   pre-print
Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces.  ...  State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with L1, L2 or  ...  Conventional techniques, such as Principal Com-ponent Analysis (PCA), assume that the data is drawn from a single low-dimensional subspace of the high-dimensional space.  ... 
arXiv:1608.01793v1 fatcat:anhezfsyqncbfl3xo7lb6gjuxa

Random projection in dimensionality reduction

Ella Bingham, Heikki Mannila
2001 Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '01  
We present experimental results on using random projection as a dimensionality reduction tool in a number of cases, where the high dimensionality of the data would otherwise lead to burdensome computations  ...  We show that projecting the data onto a random lower-dimensional subspace yields results comparable to conventional dimensionality reduction methods such as principal component analysis: the similarity  ...  data and dimensionality reduced data; this is a topic of a further study.  ... 
doi:10.1145/502512.502546 fatcat:q3ifxgmpnfe35mpvbvcdfvdgky

Sparse Subspace Clustering: Algorithm, Theory, and Applications

E. Elhamifar, R. Vidal
2013 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces.  ...  This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces.  ...  In Section 6, we verify our theoretical analysis through experiments on synthetic data.  ... 
doi:10.1109/tpami.2013.57 pmid:24051734 fatcat:34st7xdfw5gadp2ud5r3f7kzhm

Learning Transformations

Qiang Qiu, Guillermo Sapiro
2014 2014 IEEE International Conference on Image Processing (ICIP)  
Many highdimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces.  ...  The corresponding subspace clustering problem has been extensively studied in the literature, partitioning such highdimensional data into clusters corresponding to their underlying low-dimensional subspaces  ...  At the theoretical level, extending the analysis to the noisy case is needed. Furthermore, the study of the framework in its compressed dimensionality form is of critical significance.  ... 
doi:10.1109/icip.2014.7025814 dblp:conf/icip/QiuS14 fatcat:xvo7kogj5ba6dnbvojkwkjqzqa

Bringing in the outliers: A sparse subspace clustering approach to learn a dictionary of mouse ultrasonic vocalizations [article]

Jiaxi Wang and Karel Mundnich and Allison T. Knoll and Pat Levitt and Shrikanth Narayanan
2020 arXiv   pre-print
We propose a new method to automatically create a dictionary of USVs based on a two-step spectral clustering approach, where we split the set of USVs into inlier and outlier data sets.  ...  This approach is motivated by the known degrading performance of sparse subspace clustering with outliers.  ...  ACKNOWLEDGEMENTS We thank the USC Viterbi School of Engineering and the Feng Deng Foundation in Tsinghua for their support.  ... 
arXiv:2003.05897v1 fatcat:zpmda5mxdbawdkqvt7jj6wego4

Dictionary Learning

Ivana Tosic, Pascal Frossard
2011 IEEE Signal Processing Magazine  
We further show that dimensionality reduction based on dictionary representation can be extended to address specific tasks such as data analysis or classification when the learning includes a class separability  ...  We present methods for determining the proper representation of data sets by means of reduced dimensionality subspaces, which are adaptive to both the characteristics of the signals and the processing  ...  [ FIG6] Illustration of dimensionality reduction of a two-class data set, by projection on a linear subspace defined by vectors 1v 1 ,v 2 2.  ... 
doi:10.1109/msp.2010.939537 fatcat:yvxjzm5margvncs73m2jjjyfhy

Exactly Robust Kernel Principal Component Analysis

Jicong Fan, Tommy W. S. Chow
2019 IEEE Transactions on Neural Networks and Learning Systems  
We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially corrupted matrix as a sparse matrix plus a high- or full-rank matrix with low latent dimensionality  ...  Comparative studies in noise removal and robust subspace clustering corroborate the effectiveness and the superiority of RKPCA.  ...  The proposed RKPCA solved the problem of high/fullrank matrix plus sparse noises, which is a challenge to existing methods such as RPCA. We proved the superiority of RKPCA over RPCA theoretically.  ... 
doi:10.1109/tnnls.2019.2909686 pmid:31034425 fatcat:xcvoiestwvbnrg4yar6km4c3he

A review on low-rank models in data analysis

Zhouchen Lin
2016 Big Data & Information Analytics  
Nowadays we are in the big data era. The high-dimensionality of data imposes big challenge on how to process them effectively and efficiently. Fortunately, in practice data are not unstructured.  ...  My review also provides theoretical analysis and randomized algorithms.  ...  Their main purpose is to cluster data, drastically in contrast to that of single-subspace ones, i.e., to denoise data. Theoretical analysis.  ... 
doi:10.3934/bdia.2016001 fatcat:4da3afzepjf3zisipwoq4jce34
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