scholarly journals Low Rank Correlation Representation and Clustering

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wenyun Gao ◽  
Sheng Dai ◽  
Stanley Ebhohimhen Abhadiomhen ◽  
Wei He ◽  
Xinghui Yin
Keyword(s):  
State Of The Art ◽  
Rank Correlation ◽  
Laplacian Matrix ◽  
Low Rank ◽  
Superior Performance ◽  
Cross Domain ◽  
Common Representation ◽  
Correlation Learning ◽  
Low Rank Representation ◽  
The Common

Correlation learning is a technique utilized to find a common representation in cross-domain and multiview datasets. However, most existing methods are not robust enough to handle noisy data. As such, the common representation matrix learned could be influenced easily by noisy samples inherent in different instances of the data. In this paper, we propose a novel correlation learning method based on a low-rank representation, which learns a common representation between two instances of data in a latent subspace. Specifically, we begin by learning a low-rank representation matrix and an orthogonal rotation matrix to handle the noisy samples in one instance of the data so that a second instance of the data can linearly reconstruct the low-rank representation. Our method then finds a similarity matrix that approximates the common low-rank representation matrix much better such that a rank constraint on the Laplacian matrix would reveal the clustering structure explicitly without any spectral postprocessing. Extensive experimental results on ORL, Yale, Coil-20, Caltech 101-20, and UCI digits datasets demonstrate that our method has superior performance than other state-of-the-art compared methods in six evaluation metrics.

Cross-Domain Object Representation via Robust Low-Rank Correlation Analysis

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Xiangjun Shen ◽  
Jinghui Zhou ◽  
Zhongchen Ma ◽  
Bingkun Bao ◽  
Zhengjun Zha
Keyword(s):  
Correlation Analysis ◽  
Object Representation ◽  
Rank Correlation ◽  
Data Representation ◽  
Low Rank ◽  
Superior Performance ◽  
Image Clustering ◽  
Cross Domain ◽  
Clustering And Classification ◽  
Correlated Components

Cross-domain data has become very popular recently since various viewpoints and different sensors tend to facilitate better data representation. In this article, we propose a novel cross-domain object representation algorithm (RLRCA) which not only explores the complexity of multiple relationships of variables by canonical correlation analysis (CCA) but also uses a low rank model to decrease the effect of noisy data. To the best of our knowledge, this is the first try to smoothly integrate CCA and a low-rank model to uncover correlated components across different domains and to suppress the effect of noisy or corrupted data. In order to improve the flexibility of the algorithm to address various cross-domain object representation problems, two instantiation methods of RLRCA are proposed from feature and sample space, respectively. In this way, a better cross-domain object representation can be achieved through effectively learning the intrinsic CCA features and taking full advantage of cross-domain object alignment information while pursuing low rank representations. Extensive experimental results on CMU PIE, Office-Caltech, Pascal VOC 2007, and NUS-WIDE-Object datasets, demonstrate that our designed models have superior performance over several state-of-the-art cross-domain low rank methods in image clustering and classification tasks with various corruption levels.

Computing Robust Principal Components by A* Search

2018 ◽  
Vol 27 (07) ◽  
pp. 1860013 ◽  
Author(s):  
Swair Shah ◽  
Baokun He ◽  
Crystal Maung ◽  
Haim Schweitzer
Keyword(s):  
State Of The Art ◽  
Principal Component ◽  
Low Rank ◽  
A Algorithm ◽  
Running Time ◽  
Current State ◽  
Dimensionality Reduction Technique ◽  
Related Variant ◽  
Low Rank Representation ◽  
The Cost

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We show how to convert this problem into graph search, and describe an algorithm that solves this problem optimally by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal in terms of accuracy, and are shown to be more accurate than results obtained by the current state-of-the- art algorithms which are shown not to be optimal. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster than the optimal variant and produces a solution that is guaranteed to be near the optimal. This variant is shown experimentally to be more accurate than the current state-of-the-art and has a comparable running time.

Multiview Common Subspace Clustering via Coupled Low Rank Representation

2021 ◽  
Vol 12 (4) ◽  
pp. 1-25
Author(s):  
Stanley Ebhohimhen Abhadiomhen ◽  
Zhiyang Wang ◽  
Xiangjun Shen ◽  
Jianping Fan
Keyword(s):  
Common Knowledge ◽  
Subspace Clustering ◽  
Laplacian Matrix ◽  
Low Rank ◽  
Connected Components ◽  
Similarity Matrix ◽  
Benchmark Datasets ◽  
Low Rank Representation ◽  
Low Dimensional ◽  
Shared Structure

Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representation to address the above limitation. Our method first obtains a low-rank representation for each view, constrained to be a linear combination of the view-specific representation and the shared representation by simultaneously encouraging the sparsity of view-specific one. Then, it uses the k -block diagonal regularizer to learn a manifold recovery matrix for each view through respective low-rank matrices to recover more manifold structures from them. In this way, the proposed method can find an ideal similarity matrix by approximating clustering projection matrices obtained from the recovery structures. Hence, this similarity matrix denotes our clustering structure with exactly k connected components by applying a rank constraint on the similarity matrix’s relaxed Laplacian matrix to avoid spectral post-processing of the low-dimensional embedding matrix. The core of our idea is such that we introduce dynamic approximation into the low-rank representation to allow the clustering structure and the shared representation to guide each other to learn cleaner low-rank matrices that would lead to a better clustering structure. Therefore, our approach is notably different from existing methods in which the local manifold structure of data is captured in advance. Extensive experiments on six benchmark datasets show that our method outperforms 10 similar state-of-the-art compared methods in six evaluation metrics.

Robust Multibit Image Watermarking Based on Contrast Modulation and Affine Rectification

2019 ◽  
Vol 33 (14) ◽  
pp. 1954036
Author(s):  
Xin Zhong ◽  
Frank Y. Shih
Keyword(s):  
Image Processing ◽  
Lower Bound ◽  
State Of The Art ◽  
Image Watermarking ◽  
Center Of Mass ◽  
Experimental Results ◽  
Superior Performance ◽  
The Common ◽  
Distortion Parameters ◽  
Watermarking Scheme

In this paper, we present a robust multibit image watermarking scheme to undertake the common image-processing attacks as well as affine distortions. This scheme combines contrast modulation and effective synchronization for large payload and high robustness. We analyze the robustness, payload, and the lower bound of fidelity. Regarding watermark resynchronization under affine distortions, we develop a self-referencing rectification method to detect the distortion parameters for reconstruction by the center of mass in affine covariant regions. The effectiveness and advantages of the proposed scheme are confirmed by experimental results, which show the superior performance as comparing against several state-of-the-art watermarking methods.

scholarly journals Low-rank Matrix Optimization for Video Segmentation Research

2017 ◽  
Vol 6 (1) ◽  
pp. 36
Author(s):  
Caiyun Huang ◽  
Guojun Qin
Keyword(s):  
Video Segmentation ◽  
Optimal Solution ◽  
Low Rank ◽  
Superior Performance ◽  
Closed Form Solutions ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Representation ◽  
Spatio Temporal ◽  
Low Rank Matrix

This paper investigates how to perform robust and efficient unsupervised video segmentation while suppressing the effects of data noises and/or corruptions. The low-rank representation is pursued for video segmentation. The supervoxels affinity matrix of an observed video sequence is given, low-rank matrix optimization seeks a optimal solution by making the matrix rank explicitly determined. We iteratively optimize them with closed-form solutions. Moreover, we incorporate a discriminative replication prior into our framework based on the obervation that small-size video patterns, and it tends to recur frequently within the same object. The video can be segmented into several spatio-temporal regions by applying the Normalized-Cut algorithm with the solved low-rank representation. To process the streaming videos, we apply our algorithm sequentially over a batch of frames over time, in which we also develop several temporal consistent constraints improving the robustness. Extensive experiments are on the public benchmarks, they demonstrate superior performance of our framework over other approaches．

Cross-domain thinking: Common representation format or generalized mapping process?

2002 ◽  
Vol 25 (6) ◽  
pp. 683-684
Author(s):  
Peter F. Dominey
Keyword(s):  
Analogical Reasoning ◽  
Specific Data ◽  
Domain Specific ◽  
Cross Domain ◽  
Common Representation ◽  
Mapping Process ◽  
The Common ◽  
Process Oriented

In Carruthers’ formulation, cross-domain thinking requires translation of domain specific data into a common format, and linguistic LF thus plays the role of the common medium of exchange. Alternatively, I propose a process-oriented characterization, in which there is no common representation and cross-domain thinking is rather the process of establishing mappings across domains, as in the process of analogical reasoning.

Discriminative Low-Rank Subspace Learning with Nonconvex Penalty

2019 ◽  
Vol 33 (10) ◽  
pp. 1951006
Author(s):  
Kan Xie ◽  
Wei Liu ◽  
Yue Lai ◽  
Weijun Li
Keyword(s):  
Face Recognition ◽  
State Of The Art ◽  
Subspace Learning ◽  
Experimental Results ◽  
Low Rank ◽  
Learning Method ◽  
Original Solution ◽  
Discriminative Subspace ◽  
Low Rank Representation ◽  
Facial Images

Subspace learning has been widely utilized to extract discriminative features for classification task, such as face recognition, even when facial images are occluded or corrupted. However, the performance of most existing methods would be degraded significantly in the scenario of that data being contaminated with severe noise, especially when the magnitude of the gross corruption can be arbitrarily large. To this end, in this paper, a novel discriminative subspace learning method is proposed based on the well-known low-rank representation (LRR). Specifically, a discriminant low-rank representation and the projecting subspace are learned simultaneously, in a supervised way. To avoid the deviation from the original solution by using some relaxation, we adopt the Schatten [Formula: see text]-norm and [Formula: see text]-norm, instead of the nuclear norm and [Formula: see text]-norm, respectively. Experimental results on two famous databases, i.e. PIE and ORL, demonstrate that the proposed method achieves better classification scores than the state-of-the-art approaches.

scholarly journals Enhancing Matrix Completion Using a Modified Second-Order Total Variation

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wendong Wang ◽  
Jianjun Wang
Keyword(s):  
Total Variation ◽  
Optimization Problem ◽  
State Of The Art ◽  
Matrix Completion ◽  
Second Order ◽  
Low Rank ◽  
Superior Performance ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix

In this paper, we propose a new method to deal with the matrix completion problem. Different from most existing matrix completion methods that only pursue the low rank of underlying matrices, the proposed method simultaneously optimizes their low rank and smoothness such that they mutually help each other and hence yield a better performance. In particular, the proposed method becomes very competitive with the introduction of a modified second-order total variation, even when it is compared with some recently emerged matrix completion methods that also combine the low rank and smoothness priors of matrices together. An efficient algorithm is developed to solve the induced optimization problem. The extensive experiments further confirm the superior performance of the proposed method over many state-of-the-art methods.

Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraints

2021 ◽  
pp. 1-15
Author(s):  
Zhixuan xu ◽  
Caikou Chen ◽  
Guojiang Han ◽  
Jun Gao
Keyword(s):  
State Of The Art ◽  
Subspace Clustering ◽  
Dimensional Subspace ◽  
Low Rank ◽  
Dimensional Structure ◽  
Clustering Methods ◽  
Benchmark Datasets ◽  
Handwritten Digit ◽  
Low Rank Representation ◽  
Low Dimensional

As a successful improvement on Low Rank Representation (LRR), Latent Low Rank Representation (LatLRR) has been one of the state-of-the-art models for subspace clustering due to the capability of discovering the low dimensional subspace structures of data, especially when the data samples are insufficient and/or extremely corrupted. However, the LatLRR method does not consider the nonlinear geometric structures within data, which leads to the loss of the locality information among data in the learning phase. Moreover, the coefficients of the learnt representation matrix can be negative, which lack the interpretability. To solve the above drawbacks of LatLRR, this paper introduces Laplacian, sparsity and non-negativity to LatLRR model and proposes a novel subspace clustering method, termed latent low rank representation with non-negative, sparse and laplacian constraints (NNSLLatLRR), in which we jointly take into account non-negativity, sparsity and laplacian properties of the learnt representation. As a result, the NNSLLatLRR can not only capture the global low dimensional structure and intrinsic non-linear geometric information of the data, but also enhance the interpretability of the learnt representation. Extensive experiments on two face benchmark datasets and a handwritten digit dataset show that our proposed method outperforms existing state-of-the-art subspace clustering methods.

scholarly journals Correlational Neural Networks

2016 ◽  
Vol 28 (2) ◽  
pp. 257-285 ◽  
Author(s):  
Sarath Chandar ◽  
Mitesh M. Khapra ◽  
Hugo Larochelle ◽  
Balaraman Ravindran
Keyword(s):  
Canonical Correlation ◽  
State Of The Art ◽  
Representation Learning ◽  
Advantages And Disadvantages ◽  
Common Representation ◽  
Series Of Experiments ◽  
The Common ◽  
Cross Language ◽  
Joint Representation ◽  
Better Than

Common representation learning (CRL), wherein different descriptions (or views) of the data are embedded in a common subspace, has been receiving a lot of attention recently. Two popular paradigms here are canonical correlation analysis (CCA)–based approaches and autoencoder (AE)–based approaches. CCA-based approaches learn a joint representation by maximizing correlation of the views when projected to the common subspace. AE-based methods learn a common representation by minimizing the error of reconstructing the two views. Each of these approaches has its own advantages and disadvantages. For example, while CCA-based approaches outperform AE-based approaches for the task of transfer learning, they are not as scalable as the latter. In this work, we propose an AE-based approach, correlational neural network (CorrNet), that explicitly maximizes correlation among the views when projected to the common subspace. Through a series of experiments, we demonstrate that the proposed CorrNet is better than AE and CCA with respect to its ability to learn correlated common representations. We employ CorrNet for several cross-language tasks and show that the representations learned using it perform better than the ones learned using other state-of-the-art approaches.

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