EquiNMF: Graph Regularized Multiview Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) methods have proved to be powerful across a wide range of real-world clustering applications. Integrating multiple types of measurements for the same objects/subjects allows us to gain a deeper understanding of the data and refine the clustering. We have developed a novel Graph-reguarized multiview NMF-based method for data integration called EquiNMF. The parameters for our method are set in a completely automated data-specific unsupervised fashion, a highly desirable property in real-world applications. We performed extensive and comprehensive experiments on multiview imaging data. We show that EquiNMF consistently outperforms other single-view NMF methods used on concatenated data and multi-view NMF methods with different types of regularizations

Graph Multiview Canonical Correlation Analysis

Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the common sources, which may be available \emph{a priori}, or can be constructed using certain domain knowledge. This prior information about the common sources can be encoded by a graph, and be invoked as a regularizer to enrich the maximum variance MCCA framework. In this context, the present paper's novel graph-regularized (G) MCCA approach minimizes the distance between the wanted canonical variables and the common low-dimensional representations, while accounting for graph-induced knowledge of the common sources. Relying on a function capturing the extent low-dimensional representations of the multiple views are similar, a generalization bound of GMCCA is established based on Rademacher's complexity. Tailored for setups where the number of data pairs is smaller than the data vector dimensions, a graph-regularized dual MCCA approach is also developed. To further deal with nonlinearities present in the data, graph-regularized kernel MCCA variants are put forward too. Interestingly, solutions of the graph-regularized linear, dual, and kernel MCCA, are all provided in terms of generalized eigenvalue decomposition. Several corroborating numerical tests using real datasets are provided to showcase the merits of the graph-regularized MCCA variants relative to several competing alternatives including MCCA, Laplacian-regularized MCCA, and (graph-regularized) PCA

Feature Concatenation Multi-view Subspace Clustering

Multi-view clustering aims to achieve more promising clustering results than single-view clustering by exploring the multi-view information. Since statistic properties of different views are diverse, even incompatible, few approaches implement multi-view clustering based on the concatenated features directly. However, feature concatenation is a natural way to combine multiple views. To this end, this paper proposes a novel multi-view subspace clustering approach dubbed Feature Concatenation Multi-view Subspace Clustering (FCMSC). Specifically, by exploring the consensus information, multi-view data are concatenated into a joint representation firstly, then, $l_{2,1}$-norm is integrated into the objective function to deal with the sample-specific and cluster-specific corruptions of multiple views for benefiting the clustering performance. Furthermore, by introducing graph Laplacians of multiple views, a graph regularized FCMSC is also introduced to explore both the consensus information and complementary information for clustering. It is noteworthy that the obtained coefficient matrix is not derived by directly applying the Low-Rank Representation (LRR) to the joint view representation simply. Finally, an effective algorithm based on the Augmented Lagrangian Multiplier (ALM) is designed to optimized the objective functions. Comprehensive experiments on six real world datasets illustrate the superiority of the proposed methods over several state-of-the-art approaches for multi-view clustering

Analysis of multiview legislative networks with structured matrix factorization: Does Twitter influence translate to the real world?

The rise of social media platforms has fundamentally altered the public discourse by providing easy to use and ubiquitous forums for the exchange of ideas and opinions. Elected officials often use such platforms for communication with the broader public to disseminate information and engage with their constituencies and other public officials. In this work, we investigate whether Twitter conversations between legislators reveal their real-world position and influence by analyzing multiple Twitter networks that feature different types of link relations between the Members of Parliament (MPs) in the United Kingdom and an identical data set for politicians within Ireland. We develop and apply a matrix factorization technique that allows the analyst to emphasize nodes with contextual local network structures by specifying network statistics that guide the factorization solution. Leveraging only link relation data, we find that important politicians in Twitter networks are associated with real-world leadership positions, and that rankings from the proposed method are correlated with the number of future media headlines.Comment: Published at http://dx.doi.org/10.1214/15-AOAS858 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Kernelized Multiview Projection

Conventional vision algorithms adopt a single type of feature or a simple concatenation of multiple features, which is always represented in a high-dimensional space. In this paper, we propose a novel unsupervised spectral embedding algorithm called Kernelized Multiview Projection (KMP) to better fuse and embed different feature representations. Computing the kernel matrices from different features/views, KMP can encode them with the corresponding weights to achieve a low-dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative. More crucially, KMP is linear for the reproducing kernel Hilbert space (RKHS) and solves the out-of-sample problem, which allows it to be competent for various practical applications. Extensive experiments on three popular image datasets demonstrate the effectiveness of our multiview embedding algorithm

Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques

We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based algorithms, diffusion map (DM) and alternating diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep dynamics by reorganizing the spectral information of an electroencephalogram (EEG) extracted from a nonlinear-type time frequency analysis tool, the synchrosqueezing transform (SST). The visualization is achieved by the nonlinear dimension reduction properties of DM and AD. Moreover, the reconstructed nonlinear geometric structure of the sleep dynamics allows us to achieve the automatic annotation purpose. The hidden Markov model is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC* and ST*, with the leave-one-subject-out cross validation. The overall accuracy and macro F1 achieve 82:57% and 76% in Sleep-EDF SC* and 77.01% and 71:53% in Sleep-EDF ST*, which is compatible with the state-of-the-art results by supervised learning-based algorithms. The results suggest the potential of the proposed algorithm for clinical applications.Comment: 41 pages, 21 figures. arXiv admin note: text overlap with arXiv:1803.0171

Depth Sequence Coding with Hierarchical Partitioning and Spatial-domain Quantisation

Depth coding in 3D-HEVC for the multiview video plus depth (MVD) architecture (i) deforms object shapes due to block-level edge-approximation; (ii) misses an opportunity for high compressibility at near-lossless quality by failing to exploit strong homogeneity (clustering tendency) in depth syntax, motion vector components, and residuals at frame-level; and (iii) restricts interactivity and limits responsiveness of independent use of depth information for "non-viewing" applications due to texture-depth coding dependency. This paper presents a standalone depth sequence coder, which operates in the lossless to near-lossless quality range while compressing depth data superior to lossy 3D-HEVC. It preserves edges implicitly by limiting quantisation to the spatial-domain and exploits clustering tendency efficiently at frame-level with a novel binary tree based decomposition (BTBD) technique. For mono-view coding of standard MVD test sequences, on average, (i) lossless BTBD achieved $\times 42.2$ compression-ratio and $-60.0\%$ coding gain against the pseudo-lossless 3D-HEVC, using the lowest quantisation parameter $QP = 1$, and (ii) near-lossless BTBD achieved $-79.4\%$ and $6.98$ dB Bj{\o}ntegaard delta bitrate (BD-BR) and distortion (BD-PSNR), respectively, against 3D-HEVC. In view-synthesis applications, decoded depth maps from BTBD rendered superior quality synthetic-views, compared to 3D-HEVC, with $-18.9\%$ depth BD-BR and $0.43$ dB synthetic-texture BD-PSNR on average.Comment: Submitted to IEEE Transactions on Image Processing. 13 pages, 5 figures, and 5 table

K-means clustering for efficient and robust registration of multi-view point sets

Generally, there are three main factors that determine the practical usability of registration, i.e., accuracy, robustness, and efficiency. In real-time applications, efficiency and robustness are more important. To promote these two abilities, we cast the multi-view registration into a clustering task. All the centroids are uniformly sampled from the initially aligned point sets involved in the multi-view registration, which makes it rather efficient and effective for the clustering. Then, each point is assigned to a single cluster and each cluster centroid is updated accordingly. Subsequently, the shape comprised by all cluster centroids is used to sequentially estimate the rigid transformation for each point set. For accuracy and stability, clustering and transformation estimation are alternately and iteratively applied to all point sets. We tested our proposed approach on several benchmark datasets and compared it with state-of-the-art approaches. Experimental results validate its efficiency and robustness for the registration of multi-view point sets

A Survey on Semi-Supervised Learning Techniques

Semisupervised learning is a learning standard which deals with the study of how computers and natural systems such as human beings acquire knowledge in the presence of both labeled and unlabeled data. Semisupervised learning based methods are preferred when compared to the supervised and unsupervised learning because of the improved performance shown by the semisupervised approaches in the presence of large volumes of data. Labels are very hard to attain while unlabeled data are surplus, therefore semisupervised learning is a noble indication to shrink human labor and improve accuracy. There has been a large spectrum of ideas on semisupervised learning. In this paper we bring out some of the key approaches for semisupervised learning.Comment: 5 Pages, 3 figures, Published with International Journal of Computer Trends and Technology (IJCTT

Multi-View Spectral Clustering via Structured Low-Rank Matrix Factorization

Multi-view data clustering attracts more attention than their single view counterparts due to the fact that leveraging multiple independent and complementary information from multi-view feature spaces outperforms the single one. Multi-view Spectral Clustering aims at yielding the data partition agreement over their local manifold structures by seeking eigenvalue-eigenvector decompositions. However, as we observed, such classical paradigm still suffers from (1) overlooking the flexible local manifold structure, caused by (2) enforcing the low-rank data correlation agreement among all views; worse still, (3) LRR is not intuitively flexible to capture the latent data clustering structures. In this paper, we present the structured LRR by factorizing into the latent low-dimensional data-cluster representations, which characterize the data clustering structure for each view. Upon such representation, (b) the laplacian regularizer is imposed to be capable of preserving the flexible local manifold structure for each view. (c) We present an iterative multi-view agreement strategy by minimizing the divergence objective among all factorized latent data-cluster representations during each iteration of optimization process, where such latent representation from each view serves to regulate those from other views, such intuitive process iteratively coordinates all views to be agreeable. (d) We remark that such data-cluster representation can flexibly encode the data clustering structure from any view with adaptive input cluster number. To this end, (e) a novel non-convex objective function is proposed via the efficient alternating minimization strategy. The complexity analysis are also presented. The extensive experiments conducted against the real-world multi-view datasets demonstrate the superiority over state-of-the-arts.Comment: Accepted to appear at IEEE Trans on Neural Networks and Learning System