Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering
- URL: http://arxiv.org/abs/2005.09229v1
- Date: Tue, 19 May 2020 05:54:14 GMT
- Title: Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering
- Authors: Chong Peng, Zhilu Zhang, Zhao Kang, Chenglizhao Chen, Qiang Cheng
- Abstract summary: We propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF.
It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step.
- Score: 50.43424130281065
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we propose a new Semi-Nonnegative Matrix Factorization method
for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of
existing methods that seriously damage the spatial information of the data by
converting 2D data to vectors in a preprocessing step. In particular,
projection matrices are sought under the guidance of building new data
representations, such that the spatial information is retained and projections
are enhanced by the goal of clustering, which helps construct optimal
projection directions. Moreover, to exploit nonlinear structures of the data,
manifold is constructed in the projected subspace, which is adaptively updated
according to the projections and less afflicted with noise and outliers of the
data and thus more representative in the projected space. Hence, seeking
projections, building new data representations, and learning manifold are
seamlessly integrated in a single model, which mutually enhance other and lead
to a powerful data representation. Comprehensive experimental results verify
the effectiveness of TS-NMF in comparison with several state-of-the-art
algorithms, which suggests high potential of the proposed method for real world
applications.
Related papers
- Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets.
In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem.
This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
arXiv Detail & Related papers (2024-02-03T19:00:19Z) - Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model [13.082805815235975]
We introduce a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data.
The effectiveness and practical merits of the proposed framework are demonstrated through experiments on both simulated and real datasets.
arXiv Detail & Related papers (2023-07-02T13:59:47Z) - VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables.
The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning.
We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
arXiv Detail & Related papers (2023-04-03T13:13:19Z) - Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data
Visualization [20.43471678277403]
We propose LaptSNE, a new graph-based dimensionality reduction method based on t-SNE.
Specifically, LaptSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding.
We show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective.
arXiv Detail & Related papers (2022-07-25T14:10:24Z) - Graph Constrained Data Representation Learning for Human Motion
Segmentation [14.611777974037194]
We propose a novel unsupervised model that learns a representation of the data and digs clustering information from the data itself.
Experimental results on four benchmark datasets for HMS demonstrate that our approach achieves significantly better clustering performance then state-of-the-art methods.
arXiv Detail & Related papers (2021-07-28T13:49:16Z) - A Local Similarity-Preserving Framework for Nonlinear Dimensionality
Reduction with Neural Networks [56.068488417457935]
We propose a novel local nonlinear approach named Vec2vec for general purpose dimensionality reduction.
To train the neural network, we build the neighborhood similarity graph of a matrix and define the context of data points.
Experiments of data classification and clustering on eight real datasets show that Vec2vec is better than several classical dimensionality reduction methods in the statistical hypothesis test.
arXiv Detail & Related papers (2021-03-10T23:10:47Z) - Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature
Selection [138.97647716793333]
We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization.
We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
arXiv Detail & Related papers (2020-12-29T04:08:38Z) - Kernel Two-Dimensional Ridge Regression for Subspace Clustering [45.651770340521786]
We propose a novel subspace clustering method for 2D data.
It directly uses 2D data as inputs such that the learning of representations benefits from inherent structures and relationships of the data.
arXiv Detail & Related papers (2020-11-03T04:52:46Z) - Robust Locality-Aware Regression for Labeled Data Classification [5.432221650286726]
We propose a new discriminant feature extraction framework, namely Robust Locality-Aware Regression (RLAR)
In our model, we introduce a retargeted regression to perform the marginal representation learning adaptively instead of using the general average inter-class margin.
To alleviate the disturbance of outliers and prevent overfitting, we measure the regression term and locality-aware term together with the regularization term by the L2,1 norm.
arXiv Detail & Related papers (2020-06-15T11:36:59Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.