Related papers: Robust Kronecker Product PCA for Spatio-Temporal C…
In this work we consider the estimation of spatio-temporal covariance matrices in the low sample non-Gaussian regime. We impose covariance structure in the form of a sum of Kronecker products decomposition (Tsiligkaridis et al. 2013,…
We consider the application of KronPCA spatio-temporal modeling techniques [Greenewald et al 2013, Tsiligkaridis et al 2013] to the extraction of spatiotemporal features for video dismount classification. KronPCA performs a low-rank type of…
In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance…
Using a noise covariance model based on a single Kronecker product of spatial and temporal covariance in the spatiotemporal analysis of MEG data was demonstrated to provide improvement in the results over that of the commonly used diagonal…
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…
We propose a new model for approximating spatiotemporal noise covariance for use in MEG/EEG source analysis. Our model is an extension of an existing model [1,2] that uses a single Kronecker product of a pair of matrices - temporal and…
We consider the problem of matrix approximation and denoising induced by the Kronecker product decomposition. Specifically, we propose to approximate a given matrix by the sum of a few Kronecker products of matrices, which we refer to as…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Sparse Principal Components Analysis (PCA) has been proposed as a way to improve both interpretability and reliability of PCA. However, use of sparse PCA in practice is hindered by the difficulty of tuning the multiple hyperparameters that…
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…
We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD)…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral…
We study the matrix-variate regression problem $Y_i = \sum_{k} \beta_{1k} X_i \beta_{2k}^{\top} + E_i$ for $i=1,2\dots,n$ in the high dimensional regime wherein the response $Y_i$ are matrices whose dimensions $p_{1}\times p_{2}$ outgrow…
This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex, elliptically symmetric (CES) distributions…
This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…
Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…
This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…