Related papers: Tensor PCA for Factor Models

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…

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…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

We consider identification, inference and validation of linear panel data models when both factors and factor loadings are accounted for by a nonparametric function. This general specification encompasses rather popular models such as the…

A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…

We propose a new framework for modeling high-dimensional matrix-variate time series by a two-way transformation, where the transformed data consist of a matrix-variate factor process, which is dynamically dependent, and three other blocks…

The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a low-rank tensor corrupted by sparse noise, has attracted much attention in many real applications. This paper develops a new Global Weighted TRPCA method (GWTRPCA),…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…