Related papers: Tensor Principal Component Analysis in High Dimens…

The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise,…

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and…

Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…