Related papers: Multilinear Common Component Analysis via Kronecke…
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
We present Deep Tensor Canonical Correlation Analysis (DTCCA), a method to learn complex nonlinear transformations of multiple views (more than two) of data such that the resulting representations are linearly correlated in high order. The…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
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…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
We propose Deep Multiset Canonical Correlation Analysis (dMCCA) as an extension to representation learning using CCA when the underlying signal is observed across multiple (more than two) modalities. We use deep learning framework to learn…
Kronecker PCA involves the use of a space vs. time Kronecker product decomposition to estimate spatio-temporal covariances. In this work the addition of a sparse correction factor is considered, which corresponds to a model of the…
We propose Cooperative Component Analysis (CoCA), a new method for unsupervised multi-view analysis: it identifies the component that simultaneously captures significant within-view variance and exhibits strong cross-view correlation. The…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
Unified representation learning for multi-source data integration faces two important challenges: blockwise missingness and blockwise signal heterogeneity. The former arises from sources observing different, yet potentially overlapping,…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…