Related papers: Generalizing Correspondence Analysis for Applicati…
In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an $\ell_2$ penalty on the CCA…
Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…
Canonical correlation analysis (CCA) is a method for reducing the dimension of data represented using two views. It has been previously used to derive word embeddings, where one view indicates a word, and the other view indicates its…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional…
Collins(2002, 2011) raised a number of issues with regards to correspondence analysis (CA), such as: qualitative information in a CA map versus quantitative information in the relevant contingency table; the interpretation of a CA map is…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust…
We build on the interpretation of the Economic Complexity method as Correspondence Analysis (CA), and propose that the Canonical form of CA (CCA), which originated in the ecology literature, can be used to calculate multi-dimensional…
Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics. These applications rely on large quantities of data gathered from automated sensors and user…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Cosine similarity is widely used to measure the similarity between two embeddings, while interpretations based on angle and correlation coefficient are common. In this study, we focus on the interpretable axes of embeddings transformed by…
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…
Identifying protein-protein interactions is crucial for a systems-level understanding of the cell. Recently, algorithms based on inverse statistical physics, e.g. Direct Coupling Analysis (DCA), have allowed to use evolutionarily related…
Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating…
Intermittency analysis of factorial moments is a promising method used for the detection of power-law scaling in high-energy collision data. In particular, it has been employed in the search of fluctuations characteristic of the critical…