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I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
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…
Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and - for a certain type of dynamics…
Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…
Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…
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), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
Structural covariance analysis is a widely used structural MRI analysis method which characterises the co-relations of morphology between brain regions over a group of subjects. To our knowledge, little has been investigated in terms of the…
Neuroscience and artificial intelligence (AI) both face the challenge of interpreting high-dimensional neural data, where the comparative analysis of such data is crucial for revealing shared mechanisms and differences between these complex…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
We propose a general, modular method for significance testing of groups (or clusters) of variables in a high-dimensional linear model. In presence of high correlations among the covariables, due to serious problems of identifiability, it is…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…