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Independent component analysis (ICA) is a fundamental problem in the field of signal processing, and numerous algorithms have been developed to address this issue. The core principle of these algorithms is to find a transformation matrix…

Capturing patterns of variation present in a dataset is important in exploratory data analysis and unsupervised learning. Contrastive dimension reduction methods, such as contrastive principal component analysis (cPCA), find patterns unique…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

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…

Spatial Independent Components Analysis (ICA) is increasingly used in the context of functional Magnetic Resonance Imaging (fMRI) to study cognition and brain pathologies. Salient features present in some of the extracted Independent…

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

We consider independent component analysis of binary data. While fundamental in practice, this case has been much less developed than ICA for continuous data. We start by assuming a linear mixing model in a continuous-valued latent space,…

In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to…

Spatial Independent Component Analysis (ICA) decomposes the time by space functional MRI (fMRI) matrix into a set of 1-D basis time courses and their associated 3-D spatial maps that are optimized for mutual independence. When applied to…

We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing…

Recent advances in nonlinear Independent Component Analysis (ICA) provide a principled framework for unsupervised feature learning and disentanglement. The central idea in such works is that the latent components are assumed to be…

Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the…

Independent component analysis (ICA), as a data driven method, has shown to be a powerful tool for functional magnetic resonance imaging (fMRI) data analysis. One drawback of this multivariate approach is, that it is not compatible to the…

Independent component analysis (ICA), is a blind source separation method that is becoming increasingly used to separate brain and non-brain related activities in electroencephalographic (EEG) and other electrophysiological recordings. It…

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of…

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

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…

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the…