Probabilistic Distance for Mixtures of Independent Component Analyzers

Adversarial Data Augmentation for HMM-Based Anomaly Detection

In this work, we concentrate on the detection of anomalous behaviors in systems operating in the physical world and for which it is usually not possible to have a complete set of all possible anomalies in advance. We present a data augmentation and retraining approach based on adversarial learning for improving anomaly detection. In particular, we first define a method for generating adversarial examples for anomaly detectors based on Hidden Markov Models (HMMs). Then, we present a data augmentation and retraining technique that uses these adversarial examples to improve anomaly detection performance. Finally, we evaluate our adversarial data augmentation and retraining approach on four datasets showing that it achieves a statistically significant performance improvement and enhances the robustness to adversarial attacks. Key differences from the state-of-the-art on adversarial data augmentation are the focus on multivariate time series (as opposed to images), the context of one-class classification (in contrast to standard multi-class classification), and the use of HMMs (in contrast to neural networks).

Improvement and Assessment of a Blind Image Deblurring Algorithm Based on Independent Component Analysis

The aim of the present paper is to improve an existing blind image deblurring algorithm, based on an independent component learning paradigm, by manifold calculus. The original technique is based on an independent component analysis algorithm applied to a set of pseudo-images obtained by Gabor-filtering a blurred image and is based on an adapt-and-project paradigm. A comparison between the original technique and the improved method shows that independent component learning on the unit hypersphere by a Riemannian-gradient algorithm outperforms the adapt-and-project strategy. A comprehensive set of numerical tests evidenced the strengths and weaknesses of the discussed deblurring technique.

Eliminating the Permutation Ambiguity of Convolutive Blind Source Separation by Using Coupled Frequency Bins

Blind source separation (BSS) is a typical unsupervised learning method that extracts latent components from their observations. In the meanwhile, convolutive BSS (CBSS) is particularly challenging as the observations are the mixtures of latent components as well as their delayed versions. CBSS is usually solved in frequency domain since convolutive mixtures in time domain is just instantaneous mixtures in frequency domain, which allows to recover source frequency components independently of each frequency bin by running ordinary BSS, and then concatenate them to form the Fourier transformation of source signals. Because BSS has inherent permutation ambiguity, this category of CBSS methods suffers from a common drawback: it is very difficult to choose the frequency components belonging to a specific source as they are estimated from different frequency bins using BSS. This paper presents a tensor framework that can completely eliminate the permutation ambiguity. By combining each frequency bin with an anchor frequency bin that is chosen arbitrarily in advance, we establish a new virtual BSS model where the corresponding correlation matrices comply with a block tensor decomposition (BTD) model. The essential uniqueness of BTD and the sparse structure of coupled mixing parameters allow the estimation of the mixing matrices free of permutation ambiguity. Extensive simulation results confirmed that the proposed algorithm could achieve higher separation accuracy compared with the state-of-the-art methods.

Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

Modeling brain dynamic state changes with adaptive mixture independent component analysis

There is a growing interest in neuroscience in assessing the continuous, endogenous, and nonstationary dynamics of brain network activity supporting the fluidity of human cognition and behavior. This non-stationarity may involve ever-changing formation and dissolution of active cortical sources and brain networks. However, unsupervised approaches to identify and model these changes in brain dynamics as continuous transitions between quasi-stable brain states using unlabeled, noninvasive recordings of brain activity have been limited. This study explores the use of adaptive mixture independent component analysis (AMICA) to model multichannel electroencephalographic (EEG) data with a set of ICA models, each of which decomposes an adaptively learned portion of the data into statistically independent sources. We first show that AMICA can segment simulated quasi-stationary EEG data and accurately identify ground-truth sources and source model transitions. Next, we demonstrate that AMICA decomposition, applied to 6-13 channel scalp recordings from the CAP Sleep Database, can characterize sleep stage dynamics, allowing 75% accuracy in identifying transitions between six sleep stages without use of EEG power spectra. Finally, applied to 30-channel data from subjects in a driving simulator, AMICA identifies models that account for EEG during faster and slower response to driving challenges, respectively. We show changes in relative probabilities of these models allow effective prediction of subject response speed and moment-by-moment characterization of state changes within single trials. AMICA thus provides a generic unsupervised approach to identifying and modeling changes in EEG dynamics. Applied to continuous, unlabeled multichannel data, AMICA may likely be used to detect and study any changes in cognitive states.