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Matrix and Tensor Decompositions and their Potential Applications
Extracting an important information from massive large-scale experimental data-sets, measurements, observations and understanding complex data (image signals, patterns) has become an important challenge and objective. Often data-sets collected from complex phenomena represent the integrated result of multi-modal data with some inter-related variables or they are combinations of underlying latent (hidden) components or factors. In many situations, the measurements are gathered and stored as sets of matrices or multi-way arrays (tensors), and described by multi-modal, multi-dimensional and multi-linear models. In this talk, we provide a wide survey of generalized models and unsupervised learning algorithms of multilinear Independent Component Analysis (ICA), Nonnegative Matrix Factorization (NMF), Sparse Component Analysis (SCA) and its various extensions and modifications, especially Multilinear Blind Source Separation (MBSS).
In the tensor decompositions high-dimensional data, such as spectrogram or images are factored or decomposed directly e.g., they are approximated by a sum of rank-one tensors. Tensor decompositions and factorizations may play a major role in a wide range of important applications, including bioinformatics, micro-array analysis, neuroscience, text mining, image understanding, air pollution research, chemometrics, and spectral data analysis.
Matrix and tensor factorizations and decompositions have many other potential applications, such as linear sparse coding, image classification, clustering, neural learning process, sound recognition, remote sensing, Brain Computer Interface (BCI) and object characterizations.
In comprehensive multichannel and multi-modal measurements, biomedical data often contains higher-order ways (modes) such as trials, mental tasks, conditions, subjects, and groups in addition to the intrinsic 3D dimensions of space, time and frequency. In fact, specific mental tasks or stimuli are often presented repeatedly in a sequence of trials leading to a large volume stream of data encompassing many dimensions : Channels (space), time-frequency, trials, subjects and conditions. For such kind of data two-way matrix factorizations (e.g., 2-way ICA, NMF) or "flat-world view" may be insufficient for analysis of complex multi-dimensional experimental data. In order, to obtain more natural and sparse representations of the original data, it is necessary to use multi-way array (tensor) decomposition and factorization approaches since additional dimensions or modes can be retained only in multi-linear models to produce latent components that are unique and which admit physical interpretations and meanings.
Biography
Andrzej Cichocki is currently senior team leader and the head of the laboratory for Advanced Brain Signal Processing, at RIKEN Brain Science Institute (Japan).
Website : http://www.open.brain.riken.go.jp/~cia/
He is leading cutting-edge researches in the field of signal processing, and more specifically :
– Biomedical Signal Processing
– Blind Signal and Image Processing
– Inverse problems
– Neural Networks and Learning Algorithms
– High Speed Neural Computation
– Intelligent Control, Circuits and Systems Theory