Search results for "matrix decomposition"

2020

Recommender systems are information software that retrieves relevant items for users from massive sources of data. The variational autoencoder (VAE) has proven to be a promising approach for recommendation systems, as it can explore high-level user-item relations and extract contingencies from the input effectively. However, the previous variants of VAE have so far seen limited application to domain-specific recommendations that require additional side information. Hence, The Ensemble Variational Autoencoder framework for recommendations (EnsVAE) is proposed. This architecture specifies a procedure to transform sub-recommenders’ predicted utility matrix into interest probabilities that allo…

Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate va…

2021

Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of ‘instantaneous’ effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index…

An overview of incremental feature extraction methods based on linear subspaces

2018

Abstract With the massive explosion of machine learning in our day-to-day life, incremental and adaptive learning has become a major topic, crucial to keep up-to-date and improve classification models and their corresponding feature extraction processes. This paper presents a categorized overview of incremental feature extraction based on linear subspace methods which aim at incorporating new information to the already acquired knowledge without accessing previous data. Specifically, this paper focuses on those linear dimensionality reduction methods with orthogonal matrix constraints based on global loss function, due to the extensive use of their batch approaches versus other linear alter…

Wordnet and semidiscrete decomposition for sub-symbolic representation of words

2009

A methodology for sub-symbolic semantic encoding of words is presented. The methodology uses the standard, semantically highly-structured WordNet lexical database and the SemiDiscrete matrix Decomposition to obtain a vector representation with low memory requirements in a semantic n-space. The application of the proposed algorithm over all the WordNet words would lead to a useful tool for the sub-symbolic processing of texts.

A Novel Semi-Supervised Methodology for Extracting Tumor Type-Specific MRS Sources in Human Brain Data

2013

Background: The clinical investigation of human brain tumors often starts with a non-invasive imaging study, providing \ud information about the tumor extent and location, but little insight into the biochemistry of the analyzed tissue. Magnetic \ud Resonance Spectroscopy can complement imaging by supplying a metabolic fingerprint of the tissue. This study analyses \ud single-voxel magnetic resonance spectra, which represent signal information in the frequency domain. Given that a single \ud voxel may contain a heterogeneous mix of tissues, signal source identification is a relevant challenge for the problem of\ud tumor type classification from the spectroscopic signal.\ud Methodology/Princ…

Unmixing of human skin optical reflectance maps by Non-negative Matrix Factorization algorithm

2013

International audience; We present in this paper the decomposition of human skin absorption spectra with a Non-negative Matrix Factorization method. In doing so, we are able to quantify the relative proportion of the main chromophores present in the epidermis and the dermis. We present experimental results showing that we obtain a good estimate of melanin and hemoglobin concentrations. Our approach has been validated by analyzing the human skin absorption spectra in areas of healthy skin and areas affected by melasma on eight patients.

Analysis of human skin hyper-spectral images by non-negative matrix factorization

2011

International audience; This article presents the use of Non-negative Matrix Factorization, a blind source separation algorithm, for the decomposition of human skin absorption spectra in its main pigments: melanin and hemoglobin. The evaluated spectra come from a Hyper-Spectral Image, which is the result of the processing of a Multi-Spectral Image by a neural network-based algorithm. The implemented source separation algorithm is based on a multiplicative coeffi cient upload. The goal is to represent a given spectrum as the weighted sum of two spectral components. The resulting weighted coefficients are used to quantify melanin and hemoglobin content in the given spectra. Results present a …

A Linear Cost Algorithm to Compute the Discrete Gabor Transform

2010

In this paper, we propose an alternative efficient method to calculate the Gabor coefficients of a signal given a synthesis window with a support of size much lesser than the length of the signal. The algorithm uses the canonical dual of the window (which does not need to be calculated beforehand) and achieves a computational cost that is linear with the signal length in both analysis and synthesis. This is done by exploiting the block structure of the matrices and using an ad hoc Cholesky decomposition of the Gabor frame matrix.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations

2021

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve …

Locally optimal invariant detector for testing equality of two power spectral densities

2018

This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…