Search results for "matrix decomposition"
showing 10 items of 43 documents
Partial Information Decomposition in the Frequency Domain: Application to Control Mechanisms of Heart Rate Variability at Rest and During Postural St…
2020
We exploit a recently proposed framework for assessing causal influences in the frequency domain to construct the partial information decomposition (PID) for informational circuits of three variables, thus obtaining the spectral decomposition of redundancy, synergy and unique information. The approach is applied to heart period (HP), systolic pressure (SP) and respiration (RESP) variability series measured in healthy subjects in baseline and head up tilt conditions. Integrating the informational quantities in the respiratory band, the total influence from RESP to HP does not change in the two conditions. However, we find that in baseline RESP causes HP mostly through the direct pathway desc…
Scalable Dense Factorizations for Heterogeneous Computational Clusters
2008
This paper discusses the design and the implementation of the LU factorization routines included in the Heterogeneous ScaLAPACK library, which is built on top of ScaLAPACK. These routines are used in the factorization and solution of a dense system of linear equations. They are implemented using optimized PBLAS, BLACS and BLAS libraries for heterogeneous computational clusters. We present the details of the implementation as well as performance results on a heterogeneous computing cluster.
TSVD as a Statistical Estimator in the Latent Semantic Analysis Paradigm
2015
The aim of this paper is to present a new point of view that makes it possible to give a statistical interpretation of the traditional latent semantic analysis (LSA) paradigm based on the truncated singular value decomposition (TSVD) technique. We show how the TSVD can be interpreted as a statistical estimator derived from the LSA co-occurrence relationship matrix by mapping probability distributions on Riemanian manifolds. Besides, the quality of the estimator model can be expressed by introducing a figure of merit arising from the Solomonoff approach. This figure of merit takes into account both the adherence to the sample data and the simplicity of the model. In our model, the simplicity…
Efficient Analysis and Synthesis Using a New Factorization of the Gabor Frame Matrix
2018
In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is …
Robust subspace DOA estimation for wireless communications
2002
This paper is concerned with array signal processing in non-Gaussian noise typical in urban and indoor radio channels. Robust and fully nonparametric high resolution algorithms for direction of arrival (DOA) estimation are presented. The algorithms are based on multivariate spatial sign and rank concepts. The performance of the algorithms is studied using simulations. The results show that almost optimal performance is obtained in wide variety of noise conditions.
cuBool: Bit-Parallel Boolean Matrix Factorization on CUDA-Enabled Accelerators
2018
Boolean Matrix Factorization (BMF) is a commonly used technique in the field of unsupervised data analytics. The goal is to decompose a ground truth matrix C into a product of two matrices A and $B$ being either an exact or approximate rank k factorization of C. Both exact and approximate factorization are time-consuming tasks due to their combinatorial complexity. In this paper, we introduce a massively parallel implementation of BMF - namely cuBool - in order to significantly speed up factorization of huge Boolean matrices. Our approach is based on alternately adjusting rows and columns of A and B using thousands of lightweight CUDA threads. The massively parallel manipulation of entries …
On Association Models Defined over Independence Graphs
1998
Conditions on joint distributions are given under which two variables will be conditionally associated whenever an independence graph does not imply a corresponding conditional independence statement. To this end the notions of parametric cancellation, of stable paths and of quasi-linear models are discussed in some detail.
Non-negative matrix factorization Vs. FastICA on mismatch negativity of children
2009
In this presentation two event-related potentials, mismatch negativity (MMN) and P3a, are extracted from EEG by non-negative matrix factorization (NMF) simultaneously. Typically MMN recordings show a mixture of MMN, P3a, and responses to repeated standard stimuli. NMF may release the source independence assumption and data length limitations required by Fast independent component analysis (FastICA). Thus, in theory NMF could reach better separation of the responses. In the current experiment MMN was elicited by auditory duration deviations in 102 children. NMF was performed on the time-frequency representation of the raw data to estimate sources. Support to Absence Ratio (SAR) of the MMN co…
Identical fits of nonnegative matrix/tensor factorization may correspond to different extracted event-related potentials
2010
Nonnegative Matrix / Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits of two algorithms are identical, it is necessary to examine whether the desired components extracted by them are identical too. In order to verify this doubt, we performed NMF and NTF on the same dataset of an auditory event-related potentials (ERPs), and found that the identical fits of NMF and …
Comparison of frequency domain measures based on spectral decomposition for spontaneous baroreflex sensitivity assessment after Acute Myocardial Infa…
2021
Abstract The objective of this study is to present a new method to assess in the frequency domain the directed interactions between the spontaneous variability of systolic arterial pressure (SAP) and heart period (HP) from their linear model representation, and to apply it for studying the baroreflex control of arterial pressure in healthy physiological states and after acute myocardial infarction (AMI). The method is based on pole decomposition of the model transfer function and on the following evaluation of causal measures of coupling and gain from the poles associated to low frequency (0.04−0.15 Hz) oscillatory components. It is compared with traditional non-causal approaches for the sp…