205,435 research outputs found
Evaluating Graph Signal Processing for Neuroimaging Through Classification and Dimensionality Reduction
Graph Signal Processing (GSP) is a promising framework to analyze
multi-dimensional neuroimaging datasets, while taking into account both the
spatial and functional dependencies between brain signals. In the present work,
we apply dimensionality reduction techniques based on graph representations of
the brain to decode brain activity from real and simulated fMRI datasets. We
introduce seven graphs obtained from a) geometric structure and/or b)
functional connectivity between brain areas at rest, and compare them when
performing dimension reduction for classification. We show that mixed graphs
using both a) and b) offer the best performance. We also show that graph
sampling methods perform better than classical dimension reduction including
Principal Component Analysis (PCA) and Independent Component Analysis (ICA).Comment: 5 pages, GlobalSIP 201
AM-FM Analysis of Structural and Functional Magnetic Resonance Images
This thesis proposes the application of multi-dimensional Amplitude-Modulation Frequency-Modulation (AM-FM) methods to magnetic resonance images (MRI). The basic goal is to provide a framework for exploring non-stationary characteristics of structural and functional MRI (sMRI and fMRI). First, we provide a comparison framework for the most popular AM-FM methods using different filterbank configurations that includes Gabor, Equirriple and multi-scale directional designs. We compare the performance and robustness to Gaussian noise using synthetic FM image examples. We show that the multi-dimensional quasi-local method (QLM) with an equiripple filterbank gave the best results in terms of instantaneous frequency (IF) estimation. We then apply the best performing AM-FM method to sMRI to compute the 3D IF features. We use a t-test on the IF magnitude for each voxel to find evidence of significant differences between healthy controls and patients diagnosed with schizophrenia (n=353) can be found in the IF. We also propose the use of the instantaneous phase (IP) as a new feature for analyzing fMRI images. Using principal component analysis and independent component analysis on the instantaneous phase from fMRI, we built spatial maps and identified brain regions that are biologically coherent with the task performed by the subject. This thesis provides the first application of AM-FM models to fMRI and sMRI
Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices
Inspired by several recent developments in regularization theory,
optimization, and signal processing, we present and analyze a numerical
approach to multi-penalty regularization in spaces of sparsely represented
functions. The sparsity prior is motivated by the largely expected
geometrical/structured features of high-dimensional data, which may not be
well-represented in the framework of typically more isotropic Hilbert spaces.
In this paper, we are particularly interested in regularizers which are able to
correctly model and separate the multiple components of additively mixed
signals. This situation is rather common as pure signals may be corrupted by
additive noise. To this end, we consider a regularization functional composed
by a data-fidelity term, where signal and noise are additively mixed, a
non-smooth and non-convex sparsity promoting term, and a penalty term to model
the noise. We propose and analyze the convergence of an iterative alternating
algorithm based on simple iterative thresholding steps to perform the
minimization of the functional. By means of this algorithm, we explore the
effect of choosing different regularization parameters and penalization norms
in terms of the quality of recovering the pure signal and separating it from
additive noise. For a given fixed noise level numerical experiments confirm a
significant improvement in performance compared to standard one-parameter
regularization methods. By using high-dimensional data analysis methods such as
Principal Component Analysis, we are able to show the correct geometrical
clustering of regularized solutions around the expected solution. Eventually,
for the compressive sensing problems considered in our experiments we provide a
guideline for a choice of regularization norms and parameters.Comment: 32 page
A Federated Data Fusion-Based Prognostic Model for Applications with Multi-Stream Incomplete Signals
Most prognostic methods require a decent amount of data for model training.
In reality, however, the amount of historical data owned by a single
organization might be small or not large enough to train a reliable prognostic
model. To address this challenge, this article proposes a federated prognostic
model that allows multiple users to jointly construct a failure time prediction
model using their multi-stream, high-dimensional, and incomplete data while
keeping each user's data local and confidential. The prognostic model first
employs multivariate functional principal component analysis to fuse the
multi-stream degradation signals. Then, the fused features coupled with the
times-to-failure are utilized to build a (log)-location-scale regression model
for failure prediction. To estimate parameters using distributed datasets and
keep the data privacy of all participants, we propose a new federated algorithm
for feature extraction. Numerical studies indicate that the performance of the
proposed model is the same as that of classic non-federated prognostic models
and is better than that of the models constructed by each user itself
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Representation of Functional Data in Neural Networks
Functional Data Analysis (FDA) is an extension of traditional data analysis
to functional data, for example spectra, temporal series, spatio-temporal
images, gesture recognition data, etc. Functional data are rarely known in
practice; usually a regular or irregular sampling is known. For this reason,
some processing is needed in order to benefit from the smooth character of
functional data in the analysis methods. This paper shows how to extend the
Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models
to functional data inputs, in particular when the latter are known through
lists of input-output pairs. Various possibilities for functional processing
are discussed, including the projection on smooth bases, Functional Principal
Component Analysis, functional centering and reduction, and the use of
differential operators. It is shown how to incorporate these functional
processing into the RBFN and MLP models. The functional approach is illustrated
on a benchmark of spectrometric data analysis.Comment: Also available online from:
http://www.sciencedirect.com/science/journal/0925231
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