19,113 research outputs found
A survey of kernel and spectral methods for clustering
Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved
A Collection of Challenging Optimization Problems in Science, Engineering and Economics
Function optimization and finding simultaneous solutions of a system of
nonlinear equations (SNE) are two closely related and important optimization
problems. However, unlike in the case of function optimization in which one is
required to find the global minimum and sometimes local minima, a database of
challenging SNEs where one is required to find stationary points (extrama and
saddle points) is not readily available. In this article, we initiate building
such a database of important SNE (which also includes related function
optimization problems), arising from Science, Engineering and Economics. After
providing a short review of the most commonly used mathematical and
computational approaches to find solutions of such systems, we provide a
preliminary list of challenging problems by writing the Mathematical
formulation down, briefly explaning the origin and importance of the problem
and giving a short account on the currently known results, for each of the
problems. We anticipate that this database will not only help benchmarking
novel numerical methods for solving SNEs and function optimization problems but
also will help advancing the corresponding research areas.Comment: Accepted as an invited contribution to the special session on
Evolutionary Computation for Nonlinear Equation Systems at the 2015 IEEE
Congress on Evolutionary Computation (at Sendai International Center, Sendai,
Japan, from 25th to 28th May, 2015.
A Framework to Control Functional Connectivity in the Human Brain
In this paper, we propose a framework to control brain-wide functional
connectivity by selectively acting on the brain's structure and parameters.
Functional connectivity, which measures the degree of correlation between
neural activities in different brain regions, can be used to distinguish
between healthy and certain diseased brain dynamics and, possibly, as a control
parameter to restore healthy functions. In this work, we use a collection of
interconnected Kuramoto oscillators to model oscillatory neural activity, and
show that functional connectivity is essentially regulated by the degree of
synchronization between different clusters of oscillators. Then, we propose a
minimally invasive method to correct the oscillators' interconnections and
frequencies to enforce arbitrary and stable synchronization patterns among the
oscillators and, consequently, a desired pattern of functional connectivity.
Additionally, we show that our synchronization-based framework is robust to
parameter mismatches and numerical inaccuracies, and validate it using a
realistic neurovascular model to simulate neural activity and functional
connectivity in the human brain.Comment: To appear in the proceedings of the 58th IEEE Conference on Decision
and Contro
Optimal projection of observations in a Bayesian setting
Optimal dimensionality reduction methods are proposed for the Bayesian
inference of a Gaussian linear model with additive noise in presence of
overabundant data. Three different optimal projections of the observations are
proposed based on information theory: the projection that minimizes the
Kullback-Leibler divergence between the posterior distributions of the original
and the projected models, the one that minimizes the expected Kullback-Leibler
divergence between the same distributions, and the one that maximizes the
mutual information between the parameter of interest and the projected
observations. The first two optimization problems are formulated as the
determination of an optimal subspace and therefore the solution is computed
using Riemannian optimization algorithms on the Grassmann manifold. Regarding
the maximization of the mutual information, it is shown that there exists an
optimal subspace that minimizes the entropy of the posterior distribution of
the reduced model; a basis of the subspace can be computed as the solution to a
generalized eigenvalue problem; an a priori error estimate on the mutual
information is available for this particular solution; and that the
dimensionality of the subspace to exactly conserve the mutual information
between the input and the output of the models is less than the number of
parameters to be inferred. Numerical applications to linear and nonlinear
models are used to assess the efficiency of the proposed approaches, and to
highlight their advantages compared to standard approaches based on the
principal component analysis of the observations
An Application of Clustering Analysis to International Private Indebtedness
This paper presents a procedure for clustering analysis that combines Kohoneâs Self organizing Feature Map (SOFM) and statistical schemes. The idea is to cluster the data in two stages: run SOFM and then minimize the segmentation dispersion. The advantages of proposed procedure will be illustrated through a synthetic experiment and a real macroeconomic problem. The procedure is then used to explore the relationship between private indebtedness and some macroeconomic variables commonly used to measure macroeconomic performance. The experiences of thirty-nine countries in the early nineties are analyzed. The procedure outperformed others clustering techniques in the job of identifying consistent groups of countries from the economic and statistical viewpoints. It found out similarities in different countries concerning their respective levels of private indebtedness when added to well accepted parameters to measure macroeconomic performance.Vector quantization, Clustering, Self-Organizing Feature Map,Macroeconomic Performance, Private Indebtedness.
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