Douglas P. Hardin

A comprehensive evaluation of multicategory classification methods for microarray gene expression cancer diagnosis

MOTIVATIONnCancer diagnosis is one of the most important emerging clinical applications of gene expression microarray technology. We are seeking to develop a computer system for powerful and reliable cancer diagnostic model creation based on microarray data. To keep a realistic perspective on clinical applications we focus on multicategory diagnosis. To equip the system with the optimum combination of classifier, gene selection and cross-validation methods, we performed a systematic and comprehensive evaluation of several major algorithms for multicategory classification, several gene selection methods, multiple ensemble classifier methods and two cross-validation designs using 11 datasets spanning 74 diagnostic categories and 41 cancer types and 12 normal tissue types.nnnRESULTSnMulticategory support vector machines (MC-SVMs) are the most effective classifiers in performing accurate cancer diagnosis from gene expression data. The MC-SVM techniques by Crammer and Singer, Weston and Watkins and one-versus-rest were found to be the best methods in this domain. MC-SVMs outperform other popular machine learning algorithms, such as k-nearest neighbors, backpropagation and probabilistic neural networks, often to a remarkable degree. Gene selection techniques can significantly improve the classification performance of both MC-SVMs and other non-SVM learning algorithms. Ensemble classifiers do not generally improve performance of the best non-ensemble models. These results guided the construction of a software system GEMS (Gene Expression Model Selector) that automates high-quality model construction and enforces sound optimization and performance estimation procedures. This is the first such system to be informed by a rigorous comparative analysis of the available algorithms and datasets.nnnAVAILABILITYnThe software system GEMS is available for download from http://www.gems-system.org for non-commercial use.nnnCONTACTnalexander.statnikov@vanderbilt.edu.

Design of prefilters for discrete multiwavelet transforms

The pyramid algorithm for computing single wavelet transform coefficients is well known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. The authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be thought of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete-time signals. The authors then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms.

Construction of Orthogonal Wavelets Using Fractal Interpolation Functions

Fractal interpolation functions are used to construct a compactly supported continuous, orthogonal wavelet basis spanning

Recurrent iterated function systems

L^2 (mathbb{R})

Hidden variable fractal interpolation functions

. The wavelets share many of the properties normally associated with spline wavelets, in particular, they have linear phase.

Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets

Recurrent iterated function systems generalize iterated function systems as introduced by Barnsley and Demko [BD] in that a Markov chain (typically with some zeros in the transition probability matrix) is used to drive a system of mapswj:K →K,j=1, 2,⋯,N, whereK is a complete metric space. It is proved that under “average contractivity,” a convergence and ergodic theorem obtains, which extends the results of Barnsley and Elton [BE]. It is also proved that a Collage Theorem is true, which generalizes the main result of Barnsleyet al. [BEHL] and which broadens the class of images which can be encoded using iterated map techniques. The theory of fractal interpolation functions [B] is extended, and the fractal dimensions for certain attractors is derived, extending the technique of Hardin and Massopust [HM]. Applications to Julia set theory and to the study of the boundary of IFS attractors are presented.

Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets

Interpolation functions

Multiwavelet prefilters. II. Optimal orthogonal prefilters

f:[0,1] to mathbb{R}

An Exact Formula for the Measure Dimensions Associated with a Class of Piecewise Linear Maps

of the following nature are constructed. Given data [ left{ {left( {t_n ,x_n } right) in [0,1] times mathbb{R}:n = 0,1,2, cdots ,N} right}] with

Dispersion population models discrete in time and continuous in space

0 = t_0 < t_1 < cdots < t_N = 1