We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy (for absolutely monotone interactions) for codes with given maximum distance and cardinality. The distance distributions of codes that attain the bounds are found in terms of the parameters of Levenshtein-type quadrature formulas. Necessary and sufficient conditions for the optimality of our bounds are derived. Further, we obtain upper bounds on the energy of codes of fixed minimum and maximum distances and cardinality.

We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distance, and universal lower bounds on the potential energy (for absolutely monotone interactions) for codes with given maximum distance and fixed cardinality. In particular, we extend the framework of Levenshtein bounds for such codes.

Polynomial Support Vector Machine models of degree d are linear functions in a feature space of monomials of at most degree d. However, the actual representation is stored in the form of support vectors and Lagrange multipliers that is unsuitable for

MOTIVATION: Cancer 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. RESULTS: Multicategory 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. AVAILABILITY: The software system GEMS is available for download from http://www.gems-system.org for non-commercial use. CONTACT: [email protected].

OBJECTIVE Finding the best scientific evidence that applies to a patient problem is becoming exceedingly difficult due to the exponential growth of medical publications. The objective of this study was to apply machine learning techniques to automatically identify high-quality, content-specific articles for one time period in internal medicine and compare their performance with previous Boolean-based PubMed clinical query filters of Haynes et al. DESIGN The selection criteria of the ACP Journal Club for articles in internal medicine were the basis for identifying high-quality articles in the areas of etiology, prognosis, diagnosis, and treatment. Naive Bayes, a specialized AdaBoost algorithm, and linear and polynomial support vector machines were applied to identify these articles. MEASUREMENTS The machine learning models were compared in each category with each other and with the clinical query filters using area under the receiver operating characteristic curves, 11-point average recall precision, and a sensitivity/specificity match method. RESULTS In most categories, the data-induced models have better or comparable sensitivity, specificity, and precision than the clinical query filters. The polynomial support vector machine models perform the best among all learning methods in ranking the articles as evaluated by area under the receiver operating curve and 11-point average recall precision. CONCLUSION This research shows that, using machine learning methods, it is possible to automatically build models for retrieving high-quality, content-specific articles using inclusion or citation by the ACP Journal Club as a gold standard in a given time period in internal medicine that perform better than the 1994 PubMed clinical query filters.

Most prevalent techniques in Support Vector Machine (SVM) feature selection are based on the intuition that the weights of features that are close to zero are not required for optimal classification. In this paper we show that indeed, in the sample limit, the irrelevant variables (in a theoretical and optimal sense) will be given zero weight by a linear SVM, both in the soft and the hard margin case. However, SVM-based methods have certain theoretical disadvantages too. We present examples where the linear SVM may assign zero weights to strongly relevant variables (i.e., variables required for optimal estimation of the distribution of the target variable) and where weakly relevant features (i.e., features that are superfluous for optimal feature selection given other features) may get non-zero weights. We contrast and theoretically compare with Markov-Blanket based feature selection algorithms that do not have such disadvantages in a broad class of distributions and could also be used for causal discovery.

This paper proposes a method to obtain optimal 2nd-order approximation preserving prefilters for a given orthogonal unbalanced multiwavelet basis. This procedure uses the prefilter construction introduced in Hardin et al., (1998). The prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. Using the DGHM multiwavelet with the obtained optimal prefilter, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition.

Prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets. In this paper, we develop two methods to obtain optimal second-order approximation preserving prefilters for a given orthogonal multiwavelet basis. These procedures use the prefilter construction introduced in part I of this paper. The first prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. The second one is achieved by minimizing the energy compaction ratio (ECR) of the wavelet coefficients for an experimentally determined average input spectrum. We use both methods to find prefilters for the cases of the DGHM and Chui-Lian (CL) multiwavelets. We then compare experimental results using these filters in an image compression scheme. Additionally, using the DGHM multiwavelet with the optimal prefilters from the first scheme, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition.

We study why prefiltering is necessary for discrete multiwavelet transforms. We propose a method to generate prefilters given a set of multiwavelet filterbanks, where they are called good prefilters.