Using Non-Additive Measure for Optimization-Based Nonlinear Classification

Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2 – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are a relatively small number of training cases available (). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered

A Surface-based Approach for Classification of 3D Neuroanatomic Structures

We present a new framework for 3D surface object classification that combines a powerful shape description method with suitable pattern classification techniques. Spherical harmonic parameterization and normalization techniques are used to describe a surface shape and derive a dual high dimensional landmark representation. A point distribution model is applied to reduce the dimensionality. Fisher\u27s linear discriminants and support vector machines are used for classification. Several feature selection schemes are proposed for learning better classifiers. After showing the effectiveness of this framework using simulated shape data, we apply it to real hippocampal data in schizophrenia and perform extensive experimental studies by examining different combinations of techniques. We achieve best leave-one-out cross-validation accuracies of 93% (whole set, N=56) and 90% (right-handed males, N=39), respectively, which are competitive with the best results in previous studies using different techniques on similar types of data. Furthermore, to help medical diagnosis in practice, we employ a threshold-free receiver operating characteristic (ROC) approach as an alternative evaluation of classification results as well as propose a new method for visualizing discriminative patterns

RandomBoost: Simplified Multi-class Boosting through Randomization

We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.Comment: 15 page