Intra-feature metric matrices for nominal data pattern classification

In machine learning problems, similarity measures (e.g. using metrics) are widely utilized in nearest neighbor, support vector machines and neural network algorithms. However, when there is one or more non-ordinal data in feature vector, metric evaluation is difficult. Although non-metric methods such as decision trees with ID3, C4.5 or CART can be employed to process such problems, many other elegant approaches cannot be applied due to the lack of numerical information. We propose constructing minimum error based intra-feature metric matrices to provide distance measure for nominal data so that metric or kernel algorithms can be used. For each nominal attribute, a matrix is first initialized to constant values with zero diagonal and then the off diagonal values are tuned based on minimizing the training error. The optimized matrices give the distance information between nominal values and thus can be referenced in various metric algorithms. Experimental results with classical Boolean nominal metric and C4.5 on various datasets show that the proposed approach gives superior performance.