Kernel-based data transformation model for nonlinear classification of symbolic data

Abstract

Symbolic data are usually composed of some categorical variables used to represent discrete entities in many real-world applications. Mining of symbolic data is more difficult than numerical data due to the lack of inherent geometric properties of this type of data. In this paper, we use two kinds of kernel learning methods to create a kernel estimation model and a non-linear classification algorithm for symbolic data. By using the kernel smoothing method, we construct a squared-error consistent probability estimator for symbolic data, followed by a new data transformation model proposed to embed symbolic data into Euclidean space. Based on the model, the inner product and distance measure between symbolic data objects are reformulated, allowing a new Support Vector Machine (SVM), called SVM-S, to be defined for non-linear classification on symbolic data using the Mercer kernel learning method. The experiment results show that SVM can be much more effective for symbolic data classification based on our proposed model and measures.Symbolic data, alternatively known as categorical data or nominal data, are widely used in real-world applications, where the attributes are represented by symbols, which are qualitative category of things [1]. Taking two attributes, named gender and height, respectively, for example, the former is usually represented by the category "male" or "female", while the latter can be with one of the categories from {"low", "medium", "high"}. Compared to numeric data, mining of symbolic data is a more challenging task due to the lack of inherent geometric characteristics [2-7]: for example, some important measures that have been successfully applied to numeric data, such as Euclidean distance, inner product and mean, are not well-defined for symbolic data [8].As an important tool in data mining, data classification, which assigns unlabeled samples to known classes by using supervised learning method, has been a subject of wide interest in categorical data mining, especially in the fields of business, finance, social sciences and health sciences. A number of methods have been developed to classify symbolic data, including decision trees (DT), Naive Bayes (NB) [9] and distance-based methods such as the k-nearest neighbors (KNN) and the prototype-based classifiers [10,11]. Since both DT and NB are typically based on the assumption that symbolic attributes are conditionally independent given the class attribute, they cannot identify the non-linear correlation between attributes, which has been validated to be useful in high-quality classification [12,13]. With an elaborate distance measure, it is possible to apply the traditional distance-based classifiers to non-linear categorical data classification; however, defining such a meaningful distance measure directly on symbolic data is currently a difficult problem due to the challenges discussed previously [8,14].Recently, kernel learning has been popular in efficiently learning the non-linear correlation between attributes and in non-linear data clas...