A semi-supervised regression model for mixed numerical and categorical variables

In this paper, we develop a semi-supervised regression algorithm to analyze data sets which contain both categorical and numerical attributes. This algorithm partitions the data sets into several clusters and at the same time fits a multivariate regression model to each cluster. This framework allows one to incorporate both multivariate regression models for numerical variables (supervised learning methods) and k-modes clustering algorithms for categorical variables (unsupervised learning methods). The estimates of regression models and k-modes parameters can be obtained simultaneously by minimizing a function which is the weighted sum of the least squares errors in the multivariate regression models and the dissimilarity measures among the categorical variables. Both synthetic and real data sets are presented to demonstrate the effectiveness of the proposed method.