Development Of An Information Retrieval System Using Tree-structured Clustering
[FRSC Benue State]

2.6    Mixed Clustering
Clustering algorithms are designed for either categorical data or numeric data. However, in the real world, a majority of datasets are described by a combination of continuous and categorical features. A general method is to transform one data type to another. In most cases, nominal attributes are encoded by simple matching or binarymapping, and then clustering is performed on the new-computed numeric proximity. Binary encoding transforms each categorical attribute to a set of binary attributes and then encodes a categorical value to this set of binary values.
Simple matching generates distance measurement in such a way that yields a difference of zero when comparing two identical categorical values, and a difference of one while comparing two distinct values. However, the coding methods have the disadvantages of losing information derivable from the ordering of different values, losing the structure of categorical value with different levels of similarity, requiring more space and time when the domain of the categorical attribute is large, ignoring the context of a pair of values, e.g., the co- occurrence with other attributes, and giving different weight to the attributes according to the number of different values they may take. Moreover, if quantitative and binary attributes are included in the same index, these procedures will generally give the latter excessive weight.
An alternative approach is to discrete numeric values and then apply symbolic clustering algorithms. The discretization process often loses the important information especially the relative difference of two values for numeric features. In addition, it causes boundary problem when two close values near the discretization boundary may be assigned to two different ranges. Another difficult problem is to estimate the optimal intervals during discretization.
Huang (1998) extended k-modes to mixed datasets and developed k-prototype algorithm. The distances of two types of features are separately calculated. The numerical distances are measured by Euclidean distances, while the categorical distances are measured by simple matching. The centers of categorical attributes are defined as the modes in the cluster. (Ahmad and Dey, 2007) proposed a fuzzy prototype k-means algorithm. Similar to k-prototype,the cost function is made up of two components. The difference is that the categorical distances are measured by the co-occurrence of two attributes and the categorical cluster centers are the lists of values in every attribute with their frequencies in the cluster.