Evolutionary Clustering Algorithm with Knowledge-Based Evaluation for Fuzzy Cluster Analysis of Gene Expression Profiles

Clustering method, which groups thousands of genes by their similarities of expression levels, has been used for identifying unknown functions of genes. Fuzzy clustering method that is one category of clustering assigns one sample to multiple groups according to their membership degrees. It is more appropriate than hard clustering algorithms for analyzing gene expression profiles since single gene might involve multiple genetic functions. However, general clustering methods have problems that they are sensitive to initialization and can be trapped into local optima. To solve the problems, we propose an evolutionary fuzzy clustering algorithm with knowledge-based evaluation. It uses a genetic algorithm for clustering and prior knowledge of data for evaluation. Yeast cell-cycle dataset has been used for experiments to show the usefulness of the proposed method. 1 Evolutionary Fuzzy Clustering with Knowledge-Based Evaluation General clustering algorithms have common problems that they are very sensitive to initial values and they can be trapped by local optima since their processes are supposed to minimize objective function [1]. Besides, there is a problem of evaluating cluster results. Since gene expression profiles vary depending on their characteristics and environments that they were collected, it is not appropriate to evaluate them with the same criteria. We propose an evolutionary fuzzy clustering and knowledge-based evaluation method to solve the problems. GA (genetic algorithm) that is an efficient method to solve optimization problem is applied for the evolutionary fuzzy clustering method. There have been many publications related to evolutionary computation for clustering. Maulik and Bandyopadhyay tried to minimize the distances between the data in the same clusters and cluster centers [1], and Hall used GA to minimize objective function value of the hard and fuzzy c-means algorithms. However, they fixed the number of clusters and used GA only for the minimization of objective function. We have encoded one cluster partition of variable number of clusters as one chromosome and formed various cluster partitions. Evolutionary Clustering Algorithm with Knowledge-Based Evaluation 641 The proposed method is divided into two parts: an evolutionary clustering part, which searches optimal cluster partition using GA, and a knowledge-based evaluation part, which obtains the optimal α -cuts from several datasets for Bayesian validation (BV) method. Fuzzy c-means algorithm known as the most widely used fuzzy clustering method is used for clustering [2]. For knowledge-based evaluation, we have used BV and decision tree (DT) rule to decide the optimal α -cut value. Original BV [3] evaluates cluster partition with the same α -cuts for all datasets, but it cannot evaluate the cluster results correctly since each dataset has different distribution and they are extracted from different environments. We have obtained α -cut value for each dataset using the DT rule. First, N gene expression profiles are clustered using the fuzzy c-means algorithm, and the results are evaluated by BV. Subsequently, the optimal α -cut for each dataset is decided, and they are used for the labels of DT training data. Rule production process trains DT, and produces rules. As Fig. 1 illustrates, the attributes of DT training data are produced using membership matrices that are the fuzzy clustering results of each dataset. Incrementing the membership degree value from 0.0 to 1.0 with the difference of 0.1, attributes are divided into 10 sections. Each section counts the frequency of samples and calculates the attribute by dividing the frequency by the total number of samples. These attributes calculated are A1~A10.