| Summary: | 碩士 === 國立臺灣大學 === 工業工程學研究所 === 93 === The unsupervised classification methods, Clustering analysis and Factor analysis, intend to find meaningful structures existing in the observed attributes. These structures are usually expressed by grouping of attributes based on the similarities, or relationships among the attributes. However, the disadvantage of Factor analysis lies on insufficiency of full-rank in numerical computation. For example, in microarray data analysis, expressions of 10,000~20,000 genes are collected for each array. The number of genes is usually far larger than number of microarray. Clustering analysis, on the other hand, can help handle with a vast amount of attributes with few samples. There are some drawbacks of Clustering analysis, including of misapplying the correlation coefficient and the difficulties of evaluating the cluster quality as well as the determination of the cluster number.
In this research, we first discuss characterization of interrelationships among attributes, and then develop clustering methods suitable for grouping interrelated attributes. The “R2 with PCA” method lays more stress on the linear relationships between two clusters, while the “Variance explanation” method focuses not only on interrelations among attributes but also on attributes variations. This research also proposes the statistics for the evaluation of the cluster quality, and these statistics take into considerations the interrelationships among clusters and the variances explained of clusters. Finally, we apply these novel methods to two cases; one is 19 blood tests of 24 human; and the other is Down syndrome microarray data.
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