LINEAR RELATION-BASED TRANSFORMATION FOR DETECTING LINEAR PATTERNS

Linear relation-based transformation method transforms the data set from positions in the Euclidean space to a relationship based space. In the original Euclidean space, proximity of data points indicates similarity between data elements, while proximity of data points in the linear relationship based space indicates similarity of relationship among variables. Clusters in the relationship based space indicate a variety of relations among variables. These clusters can then guide model building in a more effective and meaningful way. Statistical properties of this transformation and related problems are discussed in this paper. A simulation study is presented to compare this new method with LGA [1], MCLUST [2], MIXREG [3] and MLC [4]. Theorical and numerical comparisons of LRC are made with the other methods mentioned above.