On eigenfunction approach to data mining: outlier detection in high-dimensional data sets

We present two methods, one based on eigenvalue analysis, and the other, a modified version of singular value decomposition (SVD) called pseudo-SVD, for mining outliers in high-dimensional data sets. The eigenvalue analysis approach examines the spatial relationship among the column vectors of object-attribute matrix to obtain an insight into the degree of inconsistency in a cluster of data. The pseudo-SVD method, in which the singular values are allowed to have a sign, looks at the direction of vectors in the object-attribute matrix and based on the degree of their orthogonality detects the outliers. The pseudo-SVD algorithm is formulated as an optimisation problem for clustering the data on the basis of their angular inclination. A framework for this approach is formulated and further research directions are discussed.