Abstract The inverse square root of a covariance matrix is often desirable for performing data whitening in the process applying many common multivariate analysis methods. Direct calculation not available when either singular or nearly singular, as occurs high dimensions. We develop new methods, which we broadly call polynomial , to construct low-degree empirical has similar properties true (sh...

We propose a new method of discriminant analysis, called High Dimensional Discriminant Analysis (HHDA). Our approach is based on the assumption that high dimensional data live in different subspaces with low dimensionality. Thus, HDDA reduces the dimension for each class independently and regularizes class conditional covariance matrices in order to adapt the Gaussian framework to high dimensio...

Data mining applications place special requirements on clustering algorithms including: the ability to nd clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisses each of these require...