Continuous significant linear dimensionality: Geometric interpretation and statistical characteristics
A continuous measure of the degree of mutual linear independence between the vectors of a given dataset, continuous significant dimensionality (CSD), was introduced in a previous paper. In this report a simple and clear geometric interpretation of the CSD formula is determined, which has allowed to describe a parametric class of such measures and present the conventional linear dimensionality as a limiting case of that class. Two additional methods for measuring CSD are developed and their properties are investigated both theoretically and based on computational experiments. A special attention is devoted to measuring CSD of datasets with different levels of noise. An efficient method for eliminating the impact of such noise on the CSD estimate is developed. It is demonstrated that the three methods for CSD measurement have different statistical characteristics and the scopes of their practical application are outlined.
principal component analysis correlation analysis waveform set