Formation-Controlled Dimensionality Reduction

Dimensionality reduction represents the process of extracting low dimensional structure from high dimensional data. High dimensional data include multimedia databases, gene expression microarrays, and financial time series, for example. In order to deal with such real-world data properly, it is better to reduce its dimensionality to avoid undesired properties of high dimensions such as the curse of dimensionality [14, 11]. As a result, classification, visualization, and compression of data can be expedited, for example [14]. In many problems, it is presumed that the dimensionality of the measured data is only artificially high; the measured data are high-dimensional but data nearly have a lower-dimensional structure, since they are multiple, indirect measurements of an underlying factors, which typically cannot be directly calibrated [4].