A Topological Approach of Principal Component Analysis

Large datasets are increasingly widespread in many disciplines. The exponential growth of data requires the development more analysis methods order to process information efficiently. In better visualize data, such as Principal Component Analysis (PCA) and MultiDimensional Scaling (MDS) allow extract a low-dimensional structure from high-dimensional set. proposed approach, called Topological (TPCA), is multidimensional descriptive method witch studies homogeneous set continuous variables defined on same individuals. It topological that consists comparing classifying proximity measures among some most widely used for data. Proximity play an important role areas analysis, results strongly depend measure chosen. So, existing measures, which one useful? Are they all equivalent? How identify appropriate analyze correlation quantitative variables. TPCA proposes adjacency matrix associated unknown according under consideration, then analyzes visualizes, with graphic representations, relationship relating to, well known PCA problem. Its uses concept neighborhood graphs compares can be more-or-less equivalent equivalence criterion between two statistically tested considered. An example real illustrates approach.