2019/07/24 by Guihong Wan, Wan, Guihong, Crystal Maung +3
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Spectroscopy and Chemometric Analyses #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1907.11094
arxiv created 2019/07/24 · openalex publication_date 2019/07/24 · arxiv updated 2019/07/26 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, This can be used, for example, to solve the approximate nearest neighbor problem. We use random variables to model the inherent uncertainty in such approximations, and apply the Maximum Entropy Method to infer the underlying probability distribution. We propose using the expected values of distances between these random variables as improved estimates of the distance. We show by analysis and experimentally that in most cases results obtained by our method are more accurate than what is obtained by the classical approach. This improves the accuracy of a classical technique that have been used with little change for over 100 years.