Dimensionality's blessing: Clustering images by underlying distribution

• Main Authors: LIN, Wen-yan, LAI, Jian-Huang, LIU, Siying, MATSUSHITA, Yasuyuki
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Computer and Systems Architecture; Graphics and Human Computer Interfaces
• Online Access: https://ink.library.smu.edu.sg/sis_research/4810; https://ink.library.smu.edu.sg/context/sis_research/article/5813/viewcontent/Lin_Dimensionalitys_Blessing_Clustering_CVPR_2018_paper.pdf
• Institution: Singapore Management University

Many high dimensional vector distances tend to a constant. This is typically considered a negative “contrastloss” phenomenon that hinders clustering and other machine learning techniques. We reinterpret “contrast-loss” as a blessing. Re-deriving “contrast-loss” using the law of large numbers, we show it results in a distribution’s instances concentrating on a thin “hyper-shell”. The hollow center means apparently chaotically overlapping distributions are actually intrinsically separable. We use this to develop distribution-clustering, an elegant algorithm for grouping of data points by their (unknown) underlying distribution. Distribution-clustering, creates notably clean clusters from raw unlabeled data, estimates the number of clusters for itself and is inherently robust to “outliers” which form their own clusters. This enables trawling for patterns in unorganized data and may be the key to enabling machine intelligence.