Dimensionality's Blessing: Clustering Images by Underlying Distribution

Wen-Yan Lin, Siying Liu, Jian-Huang Lai, Yasuyuki Matsushita; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018, pp. 5784-5793

Many high dimensional vector distances tend to a constant. This is typically considered a negative “contrast-loss” 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.