Dimensionality's Blessing: Clustering Images by Underlying Distribution
This addresses the challenge of clustering unlabeled high-dimensional data for machine learning applications, offering a novel approach with potential broad impact.
The paper tackles the problem of clustering high-dimensional data by reinterpreting the 'contrast-loss' phenomenon as a blessing, showing that instances concentrate on a hyper-shell for separability, and results in an algorithm that creates clean clusters, estimates cluster numbers, and handles outliers effectively.
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.