k-Means Clustering on Two-Level Memory Systems

In recent work we quantified the anticipated performance boost when a sorting algorithm is modified to leverage user-addressable "near-memory," which we call scratchpad. This architectural feature is expected in the Intel Knight's Landing processors that will be used in DOE's next large-scale supercomputer. This paper expands our analytical study of the scratchpad to consider k-means clustering, a classical data-analysis technique that is ubiquitous in the literature and in practice. We present new theoretical results using the model introduced in [13], which measures memory transfers and assumes that computations are memory-bound. Our theoretical results indicate that scratchpad-aware versions of k-means clustering can expect performance boosts for high-dimensional instances with relatively few cluster centers. These constraints may limit the practical impact of scratch-pad for k-means acceleration, so we discuss their origins and practical implications. We corroborate our theory with experimental runs on a system instrumented to mimic one with scratchpad memory. We also contribute a semi-formalization of the computational properties that are necessary and sufficient to predict a performance boost from scratchpad-aware variants of algorithms. We have observed and studied these properties in the context of sorting, and now clustering. We conclude with some thoughts on the application of these properties to new areas. Specifically, we believe that dense linear algebra has similar properties to k-means, while sparse linear algebra and FFT computations are more similar to sorting. The sparse operations are more common in scientific computing, so we expect scratchpad to have significant impact in that area.