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The Word Movers Distance (WMD) measures the semantic dissimilarity betweentwo text documents by computing the cost of optimally moving all words of asource/query document to the most similar words of a target document. ComputingWMD between two documents is costly because it requires solving an$O(V^3log(V))$ optimization problem where $V$ is the number of unique words inthe document. Fortunately, WMD can be framed as an Earth Mover's Distance (EMD)for which the algorithmic complexity can be reduced to $O(V^2)$ by adding anentropy penalty to the optimization problem and solving it using theSinkhorn-Knopp algorithm. Additionally, the computation can be made highlyparallel by adopting a batching approach, i.e., computing the WMD of a singlequery document against multiple target documents at once.  Sinkhorn WMD is a key kernel used in many ML/NLP applications. and usuallygets implemented in Python. However, a straightforward Python implementationmay leave significant performance on the table even though it may internallycall optimized C++ BLAS routines. We present a new sparse {P}arallel{A}lgorithm for {S}inkhorn-Knopp {W}ord-movers {D}istance to compute thesemantic distance of one document to many other documents by adopting the$O(V^2)$ EMD algorithm. We algorithmically transform $O(V^2)$ densecompute-heavy EMD version into an equivalent sparse one using new fusedSDDMM-SpMM (sparse selection of dense-dense matrix-, sparse-densematrix-multiplication) kernels. We implemented and optimized this algorithm fortwo very different architectures -- the new Intel Programmable IntegratedUnified Memory Architecture (PIUMA) and Intel Xeon CPUs. We show that we wereable to reach close to peak performance on both platforms.

A New Parallel Algorithm for Sinkhorn Word-Movers Distance and Its Performance on PIUMA and Xeon CPU