
Dimensionality Reduction for Wasserstein Barycenter
The Wasserstein barycenter is a geometric construct which captures the n...
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Branching embedding: A heuristic dimensionality reduction algorithm based on hierarchical clustering
This paper proposes a new dimensionality reduction algorithm named branc...
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Adaptive Metric Dimensionality Reduction
We study adaptive datadependent dimensionality reduction in the context...
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Dimensionality Reduction for kDistance Applied to Persistent Homology
Given a set P of n points and a constant k, we are interested in computi...
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Random Projections for kmeans Clustering
This paper discusses the topic of dimensionality reduction for kmeans c...
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Dimensionality Reduction for Tukey Regression
We give the first dimensionality reduction methods for the overconstrain...
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Clustering with UMAP: Why and How Connectivity Matters
Topology based dimensionality reduction methods such as tSNE and UMAP h...
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Randomized Dimensionality Reduction for Facility Location and SingleLinkage Clustering
Random dimensionality reduction is a versatile tool for speeding up algorithms for highdimensional problems. We study its application to two clustering problems: the facility location problem, and the singlelinkage hierarchical clustering problem, which is equivalent to computing the minimum spanning tree. We show that if we project the input pointset X onto a random d = O(d_X)dimensional subspace (where d_X is the doubling dimension of X), then the optimum facility location cost in the projected space approximates the original cost up to a constant factor. We show an analogous statement for minimum spanning tree, but with the dimension d having an extra loglog n term and the approximation factor being arbitrarily close to 1. Furthermore, we extend these results to approximating solutions instead of just their costs. Lastly, we provide experimental results to validate the quality of solutions and the speedup due to the dimensionality reduction. Unlike several previous papers studying this approach in the context of kmeans and kmedians, our dimension bound does not depend on the number of clusters but only on the intrinsic dimensionality of X.
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