Dimensionality reduction is a commonly used step in many algorithms for visualization, classification, clustering and modeling. Most dimensionality reduction algorithms find a low dimensional embedding that preserves the structure of high-dimensional data points. This paper proposes Local Minima Embedding (LME), a technique to find a lowdimensional embedding that preserves the local minima stru...

We show analogues of Minkowski’s theorem on successive minima, where the volume is replaced by the lattice point enumerator. We further give analogous results to some recent theorems by Kannan and Lovász on covering minima.

Hodges et al (2007) proposed smoothed analysis of variance (ANOVA) and showed how to use it to smooth interactions in balanced, single-error-term ANOVAs. Besides avoiding discontinuous choices to include or exclude effects, smoothed ANOVA addresses three practical concerns: unreplicated designs, masking in effects with many degrees of freedom, and “subgroup analysis”. The present paper extends ...