  Unsupervised dimension selection is an important problem that seeks to reduce
dimensionality of data, while preserving the most useful characteristics. While
dimensionality reduction is commonly utilized to construct low-dimensional
embeddings, they produce feature spaces that are hard to interpret. Further, in
applications such as sensor design, one needs to perform reduction directly in
the input domain, instead of constructing transformed spaces. Consequently,
dimension selection (DS) aims to solve the combinatorial problem of identifying
the top-$k$ dimensions, which is required for effective experiment design,
reducing data while keeping it interpretable, and designing better sensing
mechanisms. In this paper, we develop a novel approach for DS based on graph
signal analysis to measure feature influence. By analyzing synthetic graph
signals with a blue noise spectrum, we show that we can measure the importance
of each dimension. Using experiments in supervised learning and image masking,
we demonstrate the superiority of the proposed approach over existing
techniques in capturing crucial characteristics of high dimensional spaces,
using only a small subset of the original features.
