# SqueezeFit: Label-aware dimensionality reduction by semidefinite programming

## TL;DR

SqueezeFit introduces a label-aware dimensionality reduction method using semidefinite programming, enabling effective low-dimensional projections for classification while providing theoretical guarantees for recovering the underlying projection.

## Contribution

It presents a novel semidefinite relaxation approach for label-aware dimensionality reduction with provable recovery guarantees, advancing compressive classification techniques.

## Key findings

- The method can recover the true projection operator under certain conditions.
- It offers a theoretically analyzable relaxation for label-aware dimensionality reduction.
- Applicable to compressive classification scenarios.

## Abstract

Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include compressive classification. Taking inspiration from large margin nearest neighbor classification, this paper introduces a semidefinite relaxation of this problem. Unlike its predecessors, this relaxation is amenable to theoretical analysis, allowing us to provably recover a planted projection operator from the data.