Subspace clustering of dimensionality-reduced data

04/27/2014
by   Reinhard Heckel, et al.
0

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from "undersampling" due to complexity and speed constraints on the acquisition device. More pertinently, even if one has access to the high-dimensional data set it is often desirable to first project the data points into a lower-dimensional space and to perform the clustering task there; this reduces storage requirements and computational cost. The purpose of this paper is to quantify the impact of dimensionality-reduction through random projection on the performance of the sparse subspace clustering (SSC) and the thresholding based subspace clustering (TSC) algorithms. We find that for both algorithms dimensionality reduction down to the order of the subspace dimensions is possible without incurring significant performance degradation. The mathematical engine behind our theorems is a result quantifying how the affinities between subspaces change under random dimensionality reducing projections.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/24/2016

A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data

Subspace clustering is the problem of partitioning unlabeled data points...
research
05/23/2019

Johnson-Lindenstrauss Property Implies Subspace Restricted Isometry Property

Dimensionality reduction is a popular approach to tackle high-dimensiona...
research
07/14/2019

Compressed Subspace Learning Based on Canonical Angle Preserving Property

A standard way to tackle the challenging task of learning from high-dime...
research
10/13/2019

Unsupervised Discovery of Sparse Multimodal Representations in High Dimensional Data

Extracting an understanding of the underlying system from high dimension...
research
12/02/2019

Using Dimensionality Reduction to Optimize t-SNE

t-SNE is a popular tool for embedding multi-dimensional datasets into tw...
research
03/30/2018

Fast and Robust Subspace Clustering Using Random Projections

Over the past several decades, subspace clustering has been receiving in...
research
03/20/2021

Train Deep Neural Networks in 40-D Subspaces

Although there are massive parameters in deep neural networks, the train...

Please sign up or login with your details

Forgot password? Click here to reset