# Learning for Multi-Type Subspace Clustering

## TL;DR

This paper introduces a deep learning approach for multi-type subspace clustering, learning non-linear filters to produce feature embeddings that improve clustering accuracy on synthetic and real data.

## Contribution

It formulates multi-type subspace clustering as learning non-linear filters with deep neural networks, addressing challenges like model type selection and imbalance.

## Key findings

- Achieves state-of-the-art results on synthetic data
- Effective on real-world multi-type fitting problems
- Outperforms traditional clustering methods

## Abstract

Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are non-trivial, plagued by challenges such as choice of types and numbers of models, sampling imbalance and parameter tuning. In this work, we formulate the multi-type subspace clustering problem as one of learning non-linear subspace filters via deep multi-layer perceptrons (mlps). The response to the learnt subspace filters serve as the feature embedding that is clustering-friendly, i.e., points of the same clusters will be embedded closer together through the network. For inference, we apply K-means to the network output to cluster the data. Experiments are carried out on both synthetic and real world multi-type fitting problems, producing state-of-the-art results.