Deep Subspace Clustering Networks (1709.02508v1)

Abstract: We present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the "self-expressiveness" property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard back-propagation procedure. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. We further propose pre-training and fine-tuning strategies that let us effectively learn the parameters of our subspace clustering networks. Our experiments show that the proposed method significantly outperforms the state-of-the-art unsupervised subspace clustering methods.

• The paper presents a novel self-expressive layer integrated within a deep autoencoder, enabling effective unsupervised subspace clustering.
• The network architecture uses pre-training and fine-tuning strategies to map data to a latent space and learn pairwise affinities for improved clustering.
• Experimental results on datasets like Extended Yale B, ORL, and COIL demonstrate significantly lower clustering error rates compared to traditional methods.

Deep Subspace Clustering Networks: An Overview

The paper "Deep Subspace Clustering Networks" introduces a novel approach to unsupervised subspace clustering through a deep neural network architecture. This work leverages the capabilities of deep auto-encoders to effectively map input data into a latent space conducive to clustering.

Key Contributions

The primary contribution of the paper is the introduction of a self-expressive layer within a deep neural network. This layer embodies the concept of "self-expressiveness," a well-regarded property in traditional subspace clustering wherein each data point is represented as a linear combination of other data points within the same subspace. This self-expressive layer is seamlessly integrated between the encoder and decoder of an auto-encoder architecture, allowing the affinities between data points to be learned in a differentiable manner via backpropagation.

Network Architecture and Methodology

The proposed Deep Subspace Clustering Networks (DSC-Nets) are structured upon deep auto-encoders, with the self-expressive layer bridging the encoder and decoder.

• The encoder non-linearly maps the input data to a latent representation.
• The self-expressive layer, devoid of bias and activation functions, learns the pairwise affinities, reinforcing the clustering capability.
• The decoder reconstructs the data from the latent space.

To enhance the efficacy of the learning process, the authors propose specific pre-training and fine-tuning strategies. These strategies are crucial in dealing with limited datasets, a common challenge in subspace clustering tasks.

Experimental Validation

The paper demonstrates significant performance improvements over existing state-of-the-art subspace clustering methods through empirical evaluations on several datasets, including Extended Yale B and ORL face datasets as well as COIL20/100 object datasets.

• For Extended Yale B, the DSC-Nets outperformed traditional methods with a clustering error rate significantly lower than the best baseline techniques.
• On the ORL dataset, DSC-Nets continued to exhibit robust performance even with non-linearly separable data.
• Benchmarked against COIL20 and COIL100 datasets, the proposed approach again showed superior results, underscoring its generalizability across different types of data.

Implications and Future Directions

The introduction of a self-expressive layer in neural networks represents a promising advancement in subspace clustering, offering a pathway to more nuanced and effective clustering solutions. This method could potentially extend to more complex and high-dimensional clustering tasks, especially where non-linear subspaces are involved.

Future developments could explore:

• Enhancements in network architecture to further optimize learning efficiency for larger datasets.
• Applications in other domains such as dynamic network analysis or large-scale image retrieval tasks.

In conclusion, this work establishes a solid foundation for integrating deep learning with traditional clustering principles, thereby opening new avenues in unsupervised learning and its applications. The framework not only enhances clustering accuracy but also paves the way for future explorations in scalable and adaptable clustering methodologies.