Deep $k$-Means: Jointly clustering with $k$-Means and learning representations (1806.10069v2)

Abstract: We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering algorithm can lead to better clustering performance, all the more so that the two tasks are performed jointly. We propose here such an approach for $k$-Means clustering based on a continuous reparametrization of the objective function that leads to a truly joint solution. The behavior of our approach is illustrated on various datasets showing its efficacy in learning representations for objects while clustering them.

• The paper presents a joint optimization approach that integrates k-Means clustering with deep representation learning using a continuous softmax surrogate.
• The methodology leverages stochastic gradient descent to update both cluster assignments and neural network representations, eliminating discrete steps.
• Empirical results on benchmark datasets demonstrate improved clustering accuracy, normalized mutual information, and adjusted Rand index versus state-of-the-art methods.

Overview of "Deep $k$-Means: Jointly Clustering with $k$-Means and Learning Representations"

This paper addresses the entrenched challenges of clustering high-dimensional data by introducing an innovative approach termed Deep $k$-Means (DKM). The work builds upon the limitations of traditional clustering algorithms like $k$-Means and Gaussian Mixture Models (GMMs) which suffer inefficacy when operating on high-dimensional spaces, a problem exacerbated by the curse of dimensionality. By leveraging advances in representation learning, particularly through deep neural networks (DNNs), this research explores the joint optimization of clustering and representation learning to enhance clustering performance.

Methodology

Deep $k$-Means proposes a continuous reparametrization of the $k$-Means objective function, achieving a truly joint solution for clustering and representation learning. Unlike preceding methods which separate these tasks, DKM solely utilizes continuous gradient updates, avoiding discrete cluster assignment steps. This is achieved by introducing a parameterized softmax function serving as a continuous surrogate for the discrete $k$-Means objective, thus enabling the application of stochastic gradient descent (SGD) throughout the optimization process.

Key Insights and Results

The deep $k$-Means framework significantly improves clustering accuracy as evidenced by experiments conducted on standard benchmark datasets like MNIST, USPS, 20NEWS, and RCV1. Notably, the approach excels on datasets like MNIST and USPS, confirming its efficiency in learning discriminative representations and clustering high-dimensional data points effectively.

By systematically comparing with state-of-the-art deep clustering methods, especially the Deep Clustering Network (DCN) and Improved Deep Embedded Clustering (IDEC), DKM demonstrates superior or equivalent performance without requiring pretraining in some configurations. This is highlighted by consistent improvements in metrics such as clustering accuracy (ACC), normalized mutual information (NMI), and adjusted Rand index (ARI).

Significance and Implications

DKM's ability to jointly optimize data representation and clustering implies practical efficacy in myriad real-world applications where unsupervised learning is paramount, such as image recognition and large-scale document clustering. This joint optimization paradigm fosters more meaningful clustering that adapts dynamically to the structure of the data, a noteworthy step forward compared to static post-processing clustering methods.

Theoretically, the research underscores the potential of integrating clustering objectives within the framework of representation learning, promoting clustering as an inherent part of the representation learning process rather than a subsequent application. This could inspire further explorations into other clustering objectives and their integration into deep learning architectures.

Future Directions

Looking forward, further paper could explore the adaptation of DKM to other clustering paradigms beyond $k$-Means, potentially broadening its applicability. Additionally, investigating ways to handle datasets without predefined cluster counts or extending the framework to other clustering problems such as hierarchical clustering could also be worthwhile.

Moreover, the exploration of alternative differentiable surrogate functions and their impact on convergence speed, efficiency, and clustering quality would provide deeper insights into optimizing joint clustering and representation learning.

In essence, Deep $k$-Means lays a robust foundation for advancing clustering in unsupervised machine learning, emphasizing the symbiotic relationship between representation and clustering, with promising avenues for continued research and development.