Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering (1610.04794v2)

Abstract: Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the `clustering-friendly' latent representations and to better cluster the data, we propose a joint DR and K-means clustering approach in which DR is accomplished via learning a deep neural network (DNN). The motivation is to keep the advantages of jointly optimizing the two tasks, while exploiting the deep neural network's ability to approximate any nonlinear function. This way, the proposed approach can work well for a broad class of generative models. Towards this end, we carefully design the DNN structure and the associated joint optimization criterion, and propose an effective and scalable algorithm to handle the formulated optimization problem. Experiments using different real datasets are employed to showcase the effectiveness of the proposed approach.

Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering

This paper, authored by Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos, and Mingyi Hong, proposes a novel method for data clustering, with a primary focus on enhancing the K-means algorithm's efficiency and effectiveness. The core idea is to jointly optimize dimensionality reduction (DR) and clustering tasks via a deep neural network (DNN). This integrated approach contrasts traditional methods where these tasks are treated sequentially.

Key Contributions and Methodology

The authors present three main contributions:

1. Optimization Criterion Design: The paper introduces a new optimization criterion that simultaneously addresses DR and clustering problems. This criterion is a composite of three elements: dimensionality reduction, data reconstruction, and a clustering-promoting regularization. The reconstruction component is crucial for avoiding trivial or meaningless solutions by incorporating a decoding network that ensures the preservation of significant data characteristics during dimensionality reduction.
2. Effective and Scalable Optimization Procedure: The proposed solution is notable for its scalability and efficacy. The authors develop an alternating stochastic gradient algorithm complemented by empirical initialization techniques. This approach deals effectively with the high complexity of the optimization problem due to the use of nonlinear activation functions and integer constraints from the K-means component. The algorithm employs strategies such as layer-wise pre-training and a novel adaptive learning rate for centroid updates, ensuring both robustness and scalability.
3. Comprehensive Experiments and Validation: The experimental section extensively evaluates the proposed method on various datasets, including both synthetic and real-world datasets like RCV1-v2, 20Newsgroup, MNIST (raw and pre-processed), and Pendigits. The results consistently demonstrate superior clustering performance compared to state-of-the-art techniques including various baseline methods like Spectral Clustering (SC), Sparse Subspace Clustering (SSC), stacked autoencoders (SAE), and others.

Technical Implementation and Algorithmic Details

• Network Architecture: The proposed deep clustering network (DCN) consists of an encoding network for dimensionality reduction and a mirrored decoding network for data reconstruction. The encoding network transforms the high-dimensional data into a low-dimensional latent space where K-means clustering is then applied. This joint optimization ensures that the latent space is inherently more suited for effective clustering.
• Training Procedure: The alternating optimization strategy involves updating the DNN parameters, clustering assignments, and cluster centroids iteratively. The DNN parameters are optimized to minimize both reconstruction error and clustering cost, leveraging backpropagation and stochastic gradient descent (SGD). The clustering parameters are updated using adaptive learning rates inspired by centroid-specific counts to manage their geometric centers effectively.

Numerical Results and Implications

The numerical results highlight significant improvements in clustering performance across various metrics such as normalized mutual information (NMI), adjusted Rand index (ARI), and clustering accuracy (ACC). For instance, on the RCV1-v2 dataset, DCN consistently outperformed other methods including SAE+KM and XRAY, showcasing robust performance even with an increasing number of clusters and varying complexity.

The implications of these findings are multifaceted:

1. Practical Application: The integrated approach can be directly applied to a wide range of datasets, particularly those deemed unsuitable for traditional K-means clustering due to high dimensionality or complex generative processes. This opens up new possibilities for applying K-means clustering to more sophisticated datasets encountered in real-world applications.
2. Theoretical Advancement: The paper advances the understanding of how deep learning can be effectively harnessed to improve unsupervised learning tasks like clustering. The joint optimization criterion and the scalable algorithmic solution present a deepened theoretical framework for future research in the intersection of DR and clustering.
3. Extensibility: The flexibility of the proposed approach allows for various extensions: different types of neural networks (such as convolutional neural networks) and clustering criteria can be seamlessly integrated into the framework. The methodology is also adaptable for both online and large-scale batch learning scenarios.

Future Directions

The research presents several avenues for future exploration. One important direction is enhancing the theoretical guarantees of the algorithm's convergence and performance bounds. Additionally, exploring more sophisticated initialization techniques and hyperparameter optimization strategies could further refine practical implementations. Moreover, examining the method's performance on datasets with more complex, non-linear structures and adaptability to various types of clustering tasks beyond K-means could provide valuable insights.

Ultimately, the paper sets a precedent for integrating deep learning techniques with classical clustering algorithms, compelling a shift towards more unified and holistic approaches in unsupervised learning.