Unsupervised Deep Embedding for Clustering Analysis (1511.06335v2)

Abstract: Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods.

• The paper proposes DEC, a framework that jointly optimizes deep embeddings and clustering assignments to significantly improve clustering performance.
• It leverages an autoencoder for initialization and refines clusters iteratively using soft assignment with Student’s t-distribution and KL divergence minimization.
• DEC demonstrates robust, scalable clustering with state-of-the-art accuracies on MNIST, STL-10, and REUTERS while reducing sensitivity to hyperparameter settings.

Unsupervised Deep Embedding for Clustering Analysis

"Unsupervised Deep Embedding for Clustering Analysis" proposes an innovative method termed Deep Embedded Clustering (DEC) that efficiently marries feature learning and clustering assignments. The paper addresses a fundamental issue in clustering: the reliance on predefined distance metrics in the original data space or shallow embedded spaces, which are often inadequate for complex datasets. DEC employs deep neural networks to learn a lower-dimensional feature space optimized for clustering, significantly improving clustering performance over traditional methods.

Methodology

DEC advances clustering by integrating the learning of feature representations and cluster assignments. The backbone of DEC is a deep neural network that maps data points from the original space $X$ to a lower-dimensional latent space $Z$. This allows for the application of a clustering objective optimized iteratively using stochastic gradient descent (SGD) through backpropagation. Unlike conventional methods, which treat the problem of clustering and feature embedding separately, DEC performs joint optimization, which is pivotal to its enhanced performance.

The optimization process involves two sequential steps:

1. Soft assignment of data points to clusters using Student’s t-distribution kernel.
2. Minimization of the Kullback-Leibler (KL) divergence between the soft assignments and an auxiliary target distribution, emphasizing points assigned with high confidence to refine both the feature space and the cluster centers iteratively.

An autoencoder initializes the DEC network to ensure that the latent space representations are semantically meaningful and well-separated. Critical to the efficiency of DEC is the use of a deep autoencoder for initial parameter estimation, followed by fine-tuning via KL divergence minimization.

Experimental Results

Experimental evaluation was conducted on three datasets: MNIST, STL-10, and REUTERS. DEC demonstrated superior performance in terms of both accuracy and robustness compared to k-means, LDGMI, and SEC, across a range of hyperparameter settings. Specifically, DEC achieved clustering accuracies of 84.30% on MNIST, 35.90% on STL-10, and 75.63% on the full REUTERS dataset, outperforming all competing methods.

A notable advantage of DEC is its reduced sensitivity to hyperparameter choices, which is crucial for practical applications where cross-validation is not feasible. The authors observed that DEC’s performance remained consistent across different settings of the annealing parameter $\lambda$, unlike LDGMI and SEC, which exhibited performance variability.

Furthermore, DEC’s linear complexity in the number of data points allows it to scale to large datasets efficiently, an edge over spectral clustering methods that exhibit super quadratic complexity and are computationally intensive on larger datasets.

Implications and Future Directions

The contributions of DEC are multifold:

1. Joint optimization of deep embeddings and clustering significantly enhances clustering purity and robustness.
2. Iterative refinement via soft assignment and KL divergence minimization leverages high confidence predictions, improving the clustering outcome iteratively.
3. The method offers state-of-the-art results in clustering accuracy and scalability, positioning it as a robust alternative to traditional and spectral clustering methods.

The implications of DEC extend to various domains requiring unsupervised learning, from image and text analysis to any field where data-driven clustering is pivotal. Future research could explore extensions of DEC to semi-supervised settings, adaptive learning for varying numbers of clusters, and its integration with other deep learning paradigms such as graph neural networks or generative models. Additionally, enhancing the initialization and optimization steps to further reduce computational requirements could expand DEC’s applicability to even larger datasets.

Overall, DEC represents a substantial improvement in the field of unsupervised clustering, with its methodological novelties and empirical strengths offering a valuable tool for both theoretical research and practical applications.