[Paper Review] Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering

Bo Yang, Xiao Fu+2 more|arXiv (Cornell University)|Oct 15, 2016

Face and Expression Recognition35 references597 citations

TL;DR

The paper introduces a Deep Clustering Network (DCN) that jointly learns a nonlinear dimensionality reduction and K-means clustering by incorporating a reconstruction term to prevent trivial solutions, demonstrating improved clustering performance across several real datasets.

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.

Motivation & Objective

• Motivate and formulate a joint DR and clustering framework that can handle nonlinear data transformations.
• Design a deep neural network architecture that fosters clustering-friendly latent representations while enabling data reconstruction.
• Develop a scalable optimization algorithm that alternates between updating network parameters and clustering variables.
• Demonstrate the effectiveness of the approach on synthetic and real-world datasets and compare against strong baselines.

Proposed method

• Propose a joint objective that combines dimensionality reduction, data reconstruction via a decoding network, and a K-means clustering regularization term.
• Use a Deep Clustering Network (DCN) with an encoder/decoder structure where clustering is performed at the bottleneck layer.
• Incorporate a reconstruction loss to prevent trivial solutions and promote meaningful latent representations; the loss combines a reconstruction term and a clustering-term with parameter lambda.
• Optimize via an alternating stochastic gradient method that updates network parameters with backpropagation and assigns samples to clusters online, updating centroids with a balanced-moving-average rule.
• Initialize the network with layer-wise pre-training and warm-start clustering via K-means on bottleneck outputs.
• Allow flexibility to adopt other network architectures (e.g., CNNs) and clustering criteria beyond K-means.

Experimental results

Research questions

• RQ1 Can a nonlinear DR model learned by a DNN produce latent representations that are more amenable to K-means clustering than linear DR methods?
• RQ2 Does jointly optimizing DR and clustering with a reconstruction constraint avoid trivial solutions and improve clustering quality across diverse datasets?
• RQ3 How does the proposed DCN perform relative to strong baselines (e.g., SAE+KM, DEC, NMF+KM) on large-scale and unbalanced datasets?
• RQ4 Is the optimization procedure scalable and effective in online/mini-batch settings for real-world data?
• RQ5 What is the impact of reconstruction strength (lambda) and network architecture on clustering performance?

Key findings

• DCN consistently improves clustering metrics over baselines on real datasets such as RCV1-v2 across multiple cluster counts.
• DCN outperforms SAE+KM and often surpasses DEC and other state-of-the-art baselines, especially in unbalanced clustering scenarios.
• In synthetic experiments, DCN recovers the underlying clustering-friendly latent space where other DR methods fail.
• The reconstruction component effectively prevents trivial solutions and stabilizes joint optimization, resulting in steadily improving metrics over training epochs.
• The approach demonstrates strong performance on MNIST (raw and pre-processed) and 20Newsgroup, indicating robustness across image and text data.