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This paper introduces a novel manifold learning framework for joint dimensionality reduction and clustering, addressing the challenges of clustering high-dimensional data. The framework uses Gradient Manifold Optimization to simultaneously learn the parameters of a dimension reduction technique (linear projection or neural network) and cluster the resulting features, exemplified with a Gaussian Mixture Model. Experiments on simulated and MNIST datasets demonstrate superior performance compared to existing clustering algorithms.
Jointly optimizing dimensionality reduction and clustering on a manifold yields state-of-the-art clustering performance, even surpassing established algorithms.
Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more promising direction is the joint learning of dimension reduction and clustering. In this work, we propose a Manifold Learning Framework that learns dimensionality reduction and clustering simultaneously. The proposed framework is able to jointly learn the parameters of a dimension reduction technique (e.g. linear projection or a neural network) and cluster the data based on the resulting features (e.g. under a Gaussian Mixture Model framework). The framework searches for the dimension reduction parameters and the optimal clusters by traversing a manifold,using Gradient Manifold Optimization. The obtained The proposed framework is exemplified with a Gaussian Mixture Model as one simple but efficient example, in a process that is somehow similar to unsupervised Linear Discriminant Analysis (LDA). We apply the proposed method to the unsupervised training of simulated data as well as a benchmark image dataset (i.e. MNIST). The experimental results indicate that our algorithm has better performance than popular clustering algorithms from the literature.
