Dynamic Visualization and Fast Computation for Convex Clustering via Algorithmic Regularization

Abstract

Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, guaranteeing global convergence of the approximate path to the exact solution under easily-checked non-data-dependent assumptions. The application of algorithmic regularization to convex clustering yields the Convex Clustering via Algorithmic Regularization Paths (CARP) algorithm for computing the clustering solution path. On example data sets from genomics and text analysis, CARP delivers over a 100-fold speedup over existing methods, while attaining a finer approximation grid than standard methods. Furthermore, CARP enables improved visualization of clustering solutions: the fine solution grid returned by CARP can be used to construct a convex clusteringbased dendrogram, as well as forming the basis of a dynamic path-wise visualization based on modern web technologies. Our methods are implemented in the open-source R package clustRviz, available at https://github.com/DataSlingers/clustRviz.

Fast tree aggregation for consensus hierarchical clustering

“…The form of the regularization path depends on the choice of the norm and the weights. While algorithms exist for all weights and norms [7], they are generally computationally expensive. Moreover, if the weights are not chosen appropriately, individuals can fuse at one point and split later [8].…”

Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

“…Firstly, we used the presidential speeches dataset in [ 42 ] for the experiment to jointly estimate common links across graphs and show the common structure. The dataset contains 75 most-used words (features) from several big speeches of the 44 US presidents (samples).…”

“…The dataset contains 75 most-used words (features) from several big speeches of the 44 US presidents (samples). In addition, we used the clustering result in [ 42 ], where the authors split the 44 samples into two groups with similar features, and then we obtained two classes of samples .…”

An Efficient Algorithm for Convex Biclustering

“…Firstly, we use the presidential speeches dataset preprocessed by Weylandt et al [41] that contains 75 high-frequency words taken from the significant speeches of the 44 U.S. presidents around the year 2018. We show the heatmaps in Figure 4 under a wide range of tuning parameters λ to exhibit the fusion process of biclusters.…”