Incremental Non-Greedy Clustering at Scale

Clustering is the task of organizing data into meaningful groups. Modern clustering applications such as entity resolution put several demands on clustering algorithms: (1) scalability to massive numbers of points as well as clusters, (2) incremental additions of data, (3) support for any user-specified similarity functions. Hierarchical clusterings are often desired as they represent multiple alternative flat clusterings (e.g., at different granularity levels). These tree-structured clusterings provide for both fine-grained clusters as well as uncertainty in the presence of newly arriving data. Previous work on hierarchical clustering does not fully address all three of the aforementioned desiderata. Work on incremental hierarchical clustering often makes greedy, irrevocable clustering decisions that are regretted in the presence of future data. Work on scalable hierarchical clustering does not support incremental additions or deletions. These methods often make requirements on the similarity functions used and/or empirically tend to over merge clusters, which can lead to inaccurate clusterings. In this thesis, we present incremental and scalable methods for hierarchical clustering to empirically satisfy the above desiderata. Our work aims to represent uncertainty and meaningful alternative clusterings, to efficiently reconsider past decisions in the incremental case, and to use parallelism to scale to massive datasets. Our method, Grinch, handles incrementally arriving data in a non-greedy fashion, by reconsidering past decisions using tree structure re-arrangements (e.g., rotations and grafts) invoked in accordance with the user’s specified similarity function. To achieve scalability to massive datasets, our method, SCC, builds a hierarchical clusterings in a level-wise bottom-up manner. Certain clustering decisions are made independently in parallel within each level, and a global similarity threshold schedule prevents greedy over-merging. We show how SCC can be combined with the tree-structure re-arrangements in Grinch to form a mini-batch algorithm achieving both scalable and incremental performance. Lastly, we generalize our hierarchical clustering approaches to DAG-structured ones, which can better represent uncertainty in clustering by representing overlapping clusters. We introduce an efficient bottom-up method for DAG-structured clustering, Llama. For each of the proposed methods, we provide both a theoretical and empirical analysis. Empirically, our methods achieve state-of-the-art results on clustering benchmarks in both the batch and the incremental settings, including multiple point improvements in dendrogram purity and scalability to billions of points

Parallel Hierarchical Affinity Propagation with MapReduce

The accelerated evolution and explosion of the Internet and social media is generating voluminous quantities of data (on zettabyte scales). Paramount amongst the desires to manipulate and extract actionable intelligence from vast big data volumes is the need for scalable, performance-conscious analytics algorithms. To directly address this need, we propose a novel MapReduce implementation of the exemplar-based clustering algorithm known as Affinity Propagation. Our parallelization strategy extends to the multilevel Hierarchical Affinity Propagation algorithm and enables tiered aggregation of unstructured data with minimal free parameters, in principle requiring only a similarity measure between data points. We detail the linear run-time complexity of our approach, overcoming the limiting quadratic complexity of the original algorithm. Experimental validation of our clustering methodology on a variety of synthetic and real data sets (e.g. images and point data) demonstrates our competitiveness against other state-of-the-art MapReduce clustering techniques

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference