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Register a new userFlattening a Hierarchical Clustering through Active Learning
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We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve perfect reconstruction of the tree cut. In the non-realizable setting, we rely on known important-sampling procedures to obtain regret and query complexity bounds. Our algorithms come with theoretical guarantees on the statistical error and, more importantly, lend themselves to linear-time implementations in the relevant parameters of the problem. We discuss such implementations, prove running time guarantees for them, and present preliminary experiments on real-world datasets showing the compelling practical performance of our algorithms as compared to both passive learning and simple active learning baselines.
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Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting, and thus require the entire dataset to be available. This prohibits their use on large datasets commonly encountered in modern learning applications. In this paper, we consider hierarchical clustering in the online setting, where points arrive one at a time. We propose two algorithms that seek to optimize the Moseley and Wang (MW) revenue function, a variant of the Dasgupta cost. These algorithms offer different tradeoffs between efficiency and MW revenue performance. The first algorithm, OTD, is a highly efficient Online Top Down algorithm which provably achieves a 1/3-approximation to the MW revenue under a data separation assumption. The second algorithm, OHAC, is an online counterpart to offline HAC, which is known to yield a 1/3-approximation to the MW revenue, and produce good quality clusters in practice. We show that OHAC approximates offline HAC by leveraging a novel split-merge procedure. We empirically show that OTD and OHAC offer significant efficiency and cluster quality gains respectively over baselines.
The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial parameter called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions.
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and M{e}moli to partition-based clustering, and the Isbell/Dress schools study of injective envelopes. Carlsson and M{e}moli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable properties. Our first series of results extends their theory of functorial clustering schemes to methods that allow overlapping clusters in the spirit of Jardine and Sibson. This obviates some of the unpleasant effects of chaining that occur, for example with single-linkage clustering. We prove an equivalence between these general overlapping clustering functors and projections of weight spaces to what we term clustering domains, by focusing on the order structure determined by the morphisms. As a specific application of this machinery, we are able to prove that there are no functorial projections to cut metrics, or even to tree metrics. Finally, although we focus less on the construction of clustering methods (clustering domains) derived from injective envelopes, we lay out some preliminary results, that hopefully will give a feel for how the third leg of the stool comes into play.
Hierarchical clustering is an important technique to organize big data for exploratory data analysis. However, existing one-size-fits-all hierarchical clustering methods often fail to meet the diverse needs of different users. To address this challenge, we present an interactive steering method to visually supervise constrained hierarchical clustering by utilizing both public knowledge (e.g., Wikipedia) and private knowledge from users. The novelty of our approach includes 1) automatically constructing constraints for hierarchical clustering using knowledge (knowledge-driven) and intrinsic data distribution (data-driven), and 2) enabling the interactive steering of clustering through a visual interface (user-driven). Our method first maps each data item to the most relevant items in a knowledge base. An initial constraint tree is then extracted using the ant colony optimization algorithm. The algorithm balances the tree width and depth and covers the data items with high confidence. Given the constraint tree, the data items are hierarchically clustered using evolutionary Bayesian rose tree. To clearly convey the hierarchical clustering results, an uncertainty-aware tree visualization has been developed to enable users to quickly locate the most uncertain sub-hierarchies and interactively improve them. The quantitative evaluation and case study demonstrate that the proposed approach facilitates the building of customized clustering trees in an efficient and effective manner.
Meta learning is a promising solution to few-shot learning problems. However, existing meta learning methods are restricted to the scenarios where training and application tasks share the same out-put structure. To obtain a meta model applicable to the tasks with new structures, it is required to collect new training data and repeat the time-consuming meta training procedure. This makes them inefficient or even inapplicable in learning to solve heterogeneous few-shot learning tasks. We thus develop a novel and principled HierarchicalMeta Learning (HML) method. Different from existing methods that only focus on optimizing the adaptability of a meta model to similar tasks, HML also explicitly optimizes its generalizability across heterogeneous tasks. To this end, HML first factorizes a set of similar training tasks into heterogeneous ones and trains the meta model over them at two levels to maximize adaptation and generalization performance respectively. The resultant model can then directly generalize to new tasks. Extensive experiments on few-shot classification and regression problems clearly demonstrate the superiority of HML over fine-tuning and state-of-the-art meta learning approaches in terms of generalization across heterogeneous tasks.
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