Dissimilarity-Based Sparse Subset Selection

Abstract

Finding an informative subset of a large collection of data points or models is at the center of many problems in computer vision, recommender systems, bio/health informatics as well as image and natural language processing. Given pairwise dissimilarities between the elements of a 'source set' and a 'target set,' we consider the problem of finding a subset of the source set, called representatives or exemplars, that can efficiently describe the target set. We formulate the problem as a row-sparsity regularized trace minimization problem. Since the proposed formulation is, in general, NP-hard, we consider a convex relaxation. The solution of our optimization finds representatives and the assignment of each element of the target set to each representative, hence, obtaining a clustering. We analyze the solution of our proposed optimization as a function of the regularization parameter. We show that when the two sets jointly partition into multiple groups, our algorithm finds representatives from all groups and reveals clustering of the sets. In addition, we show that the proposed framework can effectively deal with outliers. Our algorithm works with arbitrary dissimilarities, which can be asymmetric or violate the triangle inequality. To efficiently implement our algorithm, we consider an Alternating Direction Method of Multipliers (ADMM) framework, which results in quadratic complexity in the problem size. We show that the ADMM implementation allows to parallelize the algorithm, hence further reducing the computational time. Finally, by experiments on real-world datasets, we show that our proposed algorithm improves the state of the art on the two problems of scene categorization using representative images and time-series modeling and segmentation using representative models.

Transfer Shape Modeling Towards High-Throughput Microscopy Image Segmentation

“…In this paper, we model dictionary learning as a subsect selection problem which seeks a small set of representatives to summarize and describe the whole dataset X , thereby removing outliers that are not true representatives and improving the runtime computational efficiency. A straightforward way to conduct sparse subsect selection is to regularize the coefficient matrix with an ℓ 2,1 or ℓ ∞, 1 norm [6]. Meanwhile, since the number of constraints for shape control is limited, cell shapes actually lie on a low-dimensional manifold [16].…”

ProLFA: Representative prototype selection for local feature aggregation

“…For each image in Scene and Pascal, we take 90 and 150 descriptors as the input of each aggregation approach, respectively. Our ProLFA model in (9) is then employed to train the aggregation function on the training set, thus obtaining the global representations of testing set via (22). Finally, to evaluate the discrimination of aggregated representations, we choose the 1-Nearest Neighbor (1-NN) classifier with Euclidean distance since it is parameter free and the results will be easily reproducible.…”

“…Additionally, to improve the interpretability of codebook, we consider the process of finding codebook as the task of Prototype Selection (PS), which aims at finding exemplar samples from a feature collection. PS has been actively discussed in other fields [22], such as video summarization and product recommendation, since it holds several advantages over data storage, compression, synthesis and cleansing. Besides helping to reduce the computational time and memory of algorithms, due to working on several prototypical samples, PS has further improved performances of numerous applications.…”

Single shot active learning using pseudo annotators

“…Other efforts have been devoted to finding the representatives by using pairwise similarities between data points (Frey & Dueck, 2007;Elhamifar et al, 2016). For example, Elhamifar et al (2016) proposed a dissimilarity-based sparse subset selection (DS3) method to minimize the difference between source data and target data. However, some methods, e.g.…”