Clustering to minimize the maximum intercluster distance

Gonzalez, Teofilo F.

doi:10.1016/0304-3975(85)90224-5

Cited by 1,324 publications

(912 citation statements)

References 6 publications

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“…A hypothesis is that better pivots are far away from each other [8], [10]. A simple algorithm based on the hypothesis sequentially selects pivotp from a set of data objects X one by one with the same way as -net construction in [15], [21], as expressed bŷ…”

Section: Pivot Generation and Data Partitioning Algorithmsmentioning

confidence: 99%

Efficient Similarity Search with a Pivot-Based Complete Binary Tree

Yamagishi

Aoyama²,

Saito

et al. 2017

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper presents an efficient similarity search method utilizing as an index a complete binary tree (CBT) based on optimized pivots for a large-scale and high-dimensional data set. A similarity search method, in general, requires high-speed performance on both index construction off-line and similarity search itself online. To fulfill the requirement, we introduce novel techniques into an index construction and a similarity search algorithm in the proposed method for a range query. The index construction algorithm recursively employs the following two main functions, resulting in a CBT index. One is a pivot generation function that obtains one effective pivot at each node by efficiently maximizing a defined objective function. The other is a node bisection function that partitions a set of objects at a node into two almost equal-sized subsets based on the optimized pivot. The similarity search algorithm employs a three-stage process that narrows down candidate objects within a given range by pruning unnecessary branches and filtering objects in each stage. Experimental results on one million real image data set with high dimensionality demonstrate that the proposed method finds an exact solution for a range query at around one-quarter to half of the computational cost of one of the state-ofthe-art methods, by using a CBT index constructed off-line at a reasonable computational cost.

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Section: Pivot Generation and Data Partitioning Algorithmsmentioning

confidence: 99%

Efficient Similarity Search with a Pivot-Based Complete Binary Tree

Yamagishi

Aoyama²,

Saito

et al. 2017

IEICE Trans. Inf. & Syst.

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“…We will also investigate alternative rewritings for the cardinality clauses and methods to reduce the number of constraint clauses. Finally, we will extend the method here presented to other classification tasks that can be formalized as hard subset selection problems, as SNN [23], k-NN [13], k-center [17], CNNDD [2], and others.…”

Section: Discussionmentioning

confidence: 99%

“…Most useful classification tasks can be formulated as subset selection problems [6,17,12,26,28]. Subsets to be singled out have to posses certain properties guaranteeing that they represent a model of the whole training set, according to the specific classification rule.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Subset Selection for Classification through SAT Encodings

Angiulli

Basta²

Artificial Intelligence in Theory and Practice II

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In this work we propose a method for computing a minimum size training set consistent subset for the Nearest Neighbor rule (also said CNN problem) via SAT encodings. We introduce the SAT-CNN algorithm, which exploits a suitable encoding of the CNN problem in a sequence of SAT problems in order to exactly solve it, provided that enough computational resources are available. Comparison of SAT-CNN with well-known greedy methods shows that SAT-CNN is able to return a better solution. The proposed approach can be extended to several hard subset selection classification problems.

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“…In this method n sample points are divided into k clusters, where the maximum distance of a point to a cluster center is minimized. This is equal to solving the k-center problem which is NP-hard and has a greedy solution [86]. This partitioning and the use of a new multivariate Taylor expansion dramatically reduces the cost of fast Gauss transform, but at the cost of reduced accuracy.…”

Section: Related Workmentioning

confidence: 99%

Manifold learning and unwrapping using density ridges

Shaker¹

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xii 3.6 Unwrapped mnist-0 digits with a selection of images of the actual digits on top. Orientation and thickness of digits smoothly vary across horizontal and vertical directions, respectively. . 34 3.7 Unfolding mnist-0 digits using two benchmark manifold learning methods. Unlike the proposed method, no smooth variation of structure is preserved using these methods. . . . . 35 3.8 Unfolding mnist-2 digits using the proposed method and t-SNE. Similar to Figure 3.7(b) for mnist-0, no smooth variation of structure is preserved using t-SNE, while proposed method shows smooth change of thickness and shape in horizontal and vertical coordinates, respectively. 36 3.9 Unfolding mnist-9 digits using the proposed method, which shows smooth change of thickness Sylvain Bouix, who were also my mentors, for all of their guidance through this process; your discussion, ideas, and feedback have been absolutely invaluable.

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Clustering to minimize the maximum intercluster distance

Cited by 1,324 publications

References 6 publications

Efficient Similarity Search with a Pivot-Based Complete Binary Tree

Efficient Similarity Search with a Pivot-Based Complete Binary Tree

Optimal Subset Selection for Classification through SAT Encodings

Manifold learning and unwrapping using density ridges

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