A Greedy Clustering Algorithm Based on Interval Pattern Concepts and the Problem of Optimal Box Positioning

Abstract

We consider a clustering approach based on interval pattern concepts. Exact algorithms developed within the framework of this approach are unable to produce a solution for high-dimensional data in a reasonable time, so we propose a fast greedy algorithm which solves the problem in geometrical reformulation and shows a good rate of convergence and adequate accuracy for experimental high-dimensional data. Particularly, the algorithm provided high-quality clustering of tactile frames registered by Medical Tactile Endosurgical Complex.

NP-Hardness of the Problem of Optimal Box Positioning

“…The problem of optimal box positioning finds its applications in computer science, pattern recognition, and data analysis [1][2][3][4]. In this paper, we have proved that this problem is NP-hard.…”

“…On the one hand, this result means that algorithms based on optimal box positioning are in general inefficient for the analysis of high-dimensional data, thus it makes sense to develop algorithms that look for an approximately optimal box position. An example of such an algorithm used for data clustering can be found in [4].…”

“…The problem of optimal box positioning has wide applications in computational geometry, data mining, and pattern recognition (e.g., see [1][2][3]). In [4], the authors presented a clustering approach based on the greedy algorithm that finds an approximate solution of the optimal box positioning problem. The algorithm was inspired by the apparatus of maximum interval pattern concepts (see, e.g., [4,5]), a technique that allows one to select patterns from fuzzy contexts.…”

“…In [4], the authors presented a clustering approach based on the greedy algorithm that finds an approximate solution of the optimal box positioning problem. The algorithm was inspired by the apparatus of maximum interval pattern concepts (see, e.g., [4,5]), a technique that allows one to select patterns from fuzzy contexts. This approach was successfully applied to the dataset of tactile images registered by the Medical Tactile Endosurgical Complex [6][7][8], which allows intraoperative tactile examination of tissues.…”