In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee.

This paper proposes an algorithm to compute k-prototypes for a set of 3D rigid structures. Two structures are called rigid, if one can align them via translation, reflection and rotation. The authors first propose a 1-prototype algorithm to find the best representative 3D structure (the one minimizing the distance to all other structure subject to optimal rigid alignement). For k-prototype clustering, the algorithm then consists of building a correlation graph and using [11] to perform k-median clustering. For each obtained cluster, the 1-prototype algorithm is applied.

In this paper, we study the following new variant of prototype learning, called k-prototype learning problem for 3D rigid structures: Given a set of 3D rigid structures, find a set of k rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee.

In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee.

In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee. We validate our approach using two type of data sets, random data and biological data of chromosome territories. Experiments suggest that our approach can effectively learn prototypes in both types of data.

Magomedov I.A, Khazamov O.A department of Computer Science, Dagestan State Technical University, Makhachkala city, 367014 Abstract The approach of applying associative processor for decision making problem was proposed. It focuses on hardware implementations of fuzzy processing systems, associativity as effective management basis of fuzzy processor. The structural approach is being developed resulting in a quite simple and compact parallel associative memory unit (PAMU). The memory cost and speed comparison of processors with rigid and soft-variable structure is given. Also the example PAMU flashing is considered.