Visualization of Pareto Solutions by Spherical Self-Organizing Map and It’s acceleration on a GPU

Yoshimi, Masato; Kuhara, Takuya; Nishimoto, Kaname; Miki, Mitsunori; Hiroyasu, Tomoyuki

doi:10.4236/jsea.2012.53020

Cited by 14 publications

(9 citation statements)

References 11 publications

(15 reference statements)

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“…We also did not find any cellular data/space decomposition-based method for parallelism. With regard to computing SOM on GPU, some methods have been proposed in [23], [24]. These methods accelerate SOM process by parallelizing the inner steps in each basic iteration, and they mainly focus on two aspects as follows, firstly, to find out the winner neuron in parallel, secondly, to move the winner neuron and its neighbors in parallel.…”

Section: Som For Structured Meshmentioning

confidence: 99%

Parallel Structured Mesh Generation with Disparity Maps by GPU Implementation

Wang

Zhang

Créput

et al. 2015

IEEE Trans. Visual. Comput. Graphics

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The goal of structured mesh is to generate a compressed representation of the 3D surface, where near objects are provided with more details than objects far from the camera, according to the disparity map. The solution is based on the Kohonens Self-Organizing Map algorithm for the benefits of its ability to generate a topological map according to a probability distribution and its potential to be a natural massive parallel algorithm. The disparity map, which stands for a density distribution that reflects the proximity of objects to the camera, is partitioned into an appropriate number of cell units, in such a way that each cell is associated to a processing unit and responsible of a certain area of the plane. The advantage of the proposed model is that it is decentralized and based on data decomposition. The required processing units and memory are with linearly increasing relationship to the problem size. Experimental results show that our GPU implementation is able to provide near real-time performance with small size disparity maps and the running time increases in a linear way with a very weak increasing coefficient. The proposed method is suitable to deal with large scale problems in a massively parallel way.

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Section: Som For Structured Meshmentioning

confidence: 99%

Parallel Structured Mesh Generation with Disparity Maps by GPU Implementation

Wang

Zhang

Créput

et al. 2015

IEEE Trans. Visual. Comput. Graphics

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“…Instead of the traditional plane SOM, a spherical self-organizing map is proposed as a visualization technique of Pareto solutions in [13]. Neurons in a spherical SOM are placed in a geodesic dome.…”

Section: A Review Of Visualizing the Pareto Front Pointsmentioning

confidence: 99%

“…A geodesic dome is a triangulation of a polyhedron that produces a close approximation to a sphere. Yoshimi et al [13] ascertained that the spherical SOM allows us to find similarities in data otherwise undetectable by plane SOM.…”

Section: A Review Of Visualizing the Pareto Front Pointsmentioning

confidence: 99%

Visualization of Pareto Front Points when Solving Multi-objective Optimization Problems

Kurasova¹,

Petkus

Filatovas

2013

ITC

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In this paper, a new strategy of visualizing Pareto front points is proposed when solving multi-objective optimization problems. A problem of graphical representation of the Pareto front points arises when the number of objectives is larger than 2 or 3, because, in this case, the Pareto front points are multidimensional. We face the problem of multidimensional data visualization. The visualization strategy proposed is based on a combination of clustering and dimensionality reduction. Moreover, in the obtained projection of the Pareto front points onto a plane, the points are marked according to the Euclidean distance of multidimensional points, corresponding to the points visualized, from the ideal point. In the experimental investigation of the paper, neural gas is used for data clustering, and multidimensional scaling is applied to dimensionality reduction, as well as to visualizing multidimensional data. The strategy can be implemented in a decision support system and it would be useful for a decision maker, who needs to review and evaluate many points of the Pareto fronts, for example, obtained by genetic algorithms.

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“…For example, in self-organizing maps [36], artificial neural networks are trained to preserve the topological properties of the input space. Principal component analysis (PCA) [15] tries to preserve variances of data.…”

Section: Graphical Representation Of Solution Outcomesmentioning

confidence: 99%

A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

Filatovas

Podkopaev

Kurasova

2015

INT J COMPUT COMMUN

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Interactive methods of multiobjective optimization repetitively derive Pareto optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the Pareto optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS.

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Visualization of Pareto Solutions by Spherical Self-Organizing Map and It’s acceleration on a GPU

Cited by 14 publications

References 11 publications

Parallel Structured Mesh Generation with Disparity Maps by GPU Implementation

Parallel Structured Mesh Generation with Disparity Maps by GPU Implementation

Visualization of Pareto Front Points when Solving Multi-objective Optimization Problems

A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

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