Trevor Richardson

Visually Exploring a Design Space Through the Use of Multiple Contextual Self-Organizing Maps

Understanding relationships amongst n-dimensional design spaces has long been a problem in the engineering community. Many visual methods previously developed, although useful, are limited to comparing three design variables at a time. Work described in this paper builds off the idea of a self-organizing map in order to visualize n-dimensional data on a two dimensional map. By using the contextual self-organizing map, current work shows that more design space information can be gleaned from map nodes themselves. By breaking the final visualization up into three maps containing separate contextual information, an investigator can quickly obtain information about the overall behavior of a design space. Tests run on well-known optimization functions show that information such as modality and curvature may be quickly suggested by these maps, and that they may provide enough information for a designer to choose a function to proceed with formal optimization of a given data set.Copyright

Visual Design Space Exploration using Contextual Self-Organizing Maps

Self-organizing maps (SOMs) and contextual maps are methods of visualizing high dimensional data in a low dimensional space. SOMs have previously been applied to visualize characteristics of optimization problems by generating maps of the component variables to compare interactions and relationships between design variables. In this paper, SOMs and contextual maps are explored as a visualization method to directly visualize the design space. Using the techniques described in the paper, high dimensional datasets are reduced to a 2D, human readable, visual map. Preliminary results show that the topology of three optimization functions using varying dimensionality can be clustered and visualized using contextual maps, and information can be gathered from these clusters including objective function values and variability amongst differing areas of the design space. This paper focuses on the use of contextual maps to extract valuable information such as modality and curvature to aid in future work such as selection of appropriate optimization algorithm and initial point for a solution run.

Contextual Self-Organizing Map Visualization to Improve Optimization Solution Convergence

5is a type of artificial neural network that uses dimensionality reduction to allow for visualization of a high dimensional problem in a low dimensional space, while preserving the topology of the data itself. Kohnen’s SOMs, however, do not allow the map to categorize the data represented in each node. Contextual SOMs alleviate this problem by labeling individual nodes. This allows a user to quickly identify each node, providing an overall view of the design space.뀀ഀȠ Using CSOMs as a pre-optimization step allows a designer to select an initial starting point for an algorithm and to select an optimization method based on the modality and curvature of the data. By identifying nodes that may contain minimum values the optimization algorithm is passed starting points that may increase the solution accuracy, reliability while decreasing solution time. In this study multiple unimodal and multimodal optimization problems were solved using CSOMs as a pre-optimization step. Multi-modal problems were solved using a pheromone particle swarm optimization method (PSO) 6 while unimodal problems were solved using a QuasiNewton Line search implemented through Matlab 7 .뀀ഀȠ 뀀ഀȠ

Visualizing Design Spaces Using Two-Dimensional Contextual Self-Organizing Maps

Visualization of design spaces is a complex problem that has the potential to provide many benefits. Design spaces can be easily visualized with two or three design variables using a range of methods. However, once a problem exceeds this limit, direct visualization that captures all necessary behaviors becomes difficult. To visualize these higher dimensions, it is necessary to use visual cues such as color, size, and/or symbols to show the added dimensions. The disadvantage to using visual cues is the inability to expand much beyond three dimensions. This research focuses on using contextual self-organizing maps to provide a solution to visualizing high-dimensional design spaces by using the dimensionality-reduction capabilities of self-organizing maps. A visual representation is created by generating a self-organizing map and applying objective function values as the contextual labels. The map is then broken into three different maps containing separate contextual information, namely the mean, minimum, a...

Incorporating Value-Driven Design into the Visualization of Design Spaces Using Contextual Self-Organizing Maps: A Case Study of Satellite Design

This paper presents case study of satellite design using a new method to view ndimensional design or optimization data using a contextual self-organizing map. The technique allows n-dimensional data to be trained without dimensionality reduction or other “compression”. A designer can view similar design points in a true n-dimensional manner. Prior work in visual design space exploration using contextual self-organizing maps is extended through the incorporation of designer preferences using techniques founded in value-driven design. Standard techniques of the self-organizing map are used to group the ndimensional design space into discrete clusters of similar characteristics through neural network-based topological ordering. Techniques from prior work are used to present the designer with a visual display encapsulating statistical qualities of value held within the ndimensional design space. A case study involving a satellite design problem is presented and results compared with recent findings in value-driven design and traditional methods of design optimization. Initial results show unique potential of the combined methods to develop an understanding of the design space topology and to select promising areas of a design space for detailed analysis.

Improving Contextual Self-Organizing Map Solution Times Using GPU Parallel Training

Visualizing n-dimensional design or optimization data is very challenging using current methods and technologies. Many current techniques perform dimensionality reduction or other “compression” methods to show views of the data in two or three dimensions. Designers are left to infer the relationships with other independent and dependent variables being considered. Contextual self-organizing maps offer a way to process a view and interact with all dimensions of design data simultaneously. Contextual self-organizing maps are a form of neural network that can be used to understand the complex relationships between large amounts of high-dimensional data, as was shown in previous work by the authors. This original formulation of contextual self-organizing maps used a sequential training method that took significant amounts of training time with large datasets. Batch self-organizing maps provide a data-independent training method that allows the training process to be parallelized. This research parallelizes the batch self-organizing map by combining networkpartitioning and data-partitioning methods with CUDA on the GPU to achieve significant training time reductions.