Hyperspace geography: Visualizing fitness landscapes beyond 4D

Human perception is finely tuned to extract structure about the 4D world of time and space as well as properties such as color and texture. Developing intuitions about spatial structure beyond 4D requires exploiting other perceptual and cognitive abilities. One of the most natural ways to explore complex spaces is for a user to actively navigate through them, using local explorations and global summaries to develop intuitions about structure, and then testing the developing ideas by further exploration. This article provides a brief overview of a technique for visualizing surfaces defined over moderate-dimensional binary spaces, by recursively unfolding them onto a 2D hypergraph. We briefly summarize the uses of a freely available Web-based visualization tool, Hyperspace Graph Paper (HSGP), for exploring fitness landscapes and search algorithms in evolutionary computation. HSGP provides a way for a user to actively explore a landscape, from simple tasks such as mapping the neighborhood structure of different points, to seeing global properties such as the size and distribution of basins of attraction or how different search algorithms interact with landscape structure. It has been most useful for exploring recursive and repetitive landscapes, and its strength is that it allows intuitions to be developed through active navigation by the user, and exploits the visual system's ability to detect pattern and texture. The technique is most effective when applied to continuous functions over Boolean variables using 4 to 16 dimensions.

A Correlation Analysis on LSA and HAL Semantic Space Models

In this paper, we compare a well-known semantic spacemodel, Latent Semantic Analysis (LSA) with another model, Hyperspace Analogue to Language (HAL) which is widely used in different area, especially in automatic query refinement. We conduct this comparative analysis to prove our hypothesis that with respect to ability of extracting the lexical information from a corpus of text, LSA is quite similar to HAL. We regard HAL and LSA as black boxes. Through a Pearsonrsquos correlation analysis to the outputs of these two black boxes, we conclude that LSA highly co-relates with HAL and thus there is a justification that LSA and HAL can potentially play a similar role in the area of facilitating automatic query refinement. This paper evaluates LSA in a new application area and contributes an effective way to compare different semantic space models.