Compressing high dimensional datasets by fractals

Summary form only given. Fractal technique extensions to general datasets were proposed. The high-dimensional dataset can be viewed as a collection of cells that represent some measure on an integer n-D grid. The measure over different scales along the dimension´s hierarchies may exhibit self-similarities. A two-phase searching strategy was applied to overcome the increased searching time caused by additional dimensions. The search scheme checks a small number of spatially close local domain chunks. The data structure used is defined by 2ⁿ-tree which is a natural extension of quadtree (for image) and cotree (for volume). Each node, corresponding to a range chunk or a domain chunk, contains the summary information used for local matching. The experimental results have shown that the performance of fractal compression is comparable with rivals such as nonlinear model. The experiments over synthetic datasets have shown that the scalability of fractal compression techniques displays self-similar characteristics. To overcome high time complexity caused by additional dimensions, approximate multi-dimensional nearest neighbors searching techniques were presented that run in expected logarithmic time.