Current data repositories include a variety of data types, including audio, images and time series. State of the art techniques for indexing such data and doing query processing rely on a transformation of data elements into points in a multidimensional feature space. Indexing and query processing then take place in the feature space. We study algorithms for finding relationships among points in multidimensional feature spaces, specifically algorithms for multidimensional joins. Like joins of conventional relations, correlations between multidimensional feature spaces can offer valuable information about the data sets involved. We present several algorithmic paradigms for solving the multidimensional join problem, and we discuss their features and limitations. We propose a generalization of the Size Separation Spatial Join algorithm, named Multidimensional Spatial Join (MSJ), to solve the multidimensional join problem. We evaluate MSJ along with several other specific algorithms, comparing their performance for various dimensionalities on both real and synthetic multidimensional data sets. Our experimental results indicate that MSJ, which is based on space filling curves, consistently yields good performance across a wide range of dimensionalities.
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