In this investigation, we discuss high order data structure (called tensor) for efficient information retrieval and show especially how well reduction techniques of dimensionality goes while preserving Euclid distance between information. High order data structure requires much amount of space. One of the effective approaches comes from dimensionality reduction such as Latent Semantic Indexing (LSI) and Random Projection (RP) which allows us to reduce complexity of time and space dramatically. The reduction techniques can be applied to high order data structure. Here we examine High Order Random Projection (HORP) which provides us with efficient information retrieval keeping feasible dimensionality reduction.
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