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Decomposition-by-Normalization (DBN): Leveraging Approximate Functional Dependencies for Efficient Tensor Decomposition

机译:通过归一化分解(DBN):利用有效的张量分解的近似函数相关性

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For many multi-dimensional data applications, tensor operations as well as relational operations need to be supported throughout the data lifecycle. Although tensor decomposition is shown to be effective for multi-dimensional data analysis, the cost of tensor decomposition is often very high. We propose a novel decomposition-by-normalization scheme that first normalizes the given relation into smaller tensors based on the functional dependencies of the relation and then performs the decomposition using these smaller tensors. The decomposition and recombination steps of the decomposition-by-normalization scheme fit naturally in settings with multiple cores. This leads to a highly efficient, effective, and parallelized decomposition-by-normalization algorithm for both dense and sparse tensors. Experiments confirm the efficiency and effectiveness of the proposed decomposition-by-normalization scheme compared to the conventional nonnegative CP decomposition approach.
机译:对于许多多维数据应用程序,在整个数据生命周期中都需要支持张量操作以及关系操作。尽管张量分解显示对多维数据分析有效,但张量分解的成本通常很高。我们提出了一种新颖的归一化分解方案,该方案首先基于关系的功能依赖性将给定关系归一化为较小的张量,然后使用这些较小的张量执行分解。归一化分解方案的分解和重组步骤自然适用于具有多个核心的设置。这导致针对密集和稀疏张量的高效,有效和并行化的归一化分解算法。实验证实了与常规的非负CP分解方法相比,该归一化分解方案的效率和有效性。

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