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- W2300918803 abstract "This paper investigates a homotopy-based method for embedding with hundreds of thousands of data items that yields a parallel algorithm suitable for running on a distributed system. Current eigenvalue-based embedding algorithms attempt to use a sparsification of the distance matrix to approximate a low-dimensional representation when handling large-scale data sets. The main reason of taking approximation is that it is still hindered by the eigendecomposition bottleneck for high-dimensional matrices in the embedding process. In this study, a homotopy continuation algorithm is applied for improving this embedding model by parallelizing the corresponding eigendecomposition. The eigenvalue solution is converted to the operation of ordinary differential equations with initialized values, and all isolated positive eigenvalues and corresponding eigenvectors can be obtained in parallel according to predicting eigenpaths. Experiments on the real data sets show that the homotopy-based approach is potential to be implemented for millions of data sets." @default.
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- W2300918803 date "2016-01-01" @default.
- W2300918803 modified "2023-10-17" @default.
- W2300918803 title "Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation" @default.
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- W2300918803 doi "https://doi.org/10.1155/2016/5815429" @default.
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