论文标题
稳定的稀疏子空间嵌入尺寸降低
Stable Sparse Subspace Embedding for Dimensionality Reduction
论文作者
论文摘要
稀疏随机投影（RP）是减少维度的流行工具，它显示出有希望的性能，计算复杂性低。但是，在现有的稀疏RP矩阵中，通常会随机选择非零条目的位置。尽管他们采用均匀的替换采样，但由于采样差异很大，但在一个试验中生成的投影矩阵的行中的非零件数量不均匀，并且降低尺寸后可能会丢失更多数据信息。为了基于在统计数据中无需替换的随机采样而打破此瓶颈，本文构建了稳定的稀疏子空间嵌入式矩阵（S-SSE），其中非零零是均匀分布的。事实证明，S-SSE比现有矩阵是稳定器，并且可以在降低尺寸后保持欧几里得之间的距离。我们的经验研究证实了我们的理论发现，并证明我们的方法确实可以实现令人满意的表现。
Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually randomly selected. Although they adopt uniform sampling with replacement, due to large sampling variance, the number of non-zeros is uneven among rows of the projection matrix which is generated in one trial, and more data information may be lost after dimension reduction. To break this bottleneck, based on random sampling without replacement in statistics, this paper builds a stable sparse subspace embedded matrix (S-SSE), in which non-zeros are uniformly distributed. It is proved that the S-SSE is stabler than the existing matrix, and it can maintain Euclidean distance between points well after dimension reduction. Our empirical studies corroborate our theoretical findings and demonstrate that our approach can indeed achieve satisfactory performance.
