论文标题
Wasserstein k均值具有稀疏的单纯形投影
Wasserstein k-means with sparse simplex projection
论文作者
论文摘要
本文通过减少Wasserstein距离计算并利用稀疏的单纯形投影，提出了更快的Wasserstein $ K $ -MEANS算法的建议。我们收缩数据样本，质心和地面成本矩阵，这大大减少了用于解决最佳运输问题而不损失聚类质量的计算。此外，我们通过删除低价值的数据样本并利用稀疏的单纯形投影，在保持聚类质量降低的同时，动态降低了计算复杂性。我们将此提出的算法指定为基于稀疏的单纯形预测的Wasserstein $ K $ -MEANS或SSPW $ K $ -MEANS。与使用Wasserstein $ K $ -MEANS算法获得的结果相比，进行的数值评估证明了拟议的SSPW $ K $ -Means对现实世界数据集的有效性
This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection. We shrink data samples, centroids, and the ground cost matrix, which leads to considerable reduction of the computations used to solve optimal transport problems without loss of clustering quality. Furthermore, we dynamically reduced the computational complexity by removing lower-valued data samples and harnessing sparse simplex projection while keeping the degradation of clustering quality lower. We designate this proposed algorithm as sparse simplex projection based Wasserstein $k$-means, or SSPW $k$-means. Numerical evaluations conducted with comparison to results obtained using Wasserstein $k$-means algorithm demonstrate the effectiveness of the proposed SSPW $k$-means for real-world datasets
