In this paper, we show two new variants of multi-view k-means (MVKM) algorithms to address multi-view data. The general idea is to outline the distance between $h$-th view data points $x_i^h$ and $h$-th view cluster centers $a_k^h$ in a different manner of centroid-based approach. Unlike other methods, our proposed methods learn the multi-view data by calculating the similarity using Euclidean norm in the space of Gaussian-kernel, namely as multi-view k-means with exponent distance (MVKM-ED). By simultaneously aligning the stabilizer parameter $p$ and kernel coefficients $\beta^h$, the compression of Gaussian-kernel based weighted distance in Euclidean norm reduce the sensitivity of MVKM-ED. To this end, this paper designated as Gaussian-kernel multi-view k-means (GKMVKM) clustering algorithm. Numerical evaluation of five real-world multi-view data demonstrates the robustness and efficiency of our proposed MVKM-ED and GKMVKM approaches.

翻译：本文提出了两种新的多视图k均值(MVKM)算法变体来解决多视图数据问题。核心思想是以一种不同的基于质心的方法来刻画第$h$个视图数据点$x_i^h$与第$h$个视图聚类中心$a_k^h$之间的距离。与其他方法不同，我们提出的方法通过在高斯核空间中采用欧几里得范数计算相似度来学习多视图数据，即指数距离多视图k均值(MVKM-ED)。通过同时调整稳定参数$p$与核系数$\beta^h$，基于高斯核的加权距离在欧几里得范数下的压缩特性降低了MVKM-ED的敏感性。为此，本文将所提算法命名为高斯核多视图k均值(GKMVKM)聚类算法。在五个真实世界多视图数据集上的数值评估验证了所提出的MVKM-ED和GKMVKM方法的鲁棒性与高效性。