将PCA与CEM结合，快速实现高维数据聚类与嵌入
Classification EM-PCA for clustering and embedding
- 用PCA降维并融合到CEM算法中同步完成聚类与嵌入
- 在多个数据集上验证了聚类准确率和嵌入质量的提升
- 适合高维数据的快速聚类与低维表示，适用于图像等场景
混合模型无疑是聚类领域最重要的贡献之一。对于连续数据，高斯模型常被采用，而期望最大化（EM）算法特别适合从数据中估计参数以推断聚类结果。尽管这类模型在图像聚类等多个领域广受欢迎，但仍面临维度灾难和EM算法收敛缓慢的问题。分类期望最大化（CEM）算法作为其分类版本，提供了快速收敛的解决方案，但降维仍是挑战。因此，本文提出一种同时且非顺序地结合数据嵌入与聚类两个任务的算法，融合主成分分析（PCA）与CEM。我们展示了该方法在聚类和数据嵌入方面的有效性，并建立了与其他聚类方法的多种联系。
原文摘要 · Abstract (English)
The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from which clustering is inferred. If these models are particularly popular in various domains including image clustering, they however suffer from the dimensionality and also from the slowness of convergence of the EM algorithm. However, the Classification EM (CEM) algorithm, a classifying version, offers a fast convergence solution while dimensionality reduction still remains a challenge. Thus we propose in this paper an algorithm combining simultaneously and non-sequentially the two tasks --Data embedding and Clustering-- relying on Principal Component Analysis (PCA) and CEM. We demonstrate the interest of such approach in terms of clustering and data embedding. We also establish different connections with other clustering approaches.
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