In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a probabilistic, distance-based, iterative method for clustering data in very high-dimensional space, using the ℓ1-metric that is less sensitive to high dimensionality than the Euclidean distance. For K clusters in ℝ n , the problem decomposes to K problems coupled by probabilities, and an iteration reduces to finding Kn weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

中文翻译：

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高维数据聚类的概率ℓ1方法

一般来说，聚类问题是 NP 难的，不能为非平凡实例建立全局最优性。对于高维数据，基于距离的聚类或分类方法面临一个额外的困难，即非常高维空间中距离的不可靠性。我们提出了一种概率的、基于距离的迭代方法，用于在非常高维空间中对数据进行聚类，使用 ℓ1- 对高维的敏感性低于欧几里得距离的度量。为了ķℝ 中的簇 n , 问题分解为ķ由概率耦合的问题，迭代简化为寻找Kn一条线上点的加权中位数。该算法的复杂度在数据空间的维度上是线性的，并且观察到其性能随着维度的增加而显着提高。