The contribution of this paper is twofold. First, it introduces a generalized framework where sparsity is imposed to a well-known class of cost-function optimization possibilistic algorithms. In addition, under mild conditions, the algorithms in this framework have the ability to determine the number of the true clusters, starting from an overestimation of it. Second, it proposes a new algorithm that is proved to belong to the above framework, which is able to cope with linearly shaped clusters in the two-dimensional space. The algorithm employs (finite) line segments as cluster representatives and the distance of a data point from a cluster is defined as its distance from the corresponding representative line segment. In contrast to several relative algorithms, the proposed algorithm is able to identify intersecting linear clusters as well as to discriminate between collinear clusters. Finally, the experimental results that assess the performance of the proposed algorithm are provided.

中文翻译：

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在可能性聚类中引入稀疏性：统一框架和线检测范式

本文的贡献是双重的。首先，它引入了一个广义框架，其中将稀疏性强加给一类众所周知的成本函数优化可能性算法。此外，在温和的条件下，该框架中的算法有能力确定真实集群的数量，从高估开始。其次，它提出了一种新算法，该算法被证明属于上述框架，能够处理二维空间中线性形状的簇。该算法采用（有限）线段作为簇代表，数据点与簇的距离定义为它与对应的代表线段的距离。与几种相关算法相比，所提出的算法能够识别相交的线性簇以及区分共线簇。最后，提供了评估所提出算法性能的实验结果。