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The goal of clustering is to partition a set of data points into groups of similar data points, called clusters. Clustering algorithms can be classified into two categories: hard and soft clustering. Hard clustering assigns each data point to one cluster exclusively. On the other hand, soft clustering allows probabilistic assignments to clusters. In this paper, we propose a new model which combines the benefits of these two models: clarity of hard clustering and probabilistic assignments of soft clustering. Since the majority of data usually have a clear association, only a few points may require a probabilistic interpretation. Thus, we apply the ℓ₁ norm constraint to impose sparsity on probabilistic assignments. Moreover, we also incorporate outlier detection in our clustering model to simultaneously detect outliers which can cause serious problems in statistical analyses. To optimize the model, we introduce an alternating …