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The $k$-means clustering algorithm is popular but has the following maindrawbacks: 1) the number of clusters, $k$, needs to be provided by the user inadvance, 2) it can easily reach local minima with randomly selected initialcenters, 3) it is sensitive to outliers, and 4) it can only deal with wellseparated hyperspherical clusters. In this paper, we propose a Local DensityPeaks Searching (LDPS) initialization framework to address these issues. TheLDPS framework includes two basic components: one of them is the local densitythat characterizes the density distribution of a data set, and the other is thelocal distinctiveness index (LDI) which we introduce to characterize howdistinctive a data point is compared with its neighbors. Based on these twocomponents, we search for the local density peaks which are characterized withhigh local densities and high LDIs to deal with 1) and 2). Moreover, we detectoutliers characterized with low local densities but high LDIs, and exclude themout before clustering begins. Finally, we apply the LDPS initializationframework to $k$-medoids, which is a variant of $k$-means and chooses datasamples as centers, with diverse similarity measures other than the Euclideandistance to fix the last drawback of $k$-means. Combining the LDPSinitialization framework with $k$-means and $k$-medoids, we obtain two novelclustering methods called LDPS-means and LDPS-medoids, respectively.Experiments on synthetic data sets verify the effectiveness of the proposedmethods, especially when the ground truth of the cluster number $k$ is large.Further, experiments on several real world data sets, Handwritten Pendigits,Coil-20, Coil-100 and Olivetti Face Database, illustrate that our methods givea superior performance than the analogous approaches on both estimating $k$ andunsupervised object categorization.

Effective Deterministic Initialization for $k$-Means-Like Methods via Local Density Peaks Searching