We run experiments showing that algorithm clarans (, 2005) finds better K-medoids solutions than the Voronoi iteration algorithm. This finding, along with the similarity between the Voronoi iteration algorithm and Lloyd's K-means algorithm, suggests that clarans may be an effective K-means initializer. We show that this is the case, with clarans outperforming other seeding algorithms on 23 23 datasets with a mean decrease over K-means++ of 30 for initialization mse and 3 or final mse. We describe how the complexity and runtime of clarans can be improved, making it a viable initialization scheme for large datasets.
The work most similar to in the @math -means setting is that of @cite_3 , where it is indirectly shown that finds a solution within a factor 25 of the optimal @math -medoids clustering. The local search approximation algorithm they propose is a hybrid of and , alternating between the two, with sampling from a kd-tree during the -like step. Their source code includes an implementation of an algorithm they call Swap', which is exactly the algorithm of @cite_1 .
@cite_1 @cite_3
2083620785 2028788183 1508404128 2107105629
This paper proposes a new algorithm for K-medoids clustering which runs like the K-means algorithm and tests several methods for selecting initial medoids. The proposed algorithm calculates the distance matrix once and uses it for finding new medoids at every iterative step. To evaluate the proposed algorithm, we use some real and artificial data sets and compare with the results of other algorithms in terms of the adjusted Rand index. Experimental results show that the proposed algorithm takes a significantly reduced time in computation with comparable performance against the partitioning around medoids. In this paper, we propose a video summarization algorithm by multiple extractions of key frames in each shot. This algorithm is based on the k-medoid clustering algorithms to find the best representative frame for each video shot. This algorithm, which is applicable to all types of descriptors, consists of extracting key frames by similarity clustering according to the given index. In our proposal, the distance between frames is calculated using a fast full search block matching algorithm based on the frequency domain. The proposed approach is computationally tractable and robust with respect to sudden changes in mean intensity within a shot. Additionally, this approach produces different key frames even in the presence of large motion. The experiments results show that our algorithm extracts multiple representatives frames in each video shot without visual redundancy, and thus it is an effective tool for video indexing and retrieval. We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under- and over-fragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories. Various approaches for keyword proximity search have been implemented in relational databases, XML and the Web. Yet, in all of them, an answer is a Q-fragment, namely, a subtree T of the given data graph G, such that T contains all the keywords of the query Q and has no proper subtree with this property. The rank of an answer is inversely proportional to its weight. Three problems are of interest: finding an optimal (i.e., top-ranked) answer, computing the top-k answers and enumerating all the answers in ranked order. It is shown that, under data complexity, an efficient algorithm for solving the first problem is sufficient for solving the other two problems with polynomial delay. Similarly, an efficient algorithm for finding a θ-approximation of the optimal answer suffices for carrying out the following two tasks with polynomial delay, under query-and-data complexity. First, enumerating in a (θ+1)-approximate order. Second, computing a (θ+1)-approximation of the top-k answers. As a corollary, this paper gives the first efficient algorithms, under data complexity, for enumerating all the answers in ranked order and for computing the top-k answers. It also gives the first efficient algorithms, under query-and-data complexity, for enumerating in a provably approximate order and for computing an approximation of the top-k answers.