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Based on an effective clustering algorithm—Affinity Propagation (AP)—we present in this paper a novel semisupervised text clustering algorithm, called Seeds Affinity Propagation (SAP). There are two main contributions in our approach: 1) a new similarity metric that captures the structural information of texts, and 2) a novel seed construction method to improve the semisupervised clustering process. To study the performance of the new algorithm, we applied it to the benchmark data set Reuters-21578 and compared it to two state-of-the-art clustering algorithms, namely, k-means algorithm and the original AP algorithm. Furthermore, we have analyzed the individual impact of the two proposed contributions. Results show that the proposed similarity metric is more effective in text clustering (F-measures ca. 21 percent higher than in the AP algorithm) and the proposed semisupervised strategy achieves both better clustering results and faster convergence (using only 76 percent iterations of the original AP). The complete SAP algorithm obtains higher F-measure (ca. 40 percent improvement over k-means and AP) and lower entropy (ca. 28 percent decrease over k-means and AP), improves significantly clustering execution time (20 times faster) in respect that k-means, and provides enhanced robustness compared with all other methods. [ABSTRACT FROM PUBLISHER]

Given a set of points P and a query set Q, a group enclosing query (Geq) fetches the point p* â P such that the maximum distance of p* to all points in Q is minimized. This problem is equivalent to the Min-Max case (minimizing the maximum distance) of aggregate nearest neighbor queries for spatial databases [27]. This work first designs a new exact solution by exploring new geometric insights, such as the minimum enclosing ball, the convex hull, and the furthest voronoi diagram of the query group. To further reduce the query cost, especially when the dimensionality increases, we turn to approximation algorithms. Our main approximation algorithm has a worst case \sqrt2-approximation ratio if one can find the exact nearest neighbor of a point. In practice, its approximation ratio never exceeds 1.05 for a large number of data sets up to six dimensions. We also discuss how to extend it to higher dimensions (up to 74 in our experiment) and show that it still maintains a very good approximation quality (still close to 1) and low query cost. In fixed dimensions, we extend the \sqrt2-approximation algorithm to get a (1 + ε)-approximate solution for the Geq problem. Both approximation algorithms have O(\log N + M) query cost in any fixed dimension, where N and M are the sizes of the data set P and query group Q. Extensive experiments on both synthetic and real data sets, up to 10 million points and 74 dimensions, confirm the efficiency, effectiveness, and scalability of the proposed algorithms, especially their significant improvement over the state-of-the-art method. [ABSTRACT FROM AUTHOR]