Abstract.Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that it has comparative performances with the original Silhouette, but is much faster in calculation. Based on our analysis, we conclude that for a given dataset the k-means Cost Function is still the most valid and efficient measure in the evaluation of the validity of k-means clustering with the same k value, but that Simplified Silhouette is more suitable than the original Silhouette in the selection of the best result from k-means clustering with different k values.

This article explores how to build a system for detecting users in a need of attention on ReachOut.com forums. The proposed method uses Tree Kernels over binary Support Vector Machines classification and linear regression, comparing these two machine learning techniques. Predictions from one of these systems were submitted to the CLPsych 2016 Shared Task. Nonetheless, results indicate that it is possible to build an accurate system using only text features without the use of other meta data.

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Abstract:Both 'distance' and 'similarity' measures have been proposed for the comparison of sequences and for the comparison of trees, based on scoring mappings, and the paper concerns the equivalence or otherwise of these. These measures are usually parameterised by an atomic 'cost' table, defining label-dependent values for swaps, deletions and insertions. We look at the question of whether orderings induced by a 'distance' measure, with some cost-table, can be dualized by a 'similarity' measure, with some other cost-table, and vice-versa. Three kinds of orderings are considered: alignment-orderings, for fixed source S and target T , neighbour-orderings, where for a fixed S, varying candidate neighbours T i are ranked, and pair-orderings, where for varying S i , and varying T j , the pairings S i , T j are ranked. We show that (1) alignment-orderings by distance can be dualized by similarity, and vice-versa; (2) neigbour-ordering and pair-ordering by distance can be dualized by similarity; (3) neighbour-ordering and pair-ordering by similarity can sometimes not be dualized by distance. A consequence of this is that there are categorisation and hierarchical clustering outcomes which can be achieved via similarity but not via distance TREE DISTANCE AND SIMILARITYIn many pattern-recognition scenarios the data either takes the form of, or can be encoded as, sequences or trees. Accordingly, there has been much work on the definition, implementation and deployment of measures for the comparison of sequences and for the comparison of trees. These measures are sometimes described as 'distances' and sometimes as 'similarities'. We are concerned in what follows in first distinguishing between these, and then with the question whether orderings induced by a 'distance' measure can be dualized by a 'similarity' measure, and vice-versa. To some extent this can be seen as applying the same kind of analysis to sequence and tree comparison measures as has been applied to set and vector comparison measures (Batagelj and Bren, 1995;Omhover et al., 2005;Lesot and Rifqi, 2010).From statements such as the followingTo compare RNA structures, we need a score system, or alternatively a distance, which measures the similarity (or the difference) between the structures. These two versions of the problem score and distance are equivalent.

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