Concept Vector for Similarity Measurement Based on Hierarchical Domain Structure

The concept vector model generalizes standard representations of similarity concept in terms of tree-like structure. In the model, each concept node in the hierarchical tree has ancestor and descendent concept nodes composing its relevancy nodes, thus a concept node is represented as a concept vector according to its relevancy nodes' density and the similarity of the two concepts is obtained by computing cosine similarity between their vectors. In addition, the model is adjusted in terms of local density and multiple descendents problem. The model contains structure information inherent and hidden in the tree. We show that this measure compares favorably to other measures, and it is flexible in that it can make comparisons between any two concepts in a hierarchical tree without relying on additional dictionary or corpus information

Optimal Bounds for Neuman-Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means

We present the best possible lower and upper bounds for the Neuman-Sándor mean in terms of the convex combinations of either the harmonic and quadratic means or the geometric and quadratic means or the harmonic and contraharmonic means