Partially Proportional and Adaptive Similarity Indices

A good deal of science and technology concepts and methods rely on comparing and relating entities in quantitative terms. Among the several possible approaches, similarity indices allow some interesting features, especially the ability to quantify how much two entities resemble one another. In this work, the Jaccard similarity for comparing non-zero real-valued vectors is modified so as to estimate similarity while focusing on the distinct parts of the signals. The resulting operator, which is called partially proportional similarity index, not only allows more strict comparisons, but also paves the way to develop an adaptive approach to similarity estimation in which the size and orientation of the comparisons adapt to those of a respective calibration field expressing how the observed features are related to original counterparts. Being a particularly relevant concept in data analysis and modeling, emphasis is placed on presenting and discussing the concept of calibration field and how they can be taken into account while performing similarity comparisons. Several results are described which illustrate the potential of the reported concepts and approaches for enhancing, and even simultaneously normalizing to some extent the representation of entities in terms of their features, as frequently required in scientific modeling and pattern recognition.