Abstract
Measuring similarities between objects based on their attributes has been an important problem in many disciplines. Object-attribute associations can be depicted as links on a bipartite graph. A similarity measure can be thought as a unipartite projection of this bipartite graph. The most widely used bipartite projection techniques make assumptions that are not often fulfilled in real life systems, or have the focus on the bipartite connections more than on the unipartite connections. Here, we define a new similarity measure that utilizes a practical procedure to extract unipartite graphs without making a priori assumptions about underlying distributions. Our similarity measure captures the relatedness between two objects via the likelihood of a random walker passing through these nodes sequentially on the bipartite graph. An important aspect of the method is that it is robust to heterogeneous bipartite structures and it controls for the transitivity similarity, avoiding the creation of unrealistic homogeneous degree distributions in the resulting unipartite graphs. We test this method using real world examples and compare the obtained results with alternative similarity measures, by validating the actual and orthogonal relations between the entities.
Highlights
An object can be described by its attributes
We compare the performances of all the methods using the experiments described in [19], on the very same dataset extracted from MovieLens and processed as described there
In a second set of experiments, we study the projection of four real-world bipartite graphs
Summary
An object can be described by its attributes. Given a set of objects, it is often desirable to quantify the similarity between any two objects based on the attributes that they possess. One can quantify the likelihood of a person switching occupations based on the task similarities between the occupations. We think of the object attribute associations as a bipartite graph of two types of nodes (i.e., objects and attributes), where a link is present (often with a weight) between an object and the attribute if the object possesses that attribute. The objectobject similarities can be modeled as a unipartite graph. Most of the recent interest in large-scale social, biological, and communication networks has been devoted to unipartite graphs [1,2]. Unipartite graphs are well understood in literature [3]. An impressive number of tools helps us extracting knowledge from such structures
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