Similarity for heterogeneous networks


We propose a generalization of SimRank similarity measure for heterogeneous information networks. Each node is associated with a set of objects and there are different possible relations. This is encoded into the adjacency tensor, and the TensorSimRank equation is given as

$$s_{\alpha \beta} = \sum_{\gamma} w_{\alpha \beta \gamma} r_{\alpha \beta \gamma} s_{\alpha \beta} r_{\beta \alpha \gamma}, \quad s_{\alpha \alpha} = 1.$$

This equation generalizes the classical SimRank similarity measure. The simple iteration combined with low-rank approximation of \(S\) was proposed as a computational algorithm.
The model was tested both on synthetic datasets and a real Book-Crossing Dataset. The final network has the structure (Book, Author, Year, Publisher), and an example of a “closest book” request to the Psychic Sisters is given in the Table below.

Psychic Sisters (Sweet Valley Twins and Friends, No 70)
The Love Potion (Sweet Valley Twins and Friends, No 72)
The Curse of the Ruby Necklace (Sweet Valley Twins and Friends Super, No 5)
She’s Not What She Seems (Sweet Valley High No. 92)
Are We in Love? (Sweet Valley High, No 94)
Don’t Go Home With John (Sweet Valley High No. 90)
In Love With a Prince (Sweet Valley High, No 91)


26/05/2016 A TT-eigenvalue solver that finally works Papers
12/05/2016 Exponential machines and tensor trains Papers
06/04/2016 Convergence analysis of a projected fixed-point iteration Papers
30/03/2016 Compress-and-eliminate solver for sparse matrices Papers
01/12/2015 New paper in SIMAX Papers


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