Beyza Ermis

Link prediction in heterogeneous data via generalized coupled tensor factorization

This study deals with missing link prediction, the problem of predicting the existence of missing connections between entities of interest. We approach the problem as filling in missing entries in a relational dataset represented by several matrices and multiway arrays, that will be simply called tensors. Consequently, we address the link prediction problem by data fusion formulated as simultaneous factorization of several observation tensors where latent factors are shared among each observation. Previous studies on joint factorization of such heterogeneous datasets have focused on a single loss function (mainly squared Euclidean distance or Kullback–Leibler-divergence) and specific tensor factorization models (CANDECOMP/PARAFAC and/or Tucker). However, in this paper, we study various alternative tensor models as well as loss functions including the ones already studied in the literature using the generalized coupled tensor factorization framework. Through extensive experiments on two real-world datasets, we demonstrate that (i) joint analysis of data from multiple sources via coupled factorization significantly improves the link prediction performance, (ii) selection of a suitable loss function and a tensor factorization model is crucial for accurate missing link prediction and loss functions that have not been studied for link prediction before may outperform the commonly-used loss functions, (iii) joint factorization of datasets can handle difficult cases, such as the cold start problem that arises when a new entity enters the dataset, and (iv) our approach is scalable to large-scale data.

Generalized coupled symmetric tensor factorization for link prediction

This study deals with the missing link prediction, the problem of predicting the existence of missing connections between entities of interest. Link prediction is addressed using coupled analysis of relational datasets represented by several matrices, including symmetric ones and multiway arrays, that will be simply called tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation (GCTF), which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with common latent factors using different loss functions. In addition, we propose the algorithm for factorization of symmetric matrices. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation and integration of symmetric matrices to models improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links.

Learning mixed divergences in coupled matrix and tensor factorization models

Coupled tensor factorization methods are useful for sensor fusion, combining information from several related datasets by simultaneously approximating them by products of latent tensors. In these methods, the choice of a suitable optimization criteria becomes difficult as observed datasets may have different statistical characteristics and their relative importance for the task at hand can vary. In this paper, we present an algorithmic framework for coupled factorization that, while estimating a latent factorization also estimates a specific ß-divergence for each dataset as well as the relative weights in an overall additive cost function. We evaluate the proposed method on both synthetical and real datasets, where we apply our methods on a link prediction problem. The results show that our method outperforms the state-of-the-art by a significant margin.