The HIM glocal metric and kernel for network comparison and classification

Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via quite different strategies, even tailored ad-hoc for the investigated problem. Here we deal with both operations by introducing the Hamming-Ipsen-Mikhailov (HIM) distance, a novel metric to quantitatively measure the difference between two graphs sharing the same vertices. The new measure combines the local Hamming distance and the global spectral Ipsen-Mikhailov distance so to overcome the drawbacks affecting the two components separately. Building then the HIM kernel function derived from the HIM distance it is possible to move from network comparison to network classification via the Support Vector Machine (SVM) algorithm. Applications of HIM distance and HIM kernel in computational biology and social networks science demonstrate the effectiveness of the proposed functions as a general purpose solution.Comment: Frontiers of Network Analysis: Methods, Models, and Applications - NIPS 2013 Worksho

Metric projection for dynamic multiplex networks

Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time series is still an open problem. Here we propose a two-steps strategy to tackle this problem based on the concept of distance (metric) between networks. Given a multiplex graph, first a network of networks is built for each time steps, and then a real valued time series is obtained by the sequence of (simple) networks by evaluating the distance from the first element of the series. The effectiveness of this approach in detecting the occurring changes along the original time series is shown on a synthetic example first, and then on the Gulf dataset of political events

How much do we know about the User-Item Matrix?: Deep Feature Extraction for Recommendation

Collaborative filtering-based recommender systems typically operate on a high-dimensional sparse user-item matrix. Matrix completion is one of the most common formulations where rows and columns represent users and items, and predicting user’s ratings in items corresponds to filling in the missing entries of the matrix. In practice, it is a very challenging task to predict one's interest based on millions of other users having each seen a small subset of thousands of items. We considered how to extract the key features of users and items in the rating matrix to capture their features in a low-dimensional vector and how to create embeddings that well represent the characteristics of users and items by exploring what kind of user/item information to use in the matrix. However, recent studies have focused on utilising side information, such as user's age or movie's genre, but it is not always available and is hard to extract. More importantly, there has been no recent research on how to efficiently extract the important latent features from a sparse data matrix with no side information (1st problem). The next (2nd) problem is that most matrix completion techniques have mainly focused on semantic similarity between users and items with data structure transformation from a rating matrix to a user/item similarity matrix or a graph, neglecting the position of each element (user, item and rating) in the matrix. However, we think that a position is one of the fundamental points in matrix completion, since a specific point to be filled is presented based on the positions of its row and column in the matrix. In order to address the first (1st) problem, we aim to generalise and represent a high-dimensional sparse user-item matrix entry into a low-dimensional space with a small number of important features, and propose a Global-Local Kernel-based matrix completion framework, named GLocal-K, which is divided into two major stages. First, we pre-train an autoencoder with the local kernelised weight matrix, which transforms the data from one space into the feature space by using a 2d-RBF kernel. Then, the pre-trained autoencoder is fine-tuned with the rating matrix, produced by a convolution-based global kernel, which captures the characteristics of each item. GLocal-K outperforms the state-of-the-art baselines on three collaborative filtering benchmarks. However, it cannot show its superior feature extraction ability when the data is very large or too extremely sparse. For the aforementioned second (2nd) problem and the GLocal-K's limitation, we propose a novel position-enhanced user/item representation training model for recommendation, SUPER-Rec. We first capture the rating position in a matrix using relative positional rating encoding and store the position-enhanced rating information and its user-item relationship to a fixed dimension of embedding that is not affected by the matrix size. Then, we apply the trained position-enhanced user and item representations to the simplest traditional machine learning models to highlight the pure novelty of the SUPER-Rec representation. We contribute to the first formal introduction and quantitative analysis of the position-enhanced user/item representation in the recommendation domain and produce a principled discussion about SUPER-Rec with the incredibly excellent RMSE/MAE/NDCG/AUC results (i.e., both rating and ranking prediction accuracy) by an enormous margin compared with various state-of-the-art matrix completion models on both explicit and implicit feedback datasets. For example, SUPER-Rec showed the 28.2% RMSE error decrease in ML-1M compared to the best baseline, while the error decrease by 0.3% to 4.1% was prevalent among all the baselines

Learn to Generate Time Series Conditioned Graphs with Generative Adversarial Nets

Deep learning based approaches have been utilized to model and generate graphs subjected to different distributions recently. However, they are typically unsupervised learning based and unconditioned generative models or simply conditioned on the graph-level contexts, which are not associated with rich semantic node-level contexts. Differently, in this paper, we are interested in a novel problem named Time Series Conditioned Graph Generation: given an input multivariate time series, we aim to infer a target relation graph modeling the underlying interrelationships between time series with each node corresponding to each time series. For example, we can study the interrelationships between genes in a gene regulatory network of a certain disease conditioned on their gene expression data recorded as time series. To achieve this, we propose a novel Time Series conditioned Graph Generation-Generative Adversarial Networks (TSGG-GAN) to handle challenges of rich node-level context structures conditioning and measuring similarities directly between graphs and time series. Extensive experiments on synthetic and real-word gene regulatory networks datasets demonstrate the effectiveness and generalizability of the proposed TSGG-GAN

Multiple Tasks are Better than One: Multi-task Learning and Feature Selection for Head Pose Estimation, Action Recognition and Event Detection

Computer vision is a field that includes methods for acquiring, processing, analyzing, and understanding images and videos and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information. The classical problem in computer vision is that of determining whether or not the image or video data contains some specific object, feature, or activity. This task can normally be solved robustly and without effort by a human, but is still not satisfactorily solved in computer vision for the general case - arbitrary objects in arbitrary situations. The existing methods for dealing with this problem can at best solve it only for specific objects, such as simple geometric objects (e.g., polyhedra), human faces, printed or hand-written characters, or vehicles, and in specific situations, typically described in terms of well-defined illumination, background, and pose of the object relative to the camera. Machine Learning (ML) and Computer Vision (CV) have been put together during the development of computer vision in the past decade. Nowadays, machine learning is considered as a powerful tool to solve many computer vision problems. Multi-task learning, as one important branch of machine learning, has developed very fast during the past decade. Multi-task learning methods aim to simultaneously learn classification or regression models for a set of related tasks. This typically leads to better models as compared to a learner that does not account for task relationships. The goal of multi-task learning is to improve the performance of learning algorithms by learning classifiers for multiple tasks jointly. This works particularly well if these tasks have some commonality and are generally slightly under-sampled

A Systematic Survey on Deep Generative Models for Graph Generation

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to its wide range of applications, generative models for graphs have a rich history, which, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for the graph generation. Firstly, the formal definition of deep generative models for the graph generation as well as preliminary knowledge is provided. Secondly, two taxonomies of deep generative models for unconditional, and conditional graph generation respectively are proposed; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted