EN FR
EN FR


Section: New Results

Ongoing work

Adaptive Graph Construction

We worked on developing a new algorithm in order to construct a graph in a adaptive way for a specific task. More precisely, we looked for a metric learning algorithm that could depend on the target task. Previous works on metric learning ( [12] ) aim at learning a relevant metric using a linear approach, which cannot capture the non-linearity of the data. Our approach, instead, aims at learning the most appropriate non-linear data projection for the target task. For this purpose, we train a neural network with relative constraints depending on the target task and a target classic metric (e.g. euclidean distance, cosine similarity, ...), in order to make the metric meaningful for the new data representation and our target task.

Correlation Clustering and Similarity/Dissimilarity Links

From a mathematical point of view, signed networks are graphs whose edges carry a sign representing the positive or negative nature of the relationship between the incident nodes. These structures are extremely useful for modeling, at the same time, similarity and dissimilarity object relationships. Given an undirected signed graphs, in the Correlation Clustering problem the goal is to find a node partition into clusters minimizing the number of negative (dissimilarity) edges linking two nodes within the same cluster and the number of positive (similarity) edges between different clusters.

We focused on devising an algorithm able to solve the Correlation Clustering problem for general input signed graphs (if the input is a complete signed graph the problem is proven to be much easier). One of the main objective of this work is the use of the proposed algorithm for creating a learner able to predict the unknown edges signs of a given signed graph. This prediction task is known as Link Classification in signed graphs. In fact, given an undirected signed graph whose edge set is split into training and test set, we could use the Correlation Clustering solution working for general input graphs for partitioning the training set and using the node partition generated for predicting the test edge signs. Moreover, one could exploit such an algorithm for developing new strategies for the Link Classification problem operating within the online and active Machine Learning setting.

Since the node set partitioning turns out to be strictly related to the Link Classification problem, we also focused on the very challenging goal of obtaining a deep understanding of the complex interplay between Link and Node Classification. More precisely, we investigated the relationships between the Vapnik Chervonenkis dimension of any given set of hypothesis space of node and edge similarity functions operating within this framework.

Ranking from Pairwise Sets of User Preferences

Given a set of objects (vertices of a graph) and a set of pairwise preference labels between objects (directed edges connecting vertices) which may be non-transitive due to irrationality or arbitrary noise, what is a correct way to sample preference labels for ordering the set of objects? This long standing open problem is, as far as we know, unsolved when each pairwise preference labels refers to two (disjoint) sets of objects (vertices). This framework can be easily motivated considering that quite often, in many real world contexts, users express their preferences between sets of items rather than single items, and turns out to be strictly connected with our recent model of hypergraphs with bipartite hyperedges [4] . We are working on devising a new algorithm able to rank a given set of items (graph node set) when only comparisons between sets containing at least 2 items are allowed. This challenging and interested problem is, as far as we know, quite novel and can be studied within different Machine Learning setting (online, batch, active, ...). The preliminaries results we are obtaining, when setting the cardinality of the item sets equal to 2, are encouraging and indicate that it could be possible to extend our strategies in order to deal with larger item sets.