A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Positive definite indistinguishability operators

Peer ReviewedPostprint (author's final draft

Learning valued relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval

Changes in connectivity patterns in the kainate model of epilepsy

Epilepsy is a neurological disorder characterized by seizures, i.e. excessive and hyper synchronous activity of neurons in the brain. ElectroEncephaloGram (EEG) is the recording of brain activity in time through electrodes placed on the scalp and is one of the most used techniques to monitor brain activity. In order to identify pattern of propagation across brain areas that are specific to epilepsy, connectivity measures such as the Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC) have been developed. These measures reveal connections between different areas by exploiting statistical dependencies within multichannel EEG recordings. This work proposes a framework to identify and compare interdependencies between EEG signals in different brain states. We considered an animal model of epilepsy characterized by spontaneous recurrent seizures. In three rats we identified a normal healthy baseline state and an epileptic state for which we estimated interdependencies between EEG channels using DTF and PDC and extracted significant differences between both states. We showed the feasibility of detection of connectivity patterns in a simple animal model of epilepsy. We found common patterns of propagation in the brain of the three rats during the baseline state. After the kainic acid injection, the connectivity pattern of interictal period is significantly altered compared to the baseline situation. Inter-rat variations are observed, but the intra-rat pattern alterations are consistent in time, revealing that the kainic acid permanently changes the brain connectivity

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications