Lorenzo Livi

The graph matching problem

In this paper, we propose a survey concerning the state of the art of the graph matching problem, conceived as the most important element in the definition of inductive inference engines in graph-based pattern recognition applications. We review both methodological and algorithmic results, focusing on inexact graph matching procedures. We consider different classes of graphs that are roughly differentiated considering the complexity of the defined labels for both vertices and edges. Emphasis will be given to the understanding of the underlying methodological aspects of each identified research branch. A selection of inexact graph matching algorithms is proposed and synthetically described, aiming at explaining some significant instances of each graph matching methodology mainly considered in the technical literature.

Optimized dissimilarity space embedding for labeled graphs

This paper introduces a new general-purpose classification system able to face automatically a wide range of classification problems for labeled graphs. The proposed graph classifier explicitly embeds the input labeled graphs using the dissimilarity representation framework. We developed a method to optimize the dissimilarity space representation estimating the quadratic Renyi entropy of the underlying distribution of the generated dissimilarity values. The global optimization governing the synthesis of the classifier is implemented using a genetic algorithm and it is carried out by means of two operations that perform prototype selection and extraction on the input set of graphs. During the optimization step, we adopted a suitable objective function which includes the classification accuracy achieved by the whole classification model on a validation set. Experimental evaluations have been conducted on both synthetic and well-known benchmarking datasets, achieving competitive test set classification accuracy results with respect to other state-of-the-art graph embedding based classification systems.

A Granular Computing approach to the design of optimized graph classification systems

Research on Graph-based pattern recognition and Soft Computing systems has attracted many scientists and engineers in several different contexts. This fact is motivated by the reason that graphs are general structures able to encode both topological and semantic information in data. While the data modeling properties of graphs are of indisputable power, there are still different concerns about the best way to compute similarity functions in an effective and efficient manner. To this end, suited transformation procedures are usually conceived to address the well-known Inexact Graph Matching problem in an explicit embedding space. In this paper, we propose two graph embedding algorithms based on the Granular Computing paradigm, which are engineered as key procedures of a general-purpose graph classification system. Tests have been conducted on benchmarking datasets relying on both synthetic and real-world data, achieving competitive results in terms of test set classification accuracy.

Modeling and recognition of smart grid faults by a combined approach of dissimilarity learning and one-class classification

Detecting faults in electrical power grids is of paramount importance, both from the electricity operator and consumer point of view. Modern electric power grids (smart grids) are equipped with smart sensors that allow to gather real-time information regarding the physical status of all components belonging to the whole infrastructure (e.g., cables and related insulation, transformers, and breakers). In real-world smart grid systems, usually, additional information that are related to the operational status of the grid are collected, such as meteorological information. Designing an efficient recognition model to discriminate faults in real-world smart grid system is hence a challenging task. This follows from the heterogeneity of the information that actually determine a typical fault condition. In this paper, we deal with the problem of modeling and recognizing faults in a real-world smart grid system, which supplies the entire city of Rome, Italy. Recognition of faults is addressed by following a combined approach of dissimilarity measures learning and one-class classification techniques. We provide here an in-depth study related to the available data and to the models based on the proposed one-class classification approach. Furthermore, we perform a comprehensive analysis of the fault recognition results by exploiting a fuzzy set based decision rule.

Interval type-2 fuzzy sets to model linguistic label perception in online services satisfaction

In this paper, we propose a novel two-phase methodology based on interval type-2 fuzzy sets (T2FSs) to model the human perceptions of the linguistic terms used to describe the online services satisfaction. In the first phase, a type-1 fuzzy set (T1FS) model of an individual’s perception of the terms used in rating user satisfaction is derived through a decomposition-based procedure. The analysis is carried out by using well-established metrics and results from the Social Sciences context. In the second phase, interval T2FS models of online user satisfaction are calculated using a similarity-based data mining procedure. The procedure selects an essential and informative subset of the initial T1FSs that is used to discard the outliers automatically. Resulting interval T2FSs, which are synthesized based on the selected subset of T1FSs only, exhibit reasonable shapes and interpretability.

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.

Investigating Echo-State Networks Dynamics by Means of Recurrence Analysis

In this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called , is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem.

Entropic One-Class Classifiers

The one-class classification problem is a well-known research endeavor in pattern recognition. The problem is also known under different names, such as outlier and novelty/anomaly detection. The core of the problem consists in modeling and recognizing patterns belonging only to a so-called target class. All other patterns are termed nontarget, and therefore, they should be recognized as such. In this paper, we propose a novel one-class classification system that is based on an interplay of different techniques. Primarily, we follow a dissimilarity representation-based approach; we embed the input data into the dissimilarity space (DS) by means of an appropriate parametric dissimilarity measure. This step allows us to process virtually any type of data. The dissimilarity vectors are then represented by weighted Euclidean graphs, which we use to determine the entropy of the data distribution in the DS and at the same time to derive effective decision regions that are modeled as clusters of vertices. Since the dissimilarity measure for the input data is parametric, we optimize its parameters by means of a global optimization scheme, which considers both mesoscopic and structural characteristics of the data represented through the graphs. The proposed one-class classifier is designed to provide both hard (Boolean) and soft decisions about the recognition of test patterns, allowing an accurate description of the classification process. We evaluate the performance of the system on different benchmarking data sets, containing either feature-based or structured patterns. Experimental results demonstrate the effectiveness of the proposed technique.

Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions

In this paper, we deal with the problem of classification of interval type-2 fuzzy sets through evaluating their distinguishability. To this end, we exploit a general matching algorithm to compute their similarity measure. The algorithm is based on the aggregation of two core similarity measures applied independently on the upper and lower membership functions of the given pair of interval type-2 fuzzy sets that are to be compared. Based on the proposed matching procedure, we develop an experimental methodology for evaluating the distinguishability of collections of interval type-2 fuzzy sets. Experimental results on evaluating the proposed methodology are carried out in the context of classification by considering interval type-2 fuzzy sets as patterns of suitable classification problem instances. We show that considering only the upper and lower membership functions of interval type-2 fuzzy sets is sufficient to (i) accurately discriminate between them and (ii) judge and quantify their distinguishability.

Combining Graph Seriation and Substructures Mining for Graph Recognition

Many interesting applications of Pattern Recognition techniques can take advantage in dealing with labeled graphs as input patterns. To this aim, the most important issue is the definition of a dissimilarity measure between graphs. In this paper, we outline an ensemble of methods for dealing with such data, focusing on two specific methods. The first one is simply based on a global alignment approach applied to seriated versions of the graphs. The second one is a twostages method, which applies a recurrent substructures analysis to the seriated graphs, individuating a set of frequent subsequences, employed for embedding the graphs into a real valued feature vector space. Tests have been performed by synthetically generating a set of classification problem instances with increasing problem hardness, and with a shared benchmarking database of labeled graphs.