Thiago Henrique Cupertino

Optimal structure of complex networks for minimizing traffic congestion

To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.

Chaotic synchronization in general network topology for scene segmentation

Chaotic synchronization has been discovered to be an important property of neural activities, which in turn has encouraged many researchers to develop chaotic neural networks for scene and data analysis. In this paper, we study the synchronization role of coupled chaotic oscillators in networks of general topology. Specifically, a rigorous proof is presented to show that a large number of oscillators with arbitrary geometrical connections can be synchronized by providing a sufficiently strong coupling strength. Moreover, the results presented in this paper not only are valid to a wide class of chaotic oscillators, but also cover the parameter mismatch case. Finally, we show how the obtained result can be applied to construct an oscillatory network for scene segmentation.

Data clustering using controlled consensus in complex networks

Recently, many network-based methods have been developed and successfully applied to cluster data. Once the underlying network has been constructed, a clustering method can be applied over its vertices and edges. In this paper, the concept of pinning control in complex networks is applied to cluster data. Firstly, an adaptive method for constructing sparse and connected networks is proposed. Secondly, a dissimilarity measure is computed via a dynamic system in which vertices are expected to reach a consensus state regarding a reference trajectory. The reference is forced into the system by pinning control. A theoretical analysis was carried out to prove the convergence of the dynamic system under certain parameter constraints. The results using real data sets have showed that the proposed method performs well in the presence of clusters with different sizes and shapes comparing to some well-known clustering methods.

Attack induced cascading breakdown in complex networks

The possibility that a complex network can be brought down by attack on a single or very few nodes through the process of cascading failures is of significant concern. In this paper, we investigate cascading failures in complex networks and uncover a phase-transition phenomenon in terms of the key parameter characterizing the node capacity. For parameter value below the phase-transition point, cascading failures can cause the network to disintegrate almost entirely. Then we show how to design networks of finite capacity that are safe against cascading breakdown. Our theory yields estimates for the maximally achievable network integrity via controlled removal of a small set of low-degree nodes.

Classification of multiple observation sets via network modularity

This paper deals with the classification of multiple pattern observations sets. A set of observations consists of different transformations, possibly including rotation, perspectives and projections. Each set belongs to a single pattern, that is, the pattern is considered invariant under such transformations. The method uses a network representation of the input data to take advantage of the topological relations between the patterns revealed by a low-dimensional manifold. A measurement called modularity is computed to numerically indicate the topological characteristics of the constructed networks. Simulations were carried out in real image data sets, and results have showed that the proposed method outperforms some recent and state-of-the-art techniques.

Using Katz Centrality to Classify Multiple Pattern Transformations

Among the many machine learning methods developed for classification tasks, the network-based learning algorithms made great success. Usually, these methods consist of two stages: the construction of a network from the original vector-based data set and the learning in the constructed network. In this paper, a network concept, called vertex centrality, is used to perform pattern classification. A group of multiple invariant transformations of a same pattern is given and the network classifier must predict the pattern class the group belongs to. The prediction is based on the Katz centrality network measurement. Due to the ability of characterizing topological structure of input patterns, the method has been shown very competitive comparing to some state-of-the-art methods.

Dimensionality reduction with the k-associated optimal graph applied to image classification

In this paper, we aim to study the usage of different network formation methods into a graph embedding framework to perform supervised dimensionality reduction. Images are often high-dimensional patterns, and dimensionality reduction can enhance processing and also increase classification accuracy. Specifically, our technique maps images into networks and constructs two network adjacency matrices to convey information about intra-class components and inter-class penalty connections. Both matrices are inserted into an optimization framework in order to achieve a projection vector that is used to project high-dimension data samples into a low-dimensional space. One advantage of the technique is that no parameter is required, that is, there is no need to select a model for the input data. Applications on handwritten digits recognition are performed, and the proposed technique is compared to some classical network formation methods. Numerical results show the approach is promising.

Network-based supervised data classification by using an heuristic of ease of access

We propose a new supervised classification technique which considers the ease of access of unlabeled instances to training classes through an underlying network. The training data set is used to construct a network, in which instances (nodes) represent the states that a random walker visits, and the network link structure is modified by performing a link weight composition between the unlabeled instance bias and the initial network link weights. Different from traditional classification heuristics, which divide the training data set into subspaces, the proposed scheme uses random walk limiting probabilities to measure the limiting state transitions among training nodes. An unlabeled instance receives the label of the class that is most easily reached by the random walker, that is, the limiting transition to that class is large. Simulation results suggest that the proposed technique is comparable to some well-known classification techniques.

K-associated optimal network for graph embedding dimensionality reduction

In machine learning, dimensionality reduction aims at reducing the dimension of the input data in order to achieve a small set of features that keeps the most important original relationships among data samples. In this paper, we investigate the usage of a non-parametric network formation algorithm into a graph embedding framework to perform supervised dimensionality reduction. Specifically, our technique maps data into networks and constructs two network adjacency matrices which convey information about intra-class components and inter-class penalty connections. Both matrices are inserted into an optimization framework in order to achieve a projection vector that is used to project high-dimension data samples into a low-dimensional space. One advantage of the technique is that no parameter is required, that is, there is no need to select a model for the input data. Computer simulations on real-world data sets have been performed to compare the proposed technique to some classical network formation methods such as k-NN and e-radius, and to well-known dimensionality reduction algorithms such as PCA and LDA. Statistical tests have shown that our approach outperforms those algorithms.

Using Interacting Forces to Perform Semi-supervised Learning

Semi-Supervised Learning (SSL) is a learning paradigm in which the classification task is performed by taking into account just a few labeled instances. The unlabeled instances also participate in the process, but by providing additional information about the dataset. In this paper, a new semi-supervised technique based on interacting forces is proposed. Both labeled and unlabeled instances play different roles in the proposed mechanism: the labeled instances perform attraction forces over the unlabeled instances to accomplish label propagation. Inside a defined neighborhood, a label in able to propagates to an unlabeled instance. The technique mainly takes into account two important SSL assumptions: smoothness and cluster. Results obtained from simulations performed on artificial and real datasets exhibit the effectiveness of the proposed method.