A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

Approximate axial symmetries from continuous time quantum walks

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data. © 2012 Springer-Verlag Berlin Heidelberg.

Information theoretic prototype selection for unattributed graphs

In this paper we propose a prototype size selection method for a set of sample graphs. Our first contribution is to show how approximate set coding can be extended from the vector to graph domain. With this framework to hand we show how prototype selection can be posed as optimizing the mutual information between two partitioned sets of sample graphs. We show how the resulting method can be used for prototype graph size selection. In our experiments, we apply our method to a real-world dataset and investigate its performance on prototype size selection tasks. © 2012 Springer-Verlag Berlin Heidelberg.

Supervised learning of graph structure

Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. In this paper we take a simple yet effective Bayesian approach to attributed graph learning. We present a naïve node-observation model, where we make the important assumption that the observation of each node and each edge is independent of the others, then we propose an EM-like approach to learn a mixture of these models and a Minimum Message Length criterion for components selection. Moreover, in order to avoid the bias that could arise with a single estimation of the node correspondences, we decide to estimate the sampling probability over all the possible matches. Finally we show the utility of the proposed approach on popular computer vision tasks such as 2D and 3D shape recognition. © 2011 Springer-Verlag.

Data Extraction from Carte Du Ciel Triple Images

Carte du Ciel (from French, map of the sky) is a part of a 19th century extensive international astronomical project whose goal was to map the entire visible sky. The results of this vast effort were collected in the form of astrographic plates and their paper representatives that are called astrographic maps and are widely distributed among many observatories and astronomical institutes over the world. Our goal is to design methods and algorithms to automatically extract data from digitized Carte du Ciel astrographic maps. This paper examines the image processing and pattern recognition techniques that can be adopted for automatic extraction of astronomical data from stars’ triple expositions that can aid variable stars detection in Carte du Ciel maps.

A Comparative Analysis of Predictive Learning Algorithms on High-Dimensional Microarray Cancer Data

This research evaluates pattern recognition techniques on a subclass of big data where the dimensionality of the input space (p) is much larger than the number of observations (n). Specifically, we evaluate massive gene expression microarray cancer data where the ratio κ is less than one. We explore the statistical and computational challenges inherent in these high dimensional low sample size (HDLSS) problems and present statistical machine learning methods used to tackle and circumvent these difficulties. Regularization and kernel algorithms were explored in this research using seven datasets where κ < 1. These techniques require special attention to tuning necessitating several extensions of cross-validation to be investigated to support better predictive performance. While no single algorithm was universally the best predictor, the regularization technique produced lower test errors in five of the seven datasets studied.

Handwritten and machine-printed text discrimination using a template matching approach

We propose a novel template matching approach for the discrimination of handwritten and machine-printed text. We first pre-process the scanned document images by performing denoising, circles/lines exclusion and word-block level segmentation. We then align and match characters in a flexible sized gallery with the segmented regions, using parallelised normalised cross-correlation. The experimental results over the Pattern Recognition & Image Analysis Research Lab-Natural History Museum (PRImA-NHM) dataset show remarkably high robustness of the algorithm in classifying cluttered, occluded and noisy samples, in addition to those with significant high missing data. The algorithm, which gives 84.0% classification rate with false positive rate 0.16 over the dataset, does not require training samples and generates compelling results as opposed to the training-based approaches, which have used the same benchmark.

Introduction to data analysis

With the latest development in computer science, multivariate data analysis methods became increasingly popular among economists. Pattern recognition in complex economic data and empirical model construction can be more straightforward with proper application of modern softwares. However, despite the appealing simplicity of some popular software packages, the interpretation of data analysis results requires strong theoretical knowledge. This book aims at combining the development of both theoretical and applicationrelated data analysis knowledge. The text is designed for advanced level studies and assumes acquaintance with elementary statistical terms. After a brief introduction to selected mathematical concepts, the highlighting of selected model features is followed by a practice-oriented introduction to the interpretation of SPSS1 outputs for the described data analysis methods. Learning of data analysis is usually time-consuming and requires efforts, but with tenacity the learning process can bring about a significant improvement of individual data analysis skills.

Signal processing of physiological signals for automated assessment of stress in computer users

The need to provide computers with the ability to distinguish the affective state of their users is a major requirement for the practical implementation of affective computing concepts. This dissertation proposes the application of signal processing methods on physiological signals to extract from them features that can be processed by learning pattern recognition systems to provide cues about a person's affective state. In particular, combining physiological information sensed from a user's left hand in a non-invasive way with the pupil diameter information from an eye-tracking system may provide a computer with an awareness of its user's affective responses in the course of human-computer interactions. In this study an integrated hardware-software setup was developed to achieve automatic assessment of the affective status of a computer user. A computer-based "Paced Stroop Test" was designed as a stimulus to elicit emotional stress in the subject during the experiment. Four signals: the Galvanic Skin Response (GSR), the Blood Volume Pulse (BVP), the Skin Temperature (ST) and the Pupil Diameter (PD), were monitored and analyzed to differentiate affective states in the user. Several signal processing techniques were applied on the collected signals to extract their most relevant features. These features were analyzed with learning classification systems, to accomplish the affective state identification. Three learning algorithms: Naïve Bayes, Decision Tree and Support Vector Machine were applied to this identification process and their levels of classification accuracy were compared. The results achieved indicate that the physiological signals monitored do, in fact, have a strong correlation with the changes in the emotional states of the experimental subjects. These results also revealed that the inclusion of pupil diameter information significantly improved the performance of the emotion recognition system. ^