Lixin Cui

Quantum kernels for unattributed graphs using discrete-time quantum walks

We propose a new family of quantum kernels using discrete-time quantum walks.We let a quantum walk evolve on each graph and compute a density matrix.We compute the quantum JensenShannon divergence for graph density matrices.The kernel is defined as the negative exponential of the quantum JSD.We also compute the kernel between spanning trees on the original graphs. In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum JensenShannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

P2P Lending Analysis Using the Most Relevant Graph-Based Features

Peer-to-Peer (P2P) lending is an online platform to facilitate borrowing and investment transactions. A central problem for these P2P platforms is how to identify the most influential factors that are closely related to the credit risks. This problem is inherently complex due to the various forms of risks and the numerous influencing factors involved. Moreover, raw data of P2P lending are often high-dimension, highly correlated and unstable, making the problem more untractable by traditional statistical and machine learning approaches. To address these problems, we develop a novel filter-based feature selection method for P2P lending analysis. Unlike most traditional feature selection methods that use vectorial features, the proposed method is based on graph-based features and thus incorporates the relationships between pairwise feature samples into the feature selection process. Since the graph-based features are by nature completed weighted graphs, we use the steady state random walk to encapsulate the main characteristics of the graph-based features. Specifically, we compute a probability distribution of the walk visiting the vertices. Furthermore, we measure the discriminant power of each graph-based feature with respect to the target feature, through the Jensen-Shannon divergence measure between the probability distributions from the random walks. We select an optimal subset of features based on the most relevant graph-based features, through the Jensen-Shannon divergence measure. Unlike most existing state-of-the-art feature selection methods, the proposed method can accommodate both continuous and discrete target features. Experiments demonstrate the effectiveness and usefulness of the proposed feature selection algorithm on the problem of P2P lending platforms in China.

A nested alignment graph kernel through the dynamic time warping framework

In this paper, we propose a novel nested alignment graph kernel drawing on depth-based complexity traces and the dynamic time warping framework. Specifically, for a pair of graphs, we commence by computing the depth-based complexity traces rooted at the centroid vertices. The resulting kernel for the graphs is defined by measuring the global alignment kernel, which is developed through the dynamic time warping framework, between the complexity traces. We show that the proposed kernel simultaneously considers the local and global graph characteristics in terms of the complexity traces, but also provides richer statistic measures by incorporating the whole spectrum of alignment costs between these traces. Our experiments demonstrate the effectiveness and efficiency of the proposed kernel.

Adaptive Feature Selection Based on the Most Informative Graph-Based Features

In this paper, we propose a novel method to adaptively select the most informative and least redundant feature subset, which has strong discriminating power with respect to the target label. Unlike most traditional methods using vectorial features, our proposed approach is based on graph-based features and thus incorporates the relationships between feature samples into the feature selection process. To efficiently encapsulate the main characteristics of the graph-based features, we probe each graph structure using the steady state random walk and compute a probability distribution of the walk visiting the vertices. Furthermore, we propose a new information theoretic criterion to measure the joint relevance of different pairwise feature combinations with respect to the target feature, through the Jensen-Shannon divergence measure between the probability distributions from the random walk on different graphs. By solving a quadratic programming problem, we use the new measure to automatically locate the subset of the most informative features, that have both low redundancy and strong discriminating power. Unlike most existing state-of-the-art feature selection methods, the proposed information theoretic feature selection method can accommodate both continuous and discrete target features. Experiments on the problem of P2P lending platforms in China demonstrate the effectiveness of the proposed method.

Shape classification with a vertex clustering graph kernel

Graph kernels are powerful tools for structural analysis in computer vision. Unfortunately, most existing state-of-the-art graph kernels ignore the locational or structural correspondence information between graphs, based on the visual background. This drawback influences the performance of existing kernels for computer vision based classification problems, e.g., classification of shapes, point clouds and digital images. The aim of this paper is to address the problem with existing kernels, by developing a novel vertex clustering graph kernel. We show that this kernel not only overcomes the shortcoming of ignoring correspondence information between isomorphic substructures that arises in most existing graph kernels, but also guarantees the transitivity between the correspondence information. Our kernel can easily outperform state-of-the-art graph kernels in terms of classification accuracy on standard shape based graph datasets.

Single Image Super Resolution via Neighbor Reconstruction

Super Resolution (SR) is a complex, ill-posed problem where the aim is to construct the mapping between the low and high resolution manifolds of image patches. Anchored neighborhood regression for SR (namely A+ [15]) has shown promising results. In this paper we present a new regression-based SR algorithm that overcomes the limitations of A+ and benefits from an innovative and simple Neighbor Reconstruction Method (NRM). This is achieved by vector operations on an anchored point and its corresponding neighborhood. NRM reconstructs new patches which are closer to the anchor point in the manifold space. Our method is robust to NRM sparsely-sampled points: increasing PSNR by 0.5 dB compared to the next best method. We comprehensively validate our technique on standardised datasets and compare favourably with the state-of-the-art methods: we obtain PSNR improvement of up to 0.21 dB compared to previously-reported work.

Directed Network Analysis Using Transfer Entropy Component Analysis

In this paper, we present a novel method for detecting directed network characteristics using histogram statistics based on degree distribution associated with transfer entropy. The proposed model in this paper established in information theory looks forward to learn the low dimensional representation of sample graphs, which can be obtained by transfer entropy component analysis (TECA) model. In particular, we apply transfer entropy to measure the transfer information between different time series data. For instances, for the fMRI time series data, we can use the transfer entropy to explore the connectivity between different brain functional regions effectively, which plays a significant role in diagnosing Alzheimers disease (AD) and its prodromal stage, mild cognitive impairment (MCI). With the properties of the directed graph in hand, we commence to further encode it into advanced representation of graphs based on the histogram statistics of degree distribution and multilinear principal component analysis (MPCA) technology. It not only reduces the memory space occupied by the huge transfer entropy matrix, but also enables the features to have a stronger representational capacity in the low-dimensional feature space. We conduct a classification experiment on the proposed model for the fMRI time series data. The experimental results verify that our model can significantly improve the diagnosis accuracy for MCI subjects.

A Preliminary Survey of Analyzing Dynamic Time-Varying Financial Networks Using Graph Kernels

In this paper, we investigate whether graph kernels can be used as a means of analyzing time-varying financial market networks. Specifically, we aim to identify the significant financial incident that changes the financial network properties through graph kernels. Our financial networks are abstracted from the New York Stock Exchange (NYSE) data over 6004 trading days, where each vertex represents the individual daily return price time series of a stock and each edge represents the correlation between pairwise series. We propose to use two state-of-the-art graph kernels for the analysis, i.e., the Jensen-Shannon graph kernel and the Weisfeiler-Lehman subtree kernel. The reason of using the two kernels is that they are the representative methods of global graph kernels and local graph kernels, respectively. We perform kernel Principle Components Analysis (kPCA) associated with each kernel matrix to embed the networks into a 3-dimensional principle space, where the time-varying networks of all trading days are visualized. Experimental results on the financial time series of NYSE dataset demonstrate that graph kernels can well distinguish abrupt changes of financial networks with time, and provide a more effective alternative way of analyzing original multiple co-evolving financial time series. We theoretically indicate the perspective of developing novel graph kernels on time-varying networks for multiple co-evolving time series analysis in future work.

A Mixed Entropy Local-Global Reproducing Kernel for Attributed Graphs

In this paper, we develop a new mixed entropy local-global reproducing kernel for vertex attributed graphs based on depth-based representations that naturally reflect both local and global entropy based graph characteristics. Specifically, for a pair of graphs, we commence by computing the nest depth-based representations rooted at the centroid vertices. The resulting mixed local-global reproducing kernel for a pair of graphs is computed by measuring a basic \(H^1\)-reproducing kernel between their nest representations associated with different entropy measures. We show that the proposed kernel not only reflect both the local and global graph characteristics through the nest depth-based representations, but also reflect rich edge connection information and vertex label information through different kinds of entropy measures. Moreover, since both the required basic \(H^1\)-reproducing kernel and the nest depth-based representation can be computed in a polynomial time, the new proposed kernel processes efficient computational complexity. Experiments on standard graph datasets demonstrate the effectiveness and efficiency of the proposed kernel.

Analyzing Time Series from Chinese Financial Market Using a Linear-Time Graph Kernel

Graph-based data has played an important role in representing complex patterns from real-world data, but there is very little work on mining time series with graphs. And those existing graph-based time series mining methods always use well-selected data. In this paper, we investigate a method for extracting graph structures, which contain the structural information that cannot be captured by vector-based data, from the whole Chinese financial time series. We call them time-varying networks, each node in these networks represents the individual time series of a stock and each undirected edge between two nodes represents the correlation between two stocks. We further review a linear-time graph kernel for labeled graphs and show whether the graph kernel, together with time-varying networks, can be used to analyze Chinese financial time series. In the experiments, we apply our method to analyze the whole Chinese Stock Market daily transaction data, i.e., the stock prices data, and use the graph kernel to measure similarities between those extracted networks. Then we compare the performances of our method and other sequence-based or vector-based methods by using kernel principle components analysis to map those results into low dimensional feature space. The experimental results demonstrate the efficiency and effectiveness of our methods together with graph kernels in analyzing Chinese financial time series.