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

HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification

In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-sized aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon Divergence (QJSD) between their transitive aligned graph structures. We show that the proposed HAQJSK kernels not only reflect richer intrinsic global graph characteristics in terms of the CTQW, but also address the drawback of neglecting structural correspondence information arising in most existing R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can simultaneously guarantee the properties of permutation invariant and positive definiteness, explaining the theoretical advantages of the HAQJSK kernels. Experiments indicate the effectiveness of the proposed kernels

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

A transitive aligned Weisfeiler-Lehman subtree kernel

In this paper, we develop a new transitive aligned Weisfeiler-Lehman subtree kernel. This kernel not only overcomes the shortcoming of ignoring correspondence information between isomorphic substructures that arises in existing R-convolution kernels, but also guarantees the transitivity between the correspondence information that is not available for existing matching kernels. Our kernel outperforms state-of-the-art graph kernels in terms of classification accuracy on standard graph datasets

Entropic Dynamic Time Warping Kernels for Co-evolving Financial Time Series Analysis

In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the commute time matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop a similarity measure based on the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed similarity measure is positive definite and thus corresponds to a kernel measure on graphs. The proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate the effectiveness of the proposed approach.Comment: Previously, the original version of this manuscript appeared as arXiv:1902.09947v2, that was submitted as a replacement by a mistake. Now, that article has been replaced to correct the error, and this manuscript is distinct from that articl

Quantum kernels for unattributed graphs using discrete-time quantum walks

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 Jensen–Shannon 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

A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondence information that is not available for most existing matching kernels. Third, it incorporates the information of all graphs under comparisons into the kernel computation process, and thus encapsulates richer characteristics. By transductively training the C-SVM classifier, experimental evaluations demonstrate the effectiveness of the new transitive-aligned kernel. The proposed kernel can outperform state-of-the-art graph kernels on standard graph-based datasets in terms of the classification accuracy

RNA 상호작용 및 DNA 서열의 정보해독을 위한 기계학습 기법

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 김선.생물체 간 표현형의 차이는 각 개체의 유전적 정보 차이로부터 기인한다. 유전적 정보의 변화에 따라서, 각 생물체는 서로 다른 종으로 진화하기도 하고, 같은 병에 걸린 환자라도 서로 다른 예후를 보이기도 한다. 이처럼 중요한 생물학적 정보는 대용량 시퀀싱 분석 기법 등을 통해 다양한 오믹스 데이터로 측정된다. 그러나, 오믹스 데이터는 고차원 특징 및 소규모 표본 데이터이기 때문에, 오믹스 데이터로부터 생물학적 정보를 해석하는 것은 매우 어려운 문제이다. 일반적으로, 데이터 특징의 개수가 샘플의 개수보다 많을 때, 오믹스 데이터의 해석을 가장 난해한 기계학습 문제들 중 하나로 만듭니다. 본 박사학위 논문은 기계학습 기법을 활용하여 고차원적인 생물학적 데이터로부터 생물학적 정보를 추출하기 위한 새로운 생물정보학 방법들을 고안하는 것을 목표로 한다. 첫 번째 연구는 DNA 서열을 활용하여 종 간 비교와 동시에 DNA 서열상에 있는 다양한 지역에 담긴 생물학적 정보를 유전적 관점에서 해석해보고자 하였다. 이를 위해, 순위 기반 k 단어 문자열 비교방법, RKSS 커널을 개발하여 다양한 게놈 상의 지역에서 여러 종 간 비교 실험을 수행하였다. RKSS 커널은 기존의 k 단어 문자열 커널을 확장한 것으로, k 길이 단어의 순위 정보와 종 간 공통점을 표현하는 비교기준점 개념을 활용하였다. k 단어 문자열 커널은 k의 길이에 따라 단어 수가 급증하지만, 비교기준점은 극소수의 단어로 이루어져 있으므로 서열 간 유사도를 계산하는 데 필요한 계산량을 효율적으로 줄일 수 있다. 게놈 상의 세 지역에 대해서 실험을 진행한 결과, RKSS 커널은 기존의 커널에 비해 종 간 유사도 및 차이를 효율적으로 계산할 수 있었다. 또한, RKSS 커널은 실험에 사용된 생물학적 지역에 포함된 생물학적 정보량 차이를 생물학적 지식과 부합되는 순서로 비교할 수 있었다. 두 번째 연구는 생물학적 네트워크를 통해 복잡하게 얽힌 유전자 상호작용 간 정보를 해석하여, 더 나아가 생물학적 기능 해석을 통해 암의 아형을 분류하고자 하였다. 이를 위해, 그래프 컨볼루션 네트워크와 어텐션 메커니즘을 활용하여 패스웨이 기반 해석 가능한 암 아형 분류 모델(GCN+MAE)을 고안하였다. 그래프 컨볼루션 네트워크를 통해서 생물학적 사전 지식인 패스웨이 정보를 학습하여 복잡한 유전자 상호작용 정보를 효율적으로 다루었다. 또한, 여러 패스웨이 정보를 어텐션 메커니즘을 통해 해석 가능한 수준으로 병합하였다. 마지막으로, 학습한 패스웨이 레벨 정보를 보다 복잡하고 다양한 유전자 레벨로 효율적으로 전달하기 위해서 네트워크 전파 알고리즘을 활용하였다. 다섯 개의 암 데이터에 대해 GCN+MAE 모델을 적용한 결과, 기존의 암 아형 분류 모델들보다 나은 성능을 보였으며 암 아형 특이적인 패스웨이 및 생물학적 기능을 발굴할 수 있었다. 세 번째 연구는 패스웨이로부터 서브 패스웨이/네트워크를 찾기 위한 연구다. 패스웨이나 생물학적 네트워크에 단일 생물학적 기능이 아니라 다양한 생물학적 기능이 포함되어 있음에 주목하였다. 단일 기능을 지닌 유전자 조합을 찾기 위해서 생물학적 네트워크상에서 조건 특이적인 유전자 모듈을 찾고자 하였으며 MIDAS라는 도구를 개발하였다. 패스웨이로부터 유전자 상호작용 간 활성도를 유전자 발현량과 네트워크 구조를 통해 계산하였다. 계산된 활성도들을 활용하여 다중 클래스에서 서로 다르게 활성화된 서브 패스들을 통계적 기법에 기반하여 발굴하였다. 또한, 어텐션 메커니즘과 그래프 컨볼루션 네트워크를 통해서 해당 연구를 패스웨이보다 더 큰 생물학적 네트워크에 확장하려고 시도하였다. 유방암 데이터에 대해 실험을 진행한 결과, MIDAS와 딥러닝 모델을 다중 클래스에서 차이가 나는 유전자 모듈을 효과적으로 추출할 수 있었다. 결론적으로, 본 박사학위 논문은 DNA 서열에 담긴 진화적 정보량 비교, 패스웨이 기반 암 아형 분류, 조건 특이적인 유전자 모듈 발굴을 위한 새로운 기계학습 기법을 제안하였다.Phenotypic differences among organisms are mainly due to the difference in genetic information. As a result of genetic information modification, an organism may evolve into a different species and patients with the same disease may have different prognosis. This important biological information can be observed in the form of various omics data using high throughput instrument technologies such as sequencing instruments. However, interpretation of such omics data is challenging since omics data is with very high dimensions but with relatively small number of samples. Typically, the number of dimensions is higher than the number of samples, which makes the interpretation of omics data one of the most challenging machine learning problems. My doctoral study aims to develop new bioinformatics methods for decoding information in these high dimensional data by utilizing machine learning algorithms. The first study is to analyze the difference in the amount of information between different regions of the DNA sequence. To achieve the goal, a ranked-based k-spectrum string kernel, RKSS kernel, is developed for comparative and evolutionary comparison of various genomic region sequences among multiple species. RKSS kernel extends the existing k-spectrum string kernel by utilizing rank information of k-mers and landmarks of k-mers that represents a species. By using a landmark as a reference point for comparison, the number of k-mers needed to calculating sequence similarities is dramatically reduced. In the experiments on three different genomic regions, RKSS kernel captured more reliable distances between species according to genetic information contents of the target region. Also, RKSS kernel was able to rearrange each region to match a biological common insight. The second study aims to efficiently decode complex genetic interactions using biological networks and, then, to classify cancer subtypes by interpreting biological functions. To achieve the goal, a pathway-based deep learning model using graph convolutional network and multi-attention based ensemble (GCN+MAE) for cancer subtype classification is developed. In order to efficiently reduce the relationships between genes using pathway information, GCN+MAE is designed as an explainable deep learning structure using graph convolutional network and attention mechanism. Extracted pathway-level information of cancer subtypes is transported into gene-level again by network propagation. In the experiments of five cancer data sets, GCN+MAE showed better cancer subtype classification performances and captured subtype-specific pathways and their biological functions. The third study is to identify sub-networks of a biological pathway. The goal is to dissect a biological pathway into multiple sub-networks, each of which is to be of a single functional unit. To achieve the goal, a condition-specific sub-module detection method in a biological network, MIDAS (MIning Differentially Activated Subpaths) is developed. From the pathway, edge activities are measured by explicit gene expression and network topology. Using the activities, differentially activated subpaths are explored by a statistical approach. Also, by extending this idea on graph convolutional network, different sub-networks are highlighted by attention mechanisms. In the experiment with breast cancer data, MIDAS and the deep learning model successfully decomposed gene-level features into sub-modules of single functions. In summary, my doctoral study proposes new computational methods to compare genomic DNA sequences as information contents, to model pathway-based cancer subtype classifications and regulations, and to identify condition-specific sub-modules among multiple cancer subtypes.Chapter 1 Introduction 1 1.1 Biological questions with genetic information 2 1.1.1 Biological Sequences 2 1.1.2 Gene expression 2 1.2 Formulating computational problems for the biological questions 3 1.2.1 Decoding biological sequences by k-mer vectors 3 1.2.2 Interpretation of complex relationships between genes 7 1.3 Three computational problems for the biological questions 9 1.4 Outline of the thesis 14 Chapter 2 Ranked k-spectrum kernel for comparative and evolutionary comparison of DNA sequences 15 2.1 Motivation 16 2.1.1 String kernel for sequence comparison 17 2.1.2 Approach: RKSS kernel 19 2.2 Methods 21 2.2.1 Mapping biological sequences to k-mer space: the k-spectrum string kernel 23 2.2.2 The ranked k-spectrum string kernel with a landmark 24 2.2.3 Single landmark-based reconstruction of phylogenetic tree 27 2.2.4 Multiple landmark-based distance comparison of exons, introns, CpG islands 29 2.2.5 Sequence Data for analysis 30 2.3 Results 31 2.3.1 Reconstruction of phylogenetic tree on the exons, introns, and CpG islands 31 2.3.2 Landmark space captures the characteristics of three genomic regions 38 2.3.3 Cross-evaluation of the landmark-based feature space 45 Chapter 3 Pathway-based cancer subtype classification and interpretation by attention mechanism and network propagation 46 3.1 Motivation 47 3.2 Methods 52 3.2.1 Encoding biological prior knowledge using Graph Convolutional Network 52 3.2.2 Re-producing comprehensive biological process by Multi-Attention based Ensemble 53 3.2.3 Linking pathways and transcription factors by network propagation with permutation-based normalization 55 3.3 Results 58 3.3.1 Pathway database and cancer data set 58 3.3.2 Evaluation of individual GCN pathway models 60 3.3.3 Performance of ensemble of GCN pathway models with multi-attention 60 3.3.4 Identification of TFs as regulator of pathways and GO term analysis of TF target genes 67 Chapter 4 Detecting sub-modules in biological networks with gene expression by statistical approach and graph convolutional network 70 4.1 Motivation 70 4.1.1 Pathway based analysis of transcriptome data 71 4.1.2 Challenges and Summary of Approach 74 4.2 Methods 78 4.2.1 Convert single KEGG pathway to directed graph 79 4.2.2 Calculate edge activity for each sample 79 4.2.3 Mining differentially activated subpath among classes 80 4.2.4 Prioritizing subpaths by the permutation test 82 4.2.5 Extension: graph convolutional network and class activation map 83 4.3 Results 84 4.3.1 Identifying 36 subtype specific subpaths in breast cancer 86 4.3.2 Subpath activities have a good discrimination power for cancer subtype classification 88 4.3.3 Subpath activities have a good prognostic power for survival outcomes 90 4.3.4 Comparison with an existing tool, PATHOME 91 4.3.5 Extension: detection of subnetwork on PPI network 98 Chapter 5 Conclusions 101 국문초록 127Docto

Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio