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.

An aligned subtree kernel for weighted graphs

In this paper, we develop a new entropic matching kernel for weighted graphs by aligning depth-based representations. We demonstrate that this kernel can be seen as an aligned subtree kernel that incorporates explicit subtree correspondences, and thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments on standard datasets demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of classification accuracy.

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.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

On the Range and the Kernel of Derivations

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

The kernel is in the least core for permutation games

Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation games the kernel is contained in the least core, even if the latter is a lower dimensional subset of the core. By means of a 5-player permutation game we demonstrate that, in sense of the lexicographic center procedure leading to the nucleolus, this inclusion result can not be strengthened. Our 5-player permutation game is also an example (of minimum size) for a game with a non-convex kernel.

Integrity-based kernel malware detection

Kernel-level malware is one of the most dangerous threats to the security of users on the Internet, so there is an urgent need for its detection. The most popular detection approach is misuse-based detection. However, it cannot catch up with today's advanced malware that increasingly apply polymorphism and obfuscation. In this thesis, we present our integrity-based detection for kernel-level malware, which does not rely on the specific features of malware. ^ We have developed an integrity analysis system that can derive and monitor integrity properties for commodity operating systems kernels. In our system, we focus on two classes of integrity properties: data invariants and integrity of Kernel Queue (KQ) requests. ^ We adopt static analysis for data invariant detection and overcome several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We identify data invariants that are critical to system runtime integrity from Linux kernel 2.4.32 and Windows Research Kernel (WRK) with very low false positive rate and very low false negative rate. We then develop an Invariant Monitor to guard these data invariants against real-world malware. In our experiment, we are able to use Invariant Monitor to detect ten real-world Linux rootkits and nine real-world Windows malware and one synthetic Windows malware. ^ We leverage static and dynamic analysis of kernel and device drivers to learn the legitimate KQ requests. Based on the learned KQ requests, we build KQguard to protect KQs. At runtime, KQguard rejects all the unknown KQ requests that cannot be validated. We apply KQguard on WRK and Linux kernel, and extensive experimental evaluation shows that KQguard is efficient (up to 5.6% overhead) and effective (capable of achieving zero false positives against representative benign workloads after appropriate training and very low false negatives against 125 real-world malware and nine synthetic attacks). ^ In our system, Invariant Monitor and KQguard cooperate together to protect data invariants and KQs in the target kernel. By monitoring these integrity properties, we can detect malware by its violation of these integrity properties during execution.^

Optimal kernel development for real-time communications

The purpose of this research is to develop an optimal kernel which would be used in a real-time engineering and communications system. Since the application is a real-time system, relevant real-time issues are studied in conjunction with kernel related issues. The emphasis of the research is the development of a kernel which would not only adhere to the criteria of a real-time environment, namely determinism and performance, but also provide the flexibility and portability associated with non-real-time environments. The essence of the research is to study how the features found in non-real-time systems could be applied to the real-time system in order to generate an optimal kernel which would provide flexibility and architecture independence while maintaining the performance needed by most of the engineering applications. Traditionally, development of real-time kernels has been done using assembly language. By utilizing the powerful constructs of the C language, a real-time kernel was developed which addressed the goals of flexibility and portability while still meeting the real-time criteria. The implementation of the kernel is carried out using the powerful 68010/20/30/40 microprocessor based systems.

Integrity-Based Kernel Malware Detection

Kernel-level malware is one of the most dangerous threats to the security of users on the Internet, so there is an urgent need for its detection. The most popular detection approach is misuse-based detection. However, it cannot catch up with today's advanced malware that increasingly apply polymorphism and obfuscation. In this thesis, we present our integrity-based detection for kernel-level malware, which does not rely on the specific features of malware. We have developed an integrity analysis system that can derive and monitor integrity properties for commodity operating systems kernels. In our system, we focus on two classes of integrity properties: data invariants and integrity of Kernel Queue (KQ) requests. We adopt static analysis for data invariant detection and overcome several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We identify data invariants that are critical to system runtime integrity from Linux kernel 2.4.32 and Windows Research Kernel (WRK) with very low false positive rate and very low false negative rate. We then develop an Invariant Monitor to guard these data invariants against real-world malware. In our experiment, we are able to use Invariant Monitor to detect ten real-world Linux rootkits and nine real-world Windows malware and one synthetic Windows malware. We leverage static and dynamic analysis of kernel and device drivers to learn the legitimate KQ requests. Based on the learned KQ requests, we build KQguard to protect KQs. At runtime, KQguard rejects all the unknown KQ requests that cannot be validated. We apply KQguard on WRK and Linux kernel, and extensive experimental evaluation shows that KQguard is efficient (up to 5.6% overhead) and effective (capable of achieving zero false positives against representative benign workloads after appropriate training and very low false negatives against 125 real-world malware and nine synthetic attacks). In our system, Invariant Monitor and KQguard cooperate together to protect data invariants and KQs in the target kernel. By monitoring these integrity properties, we can detect malware by its violation of these integrity properties during execution.