In this paper, we propose a novel network representation learning model TransPath to encode heterogeneous information networks (HINs). Traditional network representation learning models aim to learn the embeddings of a homogeneous network. TransPath is able to capture the rich semantic and structure information of a HIN via meta-paths. We take advantage of the concept of translation mechanism in knowledge graph which regards a meta-path, instead of an edge, as a translating operation from the first node to the last node. Moreover, we propose a user-guided meta-path sampling strategy which takes users' preference as a guidance, which could explore the semantics of a path more precisely, and meanwhile improve model efficiency via the avoidance of other noisy and meaningless meta-paths. We evaluate our model on two large-scale real-world datasets DBLP and YELP, and two benchmark tasks similarity search and node classification. We observe that TransPath outperforms other state-of-the-art baselines consistently and significantly.

Dictionary Learning (DL) and Sparse Representation (SR) based Classifier have impacted greatly on the classification performance and has had good recognition rate on image data. In Video Semantic Analysis (VSA), the local structure of video data contains more vital discriminative information needed for classification. However, this has not been fully exploited by the current DL based approaches. Besides, similar coding findings are not being realized from video features with the same video category. Based on the issues stated afore, a novel learning algorithm, called Sparsity based Locality-Sensitive Discriminative Dictionary Learning(SLSDDL) for VSA is proposed in this paper. In the proposed algorithm, a discriminant loss function for the category based on sparse coding of the sparse coefficients is introduced into structure of Locality-Sensitive Dictionary Learning (LSDL) algorithm. Finally, the sparse coefficients for the testing video feature sample are solved by the optimized method of SLSDDL and the classification result for video semantic is obtained by minimizing the error between the original and reconstructed samples. The experiment results show that, the proposed SLSDDL significantly improves the performance of video semantic detection compared with the comparative state-of-the-art approaches. Moreover, the robustness to various diverse environments in video is also demonstrated, which proves the universality of the novel approach.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

Scene classification plays an important role in the intelligent processing of high-resolution satellite (HRS) remotely sensed image. In HRS image classification, multiple features, e.g. shape, color, and texture features, are employed to represent scenes from different perspectives. Accordingly, effective integration of multiple features always results in better performance compared to methods based on a single feature in the interpretation of HRS image. In this paper, we introduce a multi-task joint sparse and low-rank representation model to combine the strength of multiple features for HRS image interpretation. Specifically, a multi-task learning formulation is applied to simultaneously consider sparse and low-rank structure across multiple tasks. The proposed model is optimized as a non-smooth convex optimization problem using an accelerated proximal gradient method. Experiments on two public scene classification datasets demonstrate that the proposed method achieves remarkable performance and improves upon the state-of-art methods in respective applications.

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.