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Spectral Embedding is one of the most effective dimension reduction algorithms in data mining. However, its computation complexity has to be mitigated in order to apply it for real-world large scale data analysis. Many researches have been focusing on developing approximate spectral embeddings which are more efficient, but meanwhile far less effective. This paper proposes Diverse Power Iteration Embeddings...
Detecting anomaly nodes from graphs is an important objective in many applications ranging from social networks to World Wide Web. Recently several methods have been proposed to address this problem. A limitation of most of these methods is that they are based on the random walk of the graph, and often fail to be effective. In this paper, we propose a new framework to detect anomaly nodes within a...
Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new method based on bootstrapping to reduce the bias in the sample eigenvalues: the eigenvalue estimates are...
In this paper, we define an online algorithm to learn the generalized cosine similarity measures for k-NN classification and hence a similarity matrix A corresponding to a bilinear form. In contrary to the standard cosine measure, the normalization is itself dependent on the similarity matrix which makes it impossible to use directly the algorithms developed for learning Mahanalobis distances, based...
This paper proposes a novel algorithm, named pseudo-inverse locality preserving projections (PLPP), for dimensionality reduction involving undersampled problems. This algorithm considers the matrix singularity caused by undersampled problems by substituting the Moore-Penrose pseudo-inverse for the inverse of the matrix. Under the pseudo-inverse form eigenequation, the optimal locality preserving projections...
Based on what the students have learned, the topic on encouraging active learning is present in this paper. Emphasizing process, emphasizing application, emphasizing experience and emphasizing all students' participation are the characteristics of the topic, while innovative and opening are two prominent advantages of it. Finally, eight aspects of the applications of elementary transformation are...
Burst proneness of coal seam is a necessary condition for rock burst, which tends to study the burst proneness of rock burst mechanism of coal seam. And it is the premise of forecasting the rock burst. Based on mathematical analysis, the primary components analysis (PCA) is used to analyze the burst-prone indexes of coal seam. On the basis of PCA model and scores by experts, some results are computed,...
In a recent paper we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrodinger equation on a fixed domain. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrodinger operator. The aim of this presentation is to show that these conditions are generic with respect to the uncontrolled...
We consider the problem of boundary stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. This term puts all the eigenvalues of the open-loop system in the right half of the complex plane. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate. For plants with constant...
This paper considers formation shape control of a team of four agents in the plane, motivated by an example from [1]. We utilize bidirectional, gradient-based interagent distance control laws which are designed so that the agents cooperatively achieve a specified desired formation shape. When every interagent distance is actively controlled (i.e. the information architecture is a complete graph),...
This paper gives a new computational method of the Hankel norm for the class of pseudorational transfer functions. This class and the obtained method have the advantage that they allow us to deal with a large class of systems that were not treated in the literature, for example, general retarded or neutral delay differential systems. An easily computable approximating sequence is obtained, which converges...
This paper investigates accelerated gossip algorithms for distributed computations in networks where shift-registers are utilized at each node. By using tools from matrix analysis, we prove the existence of the desired acceleration and establish the fastest rate of convergence in expectation for two-register symmetric gossip. Some classes of networks with regular graph topologies are studied in detail...
This paper explores the experimental design and identifiability problems for both closed and open quantum systems. In general, the identifiability of quantum systems depends on both the choice of model sets and experimental design. The limits of identifiability in certain experimental settings and ways to improve the identifiability of model parameters by changing experimental conditions are investigated...
In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the well-known Floquet representation theorem, a 2T-periodic real-valued factor and a real-valued matrix exponential...
In this paper, we propose an observed-based algorithm to estimate the time course of a set of not-directly measurable gene expressions for the network motif of the multi-output feed-forward loop (MO-FFL), widespread in gene transcription networks of many organisms. The MO-FFL has been modeled according to a standard ordinary differential equations approach, providing a nonlinear model in the state...
This paper deals with LTI interconnected systems whose subsystems have coupled dynamics. The objective is to decentralize a given centralized controller satisfying some prescribed design specifications. More precisely, a parameterized decentralized controller is to be designed such that the state and the input of the system under the obtained decentralized controller can become arbitrarily close to...
The problem of finding the eigenvector corresponding to the largest eigenvalue of a stochastic matrix has numerous applications in ranking search results, multi-agent consensus, networked control and data mining. The well-known power method is a typical tool for its solution. However randomized methods could be competitors vs standard ones; they require much less calculations for one iteration and...
A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite algebraic...
The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of block-oriented nonlinear systems including Hammerstein systems. This paper revisits an optimality result established by Bai in 1998 showing that the TSA provides the optimal estimation of a bilinearly parameterized Hammerstein system in the sense of a weighted nonlinear least-squares (LS) criterion formulated...
In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-2 A = I . Suppose X is a Hermitian positive definite solution of this equation. We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively.
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