Lower bounds for stability margin of n-dimensional discrete systems

This paper derives lower bounds for the stability margin of n-dimensional discrete systems in the Roesser’s state space setting. The lower bounds for stability margin are derived based on the MacLaurine series expansion. Numerical examples are given to illustrate the results.

Dynamic biometrics fusion at feature level for video-based human recognition

This paper proposes a novel human recognition method in video, which combines human face and gait traits
using a dynamic multi-modal biometrics fusion scheme. The Fisherface approach is adopted to extract face
features, while for gait features, Locality Preserving Projection (LPP) is used to achieve low-dimensional
manifold embedding of the temporal silhouette data derived from image sequences. Face and gait features are
fused dynamically at feature level based on a distance-driven fusion method. Encouraging experimental results
are achieved on the video sequences containing 20 people, which show that dynamically fused features produce
a more discriminating power than any individual biometric as well as integrated features built on common static
fusion schemes.

Stability of 2-D characteristic polynomials

This paper derives some new conditions for the bivariate characteristic polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. By using the two-dimensional (2-D) inverse Laplace transform, the bounds on the uncertainties are derived which will ensure that the bivariate characteristic polynomial to be very strict Hurwitz. Two numerical examples are given to illustrate the results.

Conditions to ensure the 2-D characteristic polynomial of uncertain matrix is very strict Hurwitz

This article derives some new conditions for the bivariate characteristic
polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. Using the two-dimensional inverse Laplace transform, we derive the bounds on the uncertainties, which will ensure that the bivariate characteristic polynomial is very strict Hurwitz. Two numerical examples are given to illustrate the results.

Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Plasma-assisted self-catalytic vapour-liquid-solid growth of β-SiC nanowires

Long and straight β-SiC nanowires are synthesized via the direct current arc discharge method with a mixture of silicon, graphite and silicon dioxide as the precursor. Detailed investigations with x-ray diffraction, scanning electron microscopy, energy dispersive x-ray spectroscopy, Raman scattering spectroscopy, transmission electron microscopy and selected area electron diffraction confirm that the β-SiC nanowires, which are about 100–200 nm in stem diameter and 10–20 µm in length, consist of a solid single-crystalline core along the (1 1 1) direction wrapped with an amorphous SiO_x layer. A broad photoluminescence emission peak with a maximum at about 336 nm is observed at room temperature. A direct current arc plasma-assisted self-catalytic vapour–liquid–solid process is proposed as the growth mechanism of the β-SiC nanowires. This synthesis technique is capable of producing SiC nanowires free of metal contamination with a preferential growth direction and a high aspect ratio, without the designed addition of transition metals as catalysts.

Document clustering in correlation similarity measure space

This paper presents a new spectral clustering method called correlation preserving indexing (CPI), which is performed in the correlation similarity measure space. In this framework, the documents are projected into a low-dimensional semantic space in which the correlations between the documents in the local patches are maximized while the correlations between the documents outside these patches are minimized simultaneously. Since the intrinsic geometrical structure of the document space is often embedded in the similarities between the documents, correlation as a similarity measure is more suitable for detecting the intrinsic geometrical structure of the document space than euclidean distance. Consequently, the proposed CPI method can effectively discover the intrinsic structures embedded in high-dimensional document space. The effectiveness of the new method is demonstrated by extensive experiments conducted on various data sets and by comparison with existing document clustering methods.

Comparative studies of structural transition between AlN nanocrystals and nanowires

The structural transition of AIN nanocrystals and nanowires were investigated simultaneously under pressures up to 37.2 GPa by in situ angle dispersive high-pressure x-ray diffraction using synchrotron radiation source and a single diamond anvil cell. The size of hexagonal AIN nanocrystals and the diameter of nanowires are 45 nm on average. A pressure-induced wurtzite to rocksalt phase transition starts at 21.5 GPa and completes at 27.8 GPa for the nanocrystals and nanowires, respectively. The high-pressure behaviors of AlN nanocrystals the same as the AIN nanowires might arise from the similar size and diameter in nanocrystals and nanowires. Hexagonal AIN nanocrystals (45 nm) display an apparent volumetric contraction as compared to the AlN nanocrystals (10 nm) which might induce the difference of transition pressure.

Fast growing self organizing map for text clustering

This paper presents an integration of a novel document vector representation technique and a novel Growing Self Organizing Process. In this new approach, documents are represented as a low dimensional vector, which is composed of the indices and weights derived from the keywords of the document.

An index based similarity calculation method is employed on this low dimensional feature space and the growing self organizing process is modified to comply with the new feature representation model.

The initial experiments show that this novel integration outperforms the state-of-the-art Self Organizing Map based techniques of text clustering in terms of its efficiency while preserving the same accuracy level.

Face recognition with image sets using manifold density divergence

In many automatic face recognition applications, a set of a person's face images is available rather than a single image. In this paper, we describe a novel method for face recognition using image sets. We propose a flexible, semi-parametric model for learning probability densities confined to highly non-linear but intrinsically low-dimensional manifolds. The model leads to a statistical formulation of the recognition problem in terms of minimizing the divergence between densities estimated on these manifolds. The proposed method is evaluated on a large data set, acquired in realistic imaging conditions with severe illumination variation. Our algorithm is shown to match the best and outperform other state-of-the-art algorithms in the literature, achieving 94% recognition rate on average.

An information-theoretic approach to face recognition from face motion manifolds

In this work, we consider face recognition from face motion manifolds (FMMs). The use of the resistor-average distance (RAD) as a dissimilarity measure between densities confined to FMMs is motivated in the proposed information-theoretic approach to modelling face appearance. We introduce a kernel-based algorithm that makes use of the simplicity of the closed-form expression for RAD between two Gaussian densities, while allowing for modelling of complex and nonlinear, but intrinsically low-dimensional manifolds. Additionally, it is shown how geodesically local FMM structure can be modelled, naturally leading to a stochastic algorithm for generalizing to unseen modes of data variation. Recognition performance of our method is demonstrated experimentally and is shown to exceed that of state-of-the-art algorithms. Recognition rate of 98% was achieved on a database of 100 people under varying illumination

Modelling multilevel data in multimedia : A hierarchical factor analysis approach

Multimedia content understanding research requires rigorous approach to deal with the complexity of the data. At the crux of this problem is the method to deal with multilevel data whose structure exists at multiple scales and across data sources. A common example is modeling tags jointly with images to improve retrieval, classification and tag recommendation. Associated contextual observation, such as metadata, is rich that can be exploited for content analysis. A major challenge is the need for a principal approach to systematically incorporate associated media with the primary data source of interest. Taking a factor modeling approach, we propose a framework that can discover low-dimensional structures for a primary data source together with other associated information. We cast this task as a subspace learning problem under the framework of Bayesian nonparametrics and thus the subspace dimensionality and the number of clusters are automatically learnt from data instead of setting these parameters a priori. Using Beta processes as the building block, we construct random measures in a hierarchical structure to generate multiple data sources and capture their shared statistical at the same time. The model parameters are inferred efficiently using a novel combination of Gibbs and slice sampling. We demonstrate the applicability of the proposed model in three applications: image retrieval, automatic tag recommendation and image classification. Experiments using two real-world datasets show that our approach outperforms various state-of-the-art related methods.

Bayesian nonparametric multilevel clustering with group-level contexts

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group- level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-measure with a nested structure to accommodate content and context observations at multiple levels. The proposed model possesses properties that link the nested Dinchiet processes (nDP) and the Dirichlet process mixture models (DPM) in an interesting way: integrating out all contents results in the DPM over contexts, whereas integrating out group-specific contexts results in the nDP mixture over content variables. We provide a Polyaurn view of the model and an efficient collapsed Gibbs inference procedure. Extensive experiments on real-world datasets demonstrate the advantage of utilizing context information via our model in both text and image domains.

Visual object clustering via mixed-norm regularization

Many vision problems deal with high-dimensional data, such as motion segmentation and face clustering. However, these high-dimensional data usually lie in a low-dimensional structure. Sparse representation is a powerful principle for solving a number of clustering problems with high-dimensional data. This principle is motivated from an ideal modeling of data points according to linear algebra theory. However, real data in computer vision are unlikely to follow the ideal model perfectly. In this paper, we exploit the mixed norm regularization for sparse subspace clustering. This regularization term is a convex combination of the l1norm, which promotes sparsity at the individual level and the block norm l2/1 which promotes group sparsity. Combining these powerful regularization terms will provide a more accurate modeling, subsequently leading to a better solution for the affinity matrix used in sparse subspace clustering. This could help us achieve better performance on motion segmentation and face clustering problems. This formulation also caters for different types of data corruptions. We derive a provably convergent algorithm based on the alternating direction method of multipliers (ADMM) framework, which is computationally efficient, to solve the formulation. We demonstrate that this formulation outperforms other state-of-arts on both motion segmentation and face clustering.

Learning vector representation of medical objects via EMR-driven nonnegative restricted Boltzmann machines (eNRBM)

Electronic medical record (EMR) offers promises for novel analytics. However, manual feature engineering from EMR is labor intensive because EMR is complex - it contains temporal, mixed-type and multimodal data packed in irregular episodes. We present a computational framework to harness EMR with minimal human supervision via restricted Boltzmann machine (RBM). The framework derives a new representation of medical objects by embedding them in a low-dimensional vector space. This new representation facilitates algebraic and statistical manipulations such as projection onto 2D plane (thereby offering intuitive visualization), object grouping (hence enabling automated phenotyping), and risk stratification. To enhance model interpretability, we introduced two constraints into model parameters: (a) nonnegative coefficients, and (b) structural smoothness. These result in a novel model called eNRBM (EMR-driven nonnegative RBM). We demonstrate the capability of the eNRBM on a cohort of 7578 mental health patients under suicide risk assessment. The derived representation not only shows clinically meaningful feature grouping but also facilitates short-term risk stratification. The F-scores, 0.21 for moderate-risk and 0.36 for high-risk, are significantly higher than those obtained by clinicians and competitive with the results obtained by support vector machines.