Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Global Optimization Algorithms and their Application to Distributed Systems

In this report, we discuss the application of global optimization and Evolutionary Computation to distributed systems. We therefore selected and classified many publications, giving an insight into the wide variety of optimization problems which arise in distributed systems. Some interesting approaches from different areas will be discussed in greater detail with the use of illustrative examples.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

Availability analysis of GMPLS connections based on physical network topology

This paper presents a study of connection availability in GMPLS over optical transport networks (OTN) taking into account different network topologies. Two basic path protection schemes are considered and compared with the no protection case. The selected topologies are heterogeneous in geographic coverage, network diameter, link lengths, and average node degree. Connection availability is also computed considering the reliability data of physical components and a well-known network availability model. Results show several correspondences between suitable path protection algorithms and several network topology characteristics

Assessment of virtual design and manufacturing techniques for fibre reinforced composite materials

Virtual tools are commonly used nowadays to optimize product design and manufacturing process of fibre reinforced composite materials. The present work focuses on two areas of interest to forecast the part performance and the production process particularities. The first part proposes a multi-physical optimization tool to support the concept stage of a composite part. The strategy is based on the strategic handling of information and, through a single control parameter, is able to evaluate the effects of design variations throughout all these steps in parallel. The second part targets the resin infusion process and the impact of thermal effects. The numerical and experimental approach allowed the identificationof improvement opportunities regarding the implementation of algorithms in commercially available simulation software.

Computer generation and quantitative morphometric analysis of virtual neurons

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.

Minimising the latency induced by consistency control, within a large scale multi-user distributed virtual reality system

Where users are interacting in a distributed virtual environment, the actions of each user must be observed by peers with sufficient consistency and within a limited delay so as not to be detrimental to the interaction. The consistency control issue may be split into three parts: update control; consistent enactment and evolution of events; and causal consistency. The delay in the presentation of events, termed latency, is primarily dependent on the network propagation delay and the consistency control algorithms. The latency induced by the consistency control algorithm, in particular causal ordering, is proportional to the number of participants. This paper describes how the effect of network delays may be reduced and introduces a scalable solution that provides sufficient consistency control while minimising its effect on latency. The principles described have been developed at Reading over the past five years. Similar principles are now emerging in the simulation community through the HLA standard. This paper attempts to validate the suggested principles within the schema of distributed simulation and virtual environments and to compare and contrast with those described by the HLA definition documents.

Virtual landmarking for locality aware peer IDs

In Peer-to-Peer (P2P) networks, it is often desirable to assign node IDs which preserve locality relationships in the underlying topology. Node locality can be embedded into node IDs by utilizing a one dimensional mapping by a Hilbert space filling curve on a vector of network distances from each node to a subset of reference landmark nodes within the network. However this approach is fundamentally limited because while robustness and accuracy might be expected to improve with the number of landmarks, the effectiveness of 1 dimensional Hilbert Curve mapping falls for the curse of dimensionality. This work proposes an approach to solve this issue using Landmark Multidimensional Scaling (LMDS) to reduce a large set of landmarks to a smaller set of virtual landmarks. This smaller set of landmarks has been postulated to represent the intrinsic dimensionality of the network space and therefore a space filling curve applied to these virtual landmarks is expected to produce a better mapping of the node ID space. The proposed approach, the Virtual Landmarks Hilbert Curve (VLHC), is particularly suitable for decentralised systems like P2P networks. In the experimental simulations the effectiveness of the methods is measured by means of the locality preservation derived from node IDs in terms of latency to nearest neighbours. A variety of realistic network topologies are simulated and this work provides strong evidence to suggest that VLHC performs better than either Hilbert Curves or LMDS use independently of each other.

Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

HIERARCHICAL DECOMPOSITION OF MULTICLASS PROBLEMS

Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

A low cost one-camera optical tracking system for indoor wide-area augmented and virtual reality environments

In the last years the number of industrial applications for Augmented Reality (AR) and Virtual Reality (VR) environments has significantly increased. Optical tracking systems are an important component of AR/VR environments. In this work, a low cost optical tracking system with adequate attributes for professional use is proposed. The system works in infrared spectral region to reduce optical noise. A highspeed camera, equipped with daylight blocking filter and infrared flash strobes, transfers uncompressed grayscale images to a regular PC, where image pre-processing software and the PTrack tracking algorithm recognize a set of retro-reflective markers and extract its 3D position and orientation. Included in this work is a comprehensive research on image pre-processing and tracking algorithms. A testbed was built to perform accuracy and precision tests. Results show that the system reaches accuracy and precision levels slightly worse than but still comparable to professional systems. Due to its modularity, the system can be expanded by using several one-camera tracking modules linked by a sensor fusion algorithm, in order to obtain a larger working range. A setup with two modules was built and tested, resulting in performance similar to the stand-alone configuration.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Allocation of protective devices in distribution circuits using nonlinear programming models and genetic algorithms

The optimized allocation of protective devices in strategic points of the circuit improves the quality of the energy supply and the system reliability index. This paper presents a nonlinear integer programming (NLIP) model with binary variables, to deal with the problem of protective device allocation in the main feeder and all branches of an overhead distribution circuit, to improve the reliability index and to provide customers with service of high quality and reliability. The constraints considered in the problem take into account technical and economical limitations, such as coordination problems of serial protective devices, available equipment, the importance of the feeder and the circuit topology. The use of genetic algorithms (GAs) is proposed to solve this problem, using a binary representation that does (1) or does not (0) show allocation of protective devices (reclosers, sectionalizers and fuses) in predefined points of the circuit. Results are presented for a real circuit (134 busses), with the possibility of protective device allocation in 29 points. Also the ability of the algorithm in finding good solutions while improving significantly the indicators of reliability is shown. (C) 2003 Elsevier B.V. All rights reserved.

Planning of secondary distribution circuits through evolutionary algorithms

In this work, the planning of secondary distribution circuits is approached as a mixed integer nonlinear programming problem (MINLP). In order to solve this problem, a dedicated evolutionary algorithm (EA) is proposed. This algorithm uses a codification scheme, genetic operators, and control parameters, projected and managed to consider the specific characteristics of the secondary network planning. The codification scheme maps the possible solutions that satisfy the requirements in order to obtain an effective and low-cost projected system-the conductors' adequate dimensioning, load balancing among phases, and the transformer placed at the center of the secondary system loads. An effective algorithm for three-phase power flow is used as an auxiliary methodology of the EA for the calculation of the fitness function proposed for solutions of each topology. Results for two secondary distribution circuits are presented, whereas one presents radial topology and the other a weakly meshed topology. © 2005 IEEE.