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Nock R.,National ICT Australia | Nielsen F.,Ecole Polytechnique - Palaiseau | Amari S.-I.,RIKEN
IEEE Transactions on Information Theory | Year: 2016

Total Bregman divergences are a recent tweak of ordinary Bregman divergences originally motivated by applications that required invariance by rotations. They have displayed superior results compared with ordinary Bregman divergences on several clustering, computer vision, medical imaging, and machine learning tasks. These preliminary results raise two important problems. First, report a complete characterization of the left and right population minimizers for this class of total Bregman divergences. Second, characterize a principled superset of total and ordinary Bregman divergences with good clustering properties, from which one could tailor the choice of a divergence to a particular application. In this paper, we provide and study one such superset with interesting geometric features, that we call conformal divergences, and focus on their left and right population minimizers. Our results are obtained in a recently coined (u, v)-geometric structure that is a generalization of the dually flat affine connections in information geometry. We characterize both analytically and geometrically the population minimizers. We prove that conformal divergences (resp. total Bregman divergences) are essentially exhaustive for their left (resp. right) population minimizers. We further report new results and extend previous results on the robustness to outliers of the left and right population minimizers, and discuss the role of the (u, v)-geometric structure in clustering. Additional results are also given. © 2015 IEEE.


Hijazi H.,National ICT Australia | Bonami P.,CNRS Laboratory of Fundamental Informatics of Marseille (LIF) | Ouorou A.,Orange S.A.
INFORMS Journal on Computing | Year: 2014

Acommon structure in convex mixed-integer nonlinear programs (MINLPs) is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region. As a side result, we exhibit a simple example where a classical implementation of the outer approximation would take an exponential number of iterations, whereas it is easily solved with our modifications. These methods have been implemented in the open source solver Bonmin and are available for download from the Computational Infrastructure for Operations Research project website. We test the effectiveness of the approach on three real-world applications and on a larger set of models from an MINLP benchmark library. Finally, we show how the techniques can be extended to perspective formulations of several problems. The proposed tools lead to an important reduction in computing time on most tested instances. © 2014 INFORMS.


Seiler K.M.,University of Sydney | Singh S.P.N.,University of Queensland | Sukkarieh S.,University of Sydney | Durrant-Whyte H.,National ICT Australia
International Journal of Robotics Research | Year: 2012

In this paper we develop an algorithmic framework allowing for fast and elegant path correction exploiting Lie group symmetries and operating without the need for explicit control strategies such as cross-track regulation. These systems occur across the gamut of robotics, notably in locomotion, be it ground, underwater, airborne, or surgical domains. Instead of reintegrating an entire trajectory, the method selectively alters small key segments of an initial trajectory in a consistent way so as to transform it via symmetry operations. The algorithm is formulated for arbitrary Lie groups and applied in the context of the special Euclidean group and subgroups thereof. A sampling-based motion planner is developed that uses this method to create paths for underactuated systems with differential constraints. It is also shown how the path correction method acts as a controller within a feedback control loop for real-time path correction. These approaches are demonstrated for ground vehicles in the plane and for flexible bevel tip needle steering in space. The results show that using symmetry-based path correction for motion planning provides a prudent and simple, yet computationally tractable, integrated planning and control strategy. © SAGE Publications 2011.


Zhang Z.,University of Sydney | Mao G.,University of Sydney | Anderson B.D.O.,National ICT Australia | Anderson B.D.O.,Australian National University
IEEE Transactions on Parallel and Distributed Systems | Year: 2012

Consider a wireless multihop network where nodes are randomly distributed in a given area following a homogeneous Poisson process. The hop count statistics, viz. the probabilities related to the number of hops between two nodes, are important for performance analysis of the multihop networks. In this paper, we provide analytical results on the probability that two nodes separated by a known euclidean distance are k hops apart in networks subject to both shadowing and small-scale fading. Some interesting results are derived which have generic significance. For example, it is shown that the locations of nodes three or more hops away provide little information in determining the relationship of a node with other nodes in the network. This observation is useful for the design of distributed routing, localization, and network security algorithms. As an illustration of the application of our results, we derive the effective energy consumption per successfully transmitted packet in end-to-end packet transmissions. We show that there exists an optimum transmission range which minimizes the effective energy consumption. The results provide useful guidelines on the design of a randomly deployed network in a more realistic radio environment. © 2012 IEEE.


Mathews G.M.,National ICT Australia
2012 IEEE International Energy Conference and Exhibition, ENERGYCON 2012 | Year: 2012

The factored decomposition technique was recently proposed as a theoretical framework for distributed and hierarchical nonlinear weighted least squares state estimation algorithms for large interconnected power networks [1]. This paper analyses the accuracy of the technique and shows it to be suboptimal when compared to the direct weighted least squares solution commonly used in existing power system state estimation systems. In addition a closed form expression is developed that predicts the expected error in the factored estimate for a given system operating point. A Monte Carlo analysis shows that the theoretical prediction is accurate for a simulated power system. The structure of the prediction is analysed and shown to be proportional to the square of the standard deviation of the measurement noise, suggesting that the error may be insignificant for power systems with reasonably accurate sensors. © 2012 IEEE.


Zhang B.,National ICT Australia | Wang Y.,National ICT Australia | Chen F.,National ICT Australia
IEEE Transactions on Image Processing | Year: 2014

Supervised machine learning techniques have been applied to multilabel image classification problems with tremendous success. Despite disparate learning mechanisms, their performances heavily rely on the quality of training images. However, the acquisition of training images requires significant efforts from human annotators. This hinders the applications of supervised learning techniques to large scale problems. In this paper, we propose a high-order label correlation driven active learning (HoAL) approach that allows the iterative learning algorithm itself to select the informative example-label pairs from which it learns so as to learn an accurate classifier with less annotation efforts. Four crucial issues are considered by the proposed HoAL: 1) unlike binary cases, the selection granularity for multilabel active learning need to be fined from example to example-label pair; 2) different labels are seldom independent, and label correlations provide critical information for efficient learning; 3) in addition to pair-wise label correlations, high-order label correlations are also informative for multilabel active learning; and 4) since the number of label combinations increases exponentially with respect to the number of labels, an efficient mining method is required to discover informative label correlations. The proposed approach is tested on public data sets, and the empirical results demonstrate its effectiveness. © 2013 IEEE.


Kameneva T.,National ICT Australia | Nesic D.,University of Melbourne
Nonlinear Analysis: Hybrid Systems | Year: 2010

This paper analyzes the stability of nonlinear systems with quantized feedback in the presence of exogenous disturbances. This paper is an extension of [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Trans. Automat. Control 52 (2007), 413-436] to nonlinear systems. Under appropriate assumptions using a nonlinear modification of the scheme proposed in [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Transactions on Automat. Control 52 (2007), 413-436], it is shown here that it is possible to achieve input-to-state and nonlinear gain l 2 stability for nonlinear systems with quantized feedback. © 2009 Elsevier Ltd. All rights reserved.


Mao G.,University of Sydney | Anderson B.D.O.,National ICT Australia | Anderson B.D.O.,Australian National University
IEEE Transactions on Information Theory | Year: 2013

This paper studies networks where all nodes are distributed on a unit square Aδ= [-1\2, 1\2]2 following a Poisson distribution with known density rho and a pair of nodes separated by an Euclidean distance x are directly connected with probability grρ(x)= g(x/rρ), independent of the event that any other pair of nodes are directly connected. Here, g:[0,)→ [0,1] satisfies the conditions of rotational invariance, nonincreasing monotonicity, integral boundedness, and g(x)=o(1/x2(log2)) ; further, rρ= (log ρ +b)(Cρ) where C=fr 2g(\left \Vert \mmb x\right \Vert)d \mmb x and b is a constant. Denote the aforementioned network by \cal G\left (\cal Xρ,g-rρ,A\right). We show that as ρ → 1) the distribution of the number of isolated nodes in \cal G\left (\cal Xρ,g-rρ,A\right) converges to a Poisson distribution with mean e-b ; 2) asymptotically almost surely (a.a.s.) there is no component in \cal G\left (\cal Xρ,g-rρ,A\right) of fixed and finite order k> 1; c) a.a.s. the number of components with an unbounded order is one. Therefore, as ρ → the network a.a.s. contains a unique unbounded component and isolated nodes only; a sufficient and necessary condition for cal G\left (cal Xρ,g rρ,A\right) to be a.a.s. connected is that there is no isolated node in the network, which occurs when b→ asρ. These results expand recent results obtained for connectivity of random geometric graphs from the unit disk model and the fewer results from the log-normal model to the more general and more practical random connection model. © 1963-2012 IEEE.


Cassez F.,National ICT Australia
IEEE Transactions on Automatic Control | Year: 2012

In this paper, we study the fault codiagnosis problem for discrete event systems given by finite automata (FA) and timed systems given by timed automata (TA). We provide a uniform characterization of codiagnosability for FA and TA which extends the necessary and sufficient condition that characterizes diagnosability. We also settle the complexity of the codiagnosability problems both for FA and TA and show that codiagnosability is PSPACE-complete in both cases. For FA this improves on the previously known bound (EXPTIME) and for TA it is a new result. We then generalize the previous results to the case of dynamic observers. Finally we show that the codiagnosis problem for TA under bounded resources is 2EXPTIME-complete. © 2012 IEEE.


Mao G.,University of Sydney | Anderson B.D.O.,National ICT Australia | Anderson B.D.O.,Australian National University
IEEE/ACM Transactions on Networking | Year: 2012

Connectivity and capacity are two fundamental properties of wireless multihop networks. The scalability of these properties has been a primary concern for which asymptotic analysis is a useful tool. Three related but logically distinct network models are often considered in asymptotic analyses, viz. the dense network model, the extended network model, and the infinite network model, which consider respectively a network deployed in a fixed finite area with a sufficiently large node density, a network deployed in a sufficiently large area with a fixed node density, and a network deployed in Re 2 with a sufficiently large node density. The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks. In this paper, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order 1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models. Therefore, extra scrutiny has to be used in order for the results obtained from the infinite network model to be applicable to the dense and extended network models. Asymptotic results are also obtained on the expected number of isolated nodes, the vanishingly small impact of the boundary effect on the number of isolated nodes, and the vanishing of components of finite order k in the dense and extended network models using a generic random connection model. © 2011 IEEE.

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