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2007


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Using reward-weighted regression for reinforcement learning of task space control

Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 262-267, Honolulu, Hawaii, April 1-5, 2007, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

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link (url) DOI [BibTex]

2007


link (url) DOI [BibTex]


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Evaluation of Policy Gradient Methods and Variants on the Cart-Pole Benchmark

Riedmiller, M., Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 254-261, ADPRL, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

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PDF [BibTex]

PDF [BibTex]


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A strategy for vision-based controlled pushing of microparticles

Lynch, N. A., Onal, C., Schuster, E., Sitti, M.

In Robotics and Automation, 2007 IEEE International Conference on, pages: 1413-1418, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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Uncertain 3D Force Fields in Reaching Movements: Do Humans Favor Robust or Average Performance?

Mistry, M., Theodorou, E., Hoffmann, H., Schaal, S.

In Abstracts of the 37th Meeting of the Society of Neuroscience, 2007, clmc (inproceedings)

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PDF [BibTex]

PDF [BibTex]


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Applying the episodic natural actor-critic architecture to motor primitive learning

Peters, J., Schaal, S.

In Proceedings of the 2007 European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, April 25-27, 2007, clmc (inproceedings)

Abstract
In this paper, we investigate motor primitive learning with the Natural Actor-Critic approach. The Natural Actor-Critic consists out of actor updates which are achieved using natural stochastic policy gradients while the critic obtains the natural policy gradient by linear regression. We show that this architecture can be used to learn the Òbuilding blocks of movement generationÓ, called motor primitives. Motor primitives are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. We show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

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link (url) [BibTex]

link (url) [BibTex]


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A computational model of human trajectory planning based on convergent flow fields

Hoffman, H., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov. 3-7, 2007, clmc (inproceedings)

Abstract
A popular computational model suggests that smooth reaching movements are generated in humans by minimizing a difference vector between hand and target in visual coordinates (Shadmehr and Wise, 2005). To achieve such a task, the optimal joint accelerations may be pre-computed. However, this pre-planning is inflexible towards perturbations of the limb, and there is strong evidence that reaching movements can be modified on-line at any moment during the movement. Thus, next-state planning models (Bullock and Grossberg, 1988) have been suggested that compute the current control command from a function of the goal state such that the overall movement smoothly converges to the goal (see Shadmehr and Wise (2005) for an overview). So far, these models have been restricted to simple point-to-point reaching movements with (approximately) straight trajectories. Here, we present a computational model for learning and executing arbitrary trajectories that combines ideas from pattern generation with dynamic systems and the observation of convergent force fields, which control a frog leg after spinal stimulation (Giszter et al., 1993). In our model, we incorporate the following two observations: first, the orientation of vectors in a force field is invariant over time, but their amplitude is modulated by a time-varying function, and second, two force fields add up when stimulated simultaneously (Giszter et al., 1993). This addition of convergent force fields varying over time results in a virtual trajectory (a moving equilibrium point) that correlates with the actual leg movement (Giszter et al., 1993). Our next-state planner is a set of differential equations that provide the desired end-effector or joint accelerations using feedback of the current state of the limb. These accelerations can be interpreted as resulting from a damped spring that links the current limb position with a virtual trajectory. This virtual trajectory can be learned to realize any desired limb trajectory and velocity profile, and learning is efficient since the time-modulated sum of convergent force fields equals a sum of weighted basis functions (Gaussian time pulses). Thus, linear algebra is sufficient to compute these weights, which correspond to points on the virtual trajectory. During movement execution, the differential equation corrects automatically for perturbations and brings back smoothly the limb towards the goal. Virtual trajectories can be rescaled and added allowing to build a set of movement primitives to describe movements more complex than previously learned. We demonstrate the potential of the suggested model by learning and generating a wide variety of movements.

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[BibTex]

[BibTex]


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Hand placement during quadruped locomotion in a humanoid robot: A dynamical system approach

Degallier, S., Righetti, L., Ijspeert, A.

In 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 2047-2052, IEEE, San Diego, USA, 2007 (inproceedings)

Abstract
Locomotion on an irregular surface is a challenging task in robotics. Among different problems to solve to obtain robust locomotion, visually guided locomotion and accurate foot placement are of crucial importance. Robust controllers able to adapt to sensory-motor feedbacks, in particular to properly place feet on specific locations, are thus needed. Dynamical systems are well suited for this task as any online modification of the parameters leads to a smooth adaptation of the trajectories, allowing a safe integration of sensory-motor feedback. In this contribution, as a first step in the direction of locomotion on irregular surfaces, we present a controller that allows hand placement during crawling in a simulated humanoid robot. The goal of the controller is to superimpose rhythmic movements for crawling with discrete (i.e. short-term) modulations of the hand placements to reach specific marks on the ground.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A Computational Model of Arm Trajectory Modification Using Dynamic Movement Primitives

Mohajerian, P., Hoffmann, H., Mistry, M., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov 3-7, 2007, clmc (inproceedings)

Abstract
Several scientists used a double-step target-displacement protocol to investigate how an unexpected upcoming new target modifies ongoing discrete movements. Interesting observations are the initial direction of the movement, the spatial path of the movement to the second target, and the amplification of the speed in the second movement. Experimental data show that the above properties are influenced by the movement reaction time and the interstimulus interval between the onset of the first and second target. Hypotheses in the literature concerning the interpretation of the observed data include a) the second movement is superimposed on the first movement (Henis and Flash, 1995), b) the first movement is aborted and the second movement is planned to smoothly connect the current state of the arm with the new target (Hoff and Arbib, 1992), c) the second movement is initiated by a new control signal that replaces the first movement's control signal, but does not take the state of the system into account (Flanagan et al., 1993), and (d) the second movement is initiated by a new goal command, but the control structure stays unchanged, and feed-back from the current state is taken into account (Hoff and Arbib, 1993). We investigate target switching from the viewpoint of Dynamic Movement Primitives (DMPs). DMPs are trajectory planning units that are formalized as stable nonlinear attractor systems (Ijspeert et al., 2002). They are a useful framework for biological motor control as they are highly flexible in creating complex rhythmic and discrete behaviors that can quickly adapt to the inevitable perturbations of dynamically changing, stochastic environments. In this model, target switching is accomplished simply by updating the target input to the discrete movement primitive for reaching. The reaching trajectory in this model can be straight or take any other route; in contrast, the Hoff and Arbib (1993) model is restricted to straight reaching movement plans. In the present study, we use DMPs to reproduce in simulation a large number of target-switching experimental data from the literature and to show that online correction and the observed target switching phenomena can be accomplished by changing the goal state of an on-going DMP, without the need to switch to different movement primitives or to re-plan the movement. :

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PDF [BibTex]

PDF [BibTex]


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Inverse dynamics control with floating base and constraints

Nakanishi, J., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1942-1947, Rome, Italy, April 10-14, 2007, clmc (inproceedings)

Abstract
In this paper, we address the issues of compliant control of a robot under contact constraints with a goal of using joint space based pattern generators as movement primitives, as often considered in the studies of legged locomotion and biological motor control. For this purpose, we explore inverse dynamics control of constrained dynamical systems. When the system is overconstrained, it is not straightforward to formulate an inverse dynamics control law since the problem becomes an ill-posed one, where infinitely many combinations of joint torques are possible to achieve the desired joint accelerations. The goal of this paper is to develop a general and computationally efficient inverse dynamics algorithm for a robot with a free floating base and constraints. We suggest an approximate way of computing inverse dynamics algorithm by treating constraint forces computed with a Lagrange multiplier method as simply external forces based on FeatherstoneÕs floating base formulation of inverse dynamics. We present how all the necessary quantities to compute our controller can be efficiently extracted from FeatherstoneÕs spatial notation of robot dynamics. We evaluate the effectiveness of the suggested approach on a simulated biped robot model.

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link (url) [BibTex]

link (url) [BibTex]


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Lower body realization of the baby humanoid - ‘iCub’

Tsagarakis, N., Becchi, F., Righetti, L., Ijspeert, A., Caldwell, D.

In 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3616-3622, IEEE, San Diego, USA, 2007 (inproceedings)

Abstract
Nowadays, the understanding of the human cognition and it application to robotic systems forms a great challenge of research. The iCub is a robotic platform that was developed within the RobotCub European project to provide the cognition research community with an open baby- humanoid platform for understanding and development of cognitive systems. In this paper we present the design requirements and mechanical realization of the lower body developed for the "iCub". In particular the leg and the waist mechanisms adopted for lower body to match the size and physical abilities of a 2 frac12 year old human baby are introduced.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Kernel carpentry for onlne regression using randomly varying coefficient model

Edakunni, N. U., Schaal, S., Vijayakumar, S.

In Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India: Jan. 6-12, 2007, clmc (inproceedings)

Abstract
We present a Bayesian formulation of locally weighted learning (LWL) using the novel concept of a randomly varying coefficient model. Based on this, we propose a mechanism for multivariate non-linear regression using spatially localised linear models that learns completely independent of each other, uses only local information and adapts the local model complexity in a data driven fashion. We derive online updates for the model parameters based on variational Bayesian EM. The evaluation of the proposed algorithm against other state-of-the-art methods reveal the excellent, robust generalization performance beside surprisingly efficient time and space complexity properties. This paper, for the first time, brings together the computational efficiency and the adaptability of Õnon-competitiveÕ locally weighted learning schemes and the modeling guarantees of the Bayesian formulation.

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link (url) [BibTex]

link (url) [BibTex]


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Autonomous 2D microparticle manipulation based on visual feedback

Onal, C. D., Sitti, M.

In Advanced intelligent mechatronics, 2007 IEEE/ASME international conference on, pages: 1-6, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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A robust quadruped walking gait for traversing rough terrain

Pongas, D., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1474-1479, Rome, April 10-14, 2007, 2007, clmc (inproceedings)

Abstract
Legged locomotion excels when terrains become too rough for wheeled systems or open-loop walking pattern generators to succeed, i.e., when accurate foot placement is of primary importance in successfully reaching the task goal. In this paper we address the scenario where the rough terrain is traversed with a static walking gait, and where for every foot placement of a leg, the location of the foot placement was selected irregularly by a planning algorithm. Our goal is to adjust a smooth walking pattern generator with the selection of every foot placement such that the COG of the robot follows a stable trajectory characterized by a stability margin relative to the current support triangle. We propose a novel parameterization of the COG trajectory based on the current position, velocity, and acceleration of the four legs of the robot. This COG trajectory has guaranteed continuous velocity and acceleration profiles, which leads to continuous velocity and acceleration profiles of the leg movement, which is ideally suited for advanced model-based controllers. Pitch, yaw, and ground clearance of the robot are easily adjusted automatically under any terrain situation. We evaluate our gait generation technique on the Little-Dog quadruped robot when traversing complex rocky and sloped terrains.

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link (url) [BibTex]

link (url) [BibTex]


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Bayesian Nonparametric Regression with Local Models

Ting, J., Schaal, S.

In Workshop on Robotic Challenges for Machine Learning, NIPS 2007, 2007, clmc (inproceedings)

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[BibTex]

[BibTex]


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STRIDE: A highly maneuverable and non-tethered water strider robot

Song, Y. S., Sitti, M.

In Robotics and Automation, 2007 IEEE International Conference on, pages: 980-984, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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Dry spinning polymeric nano/microfiber arrays using glass micropipettes with controlled porosities and fiber diameters

Nain, A. S., Gupta, A., Amon, C., Sitti, M.

In Nanotechnology, 2007. IEEE-NANO 2007. 7th IEEE Conference on, pages: 728-732, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract
We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

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PDF [BibTex]

PDF [BibTex]


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Task space control with prioritization for balance and locomotion

Mistry, M., Nakanishi, J., Schaal, S.

In IEEE International Conference on Intelligent Robotics Systems (IROS 2007), San Diego, CA: Oct. 29 Ð Nov. 2, 2007, clmc (inproceedings)

Abstract
This paper addresses locomotion with active balancing, via task space control with prioritization. The center of gravity (COG) and foot of the swing leg are treated as task space control points. Floating base inverse kinematics with constraints is employed, thereby allowing for a mobile platform suitable for locomotion. Different techniques of task prioritization are discussed and we clarify differences and similarities of previous suggested work. Varying levels of prioritization for control are examined with emphasis on singularity robustness and the negative effects of constraint switching. A novel controller for task space control of balance and locomotion is developed which attempts to address singularity robustness, while minimizing discontinuities created by constraint switching. Controllers are evaluated using a quadruped robot simulator engaging in a locomotion task.

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link (url) [BibTex]

link (url) [BibTex]


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Microrobotically fabricated biological scaffolds for tissue engineering

Nain, A. S., Chung, F., Rule, M., Jadlowiec, J. A., Campbell, P. G., Amon, C., Sitti, M.

In Robotics and Automation, 2007 IEEE International Conference on, pages: 1918-1923, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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Bacterial flagella assisted propulsion of patterned latex particles: Effect of particle size

Behkam, B., Sitti, M.

In Nanotechnology, 2007. IEEE-NANO 2007. 7th IEEE Conference on, pages: 723-727, 2007 (inproceedings)

pi

Project Page [BibTex]

Project Page [BibTex]


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A scaled bilateral control system for experimental 1-D teleoperated nanomanipulation applications

Onal, C. D., Pawashe, C., Sitti, M.

In Intelligent Robots and Systems, 2007. IROS 2007. IEEE/RSJ International Conference on, pages: 483-488, 2007 (inproceedings)

pi

[BibTex]

[BibTex]


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Guided Self-organisation for Autonomous Robot Development

Martius, G., Herrmann, J. M., Der, R.

In Advances in Artificial Life 9th European Conference, ECAL 2007, 4648, pages: 766-775, LNCS, Springer, 2007 (inproceedings)

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[BibTex]

[BibTex]

2005


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Kernel ICA for Large Scale Problems

Jegelka, S., Gretton, A., Achlioptas, D.

In pages: -, NIPS Workshop on Large Scale Kernel Machines, December 2005 (inproceedings)

ei

Web [BibTex]

2005


Web [BibTex]


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Popper, Falsification and the VC-dimension

Corfield, D., Schölkopf, B., Vapnik, V.

(145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

ei

PDF [BibTex]

PDF [BibTex]


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Training Support Vector Machines with Multiple Equality Constraints

Kienzle, W., Schölkopf, B.

In Proceedings of the 16th European Conference on Machine Learning, Lecture Notes in Computer Science, Vol. 3720, pages: 182-193, (Editors: JG Carbonell and J Siekmann), Springer, Berlin, Germany, ECML, November 2005 (inproceedings)

Abstract
In this paper we present a primal-dual decomposition algorithm for support vector machine training. As with existing methods that use very small working sets (such as Sequential Minimal Optimization (SMO), Successive Over-Relaxation (SOR) or the Kernel Adatron (KA)), our method scales well, is straightforward to implement, and does not require an external QP solver. Unlike SMO, SOR and KA, the method is applicable to a large number of SVM formulations regardless of the number of equality constraints involved. The effectiveness of our algorithm is demonstrated on a more difficult SVM variant in this respect, namely semi-parametric support vector regression.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., Schoelkopf, B.

In Algorithmic Learning Theory, Lecture Notes in Computer Science, Vol. 3734, pages: 63-78, (Editors: S Jain and H-U Simon and E Tomita), Springer, Berlin, Germany, 16th International Conference ALT, October 2005 (inproceedings)

Abstract
We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on {methodname} do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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An Analysis of the Anti-Learning Phenomenon for the Class Symmetric Polyhedron

Kowalczyk, A., Chapelle, O.

In Algorithmic Learning Theory: 16th International Conference, pages: 78-92, Algorithmic Learning Theory, October 2005 (inproceedings)

Abstract
This paper deals with an unusual phenomenon where most machine learning algorithms yield good performance on the training set but systematically worse than random performance on the test set. This has been observed so far for some natural data sets and demonstrated for some synthetic data sets when the classification rule is learned from a small set of training samples drawn from some high dimensional space. The initial analysis presented in this paper shows that anti-learning is a property of data sets and is quite distinct from overfitting of a training data. Moreover, the analysis leads to a specification of some machine learning procedures which can overcome anti-learning and generate ma- chines able to classify training and test data consistently.

ei

PDF [BibTex]

PDF [BibTex]


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A Combinatorial View of Graph Laplacians

Huang, J.

(144), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2005 (techreport)

Abstract
Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence for the normalized Laplacian. In this paper, we analyze different variants of graph Laplacians directly from the ways solving the original graph partitioning problem. The graph partitioning problem is a well-known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.

ei

[BibTex]

[BibTex]


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Beyond Pairwise Classification and Clustering Using Hypergraphs

Zhou, D., Huang, J., Schölkopf, B.

(143), Max Planck Institute for Biological Cybernetics, August 2005 (techreport)

Abstract
In many applications, relationships among objects of interest are more complex than pairwise. Simply approximating complex relationships as pairwise ones can lead to loss of information. An alternative for these applications is to analyze complex relationships among data directly, without the need to first represent the complex relationships into pairwise ones. A natural way to describe complex relationships is to use hypergraphs. A hypergraph is a graph in which edges can connect more than two vertices. Thus we consider learning from a hypergraph, and develop a general framework which is applicable to classification and clustering for complex relational data. We have applied our framework to real-world web classification problems and obtained encouraging results.

ei

PDF [BibTex]

PDF [BibTex]


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Building Sparse Large Margin Classifiers

Wu, M., Schölkopf, B., BakIr, G.

In Proceedings of the 22nd International Conference on Machine Learning, pages: 996-1003, (Editors: L De Raedt and S Wrobel ), ACM, New York, NY, USA, ICML , August 2005 (inproceedings)

Abstract
This paper presents an approach to build Sparse Large Margin Classifiers (SLMC) by adding one more constraint to the standard Support Vector Machine (SVM) training problem. The added constraint explicitly controls the sparseness of the classifier and an approach is provided to solve the formulated problem. When considering the dual of this problem, it can be seen that building an SLMC is equivalent to constructing an SVM with a modified kernel function. Further analysis of this kernel function indicates that the proposed approach essentially finds a discriminating subspace that can be spanned by a small number of vectors, and in this subspace different classes of data are linearly well separated. Experimental results over several classification benchmarks show that in most cases the proposed approach outperforms the state-of-art sparse learning algorithms.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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Learning from Labeled and Unlabeled Data on a Directed Graph

Zhou, D., Huang, J., Schölkopf, B.

In Proceedings of the 22nd International Conference on Machine Learning, pages: 1041 -1048, (Editors: L De Raedt and S Wrobel), ACM, New York, NY, USA, ICML, August 2005 (inproceedings)

Abstract
We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

ei

PostScript PDF [BibTex]

PostScript PDF [BibTex]


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Regularization on Discrete Spaces

Zhou, D., Schölkopf, B.

In Pattern Recognition, Lecture Notes in Computer Science, Vol. 3663, pages: 361-368, (Editors: WG Kropatsch and R Sablatnig and A Hanbury), Springer, Berlin, Germany, 27th DAGM Symposium, August 2005 (inproceedings)

Abstract
We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as the discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on the discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as the discrete analogue of their counterparts in the continuous case.

ei

PDF PostScript DOI [BibTex]

PDF PostScript DOI [BibTex]


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Large Margin Non-Linear Embedding

Zien, A., Candela, J.

In ICML 2005, pages: 1065-1072, (Editors: De Raedt, L. , S. Wrobel), ACM Press, New York, NY, USA, 22nd International Conference on Machine Learning, August 2005 (inproceedings)

Abstract
It is common in classification methods to first place data in a vector space and then learn decision boundaries. We propose reversing that process: for fixed decision boundaries, we ``learn‘‘ the location of the data. This way we (i) do not need a metric (or even stronger structure) -- pairwise dissimilarities suffice; and additionally (ii) produce low-dimensional embeddings that can be analyzed visually. We achieve this by combining an entropy-based embedding method with an entropy-based version of semi-supervised logistic regression. We present results for clustering and semi-supervised classification.

ei

PDF PostScript Web DOI [BibTex]

PDF PostScript Web DOI [BibTex]


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Face Detection: Efficient and Rank Deficient

Kienzle, W., BakIr, G., Franz, M., Schölkopf, B.

In Advances in Neural Information Processing Systems 17, pages: 673-680, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
This paper proposes a method for computing fast approximations to support vector decision functions in the field of object detection. In the present approach we are building on an existing algorithm where the set of support vectors is replaced by a smaller, so-called reduced set of synthesized input space points. In contrast to the existing method that finds the reduced set via unconstrained optimization, we impose a structural constraint on the synthetic points such that the resulting approximations can be evaluated via separable filters. For applications that require scanning an entire image, this decreases the computational complexity of a scan by a significant amount. We present experimental results on a standard face detection database.

ei

PDF Web [BibTex]

PDF Web [BibTex]


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Methods Towards Invasive Human Brain Computer Interfaces

Lal, T., Hinterberger, T., Widman, G., Schröder, M., Hill, J., Rosenstiel, W., Elger, C., Schölkopf, B., Birbaumer, N.

In Advances in Neural Information Processing Systems 17, pages: 737-744, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
During the last ten years there has been growing interest in the development of Brain Computer Interfaces (BCIs). The field has mainly been driven by the needs of completely paralyzed patients to communicate. With a few exceptions, most human BCIs are based on extracranial electroencephalography (EEG). However, reported bit rates are still low. One reason for this is the low signal-to-noise ratio of the EEG. We are currently investigating if BCIs based on electrocorticography (ECoG) are a viable alternative. In this paper we present the method and examples of intracranial EEG recordings of three epilepsy patients with electrode grids placed on the motor cortex. The patients were asked to repeatedly imagine movements of two kinds, e.g., tongue or finger movements. We analyze the classifiability of the data using Support Vector Machines (SVMs) and Recursive Channel Elimination (RCE).

ei

PDF Web [BibTex]

PDF Web [BibTex]


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A Machine Learning Approach to Conjoint Analysis

Chapelle, O., Harchaoui, Z.

In Advances in Neural Information Processing Systems 17, pages: 257-264, (Editors: Saul, L.K. , Y. Weiss, L. Bottou), MIT Press, Cambridge, MA, USA, Eighteenth Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
Choice-based conjoint analysis builds models of consumers preferences over products with answers gathered in questionnaires. Our main goal is to bring tools from the machine learning community to solve more efficiently this problem. Thus, we propose two algorithms to estimate quickly and accurately consumer preferences.

ei

PDF Web [BibTex]

PDF Web [BibTex]


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An Auditory Paradigm for Brain-Computer Interfaces

Hill, N., Lal, T., Bierig, K., Birbaumer, N., Schölkopf, B.

In Advances in Neural Information Processing Systems 17, pages: 569-576, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
Motivated by the particular problems involved in communicating with "locked-in" paralysed patients, we aim to develop a brain-computer interface that uses auditory stimuli. We describe a paradigm that allows a user to make a binary decision by focusing attention on one of two concurrent auditory stimulus sequences. Using Support Vector Machine classification and Recursive Channel Elimination on the independent components of averaged event-related potentials, we show that an untrained user's EEG data can be classified with an encouragingly high level of accuracy. This suggests that it is possible for users to modulate EEG signals in a single trial by the conscious direction of attention, well enough to be useful in BCI.

ei

PDF Web [BibTex]

PDF Web [BibTex]


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Matrix Exponential Gradient Updates for On-line Learning and Bregman Projection

Tsuda, K., Rätsch, G., Warmuth, M.

In Advances in Neural Information Processing Systems 17, pages: 1425-1432, (Editors: Saul, L.K. , Y. Weiss, L. Bottou), MIT Press, Cambridge, MA, USA, Eighteenth Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements.

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PDF Web [BibTex]

PDF Web [BibTex]


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Machine Learning Applied to Perception: Decision Images for Classification

Wichmann, F., Graf, A., Simoncelli, E., Bülthoff, H., Schölkopf, B.

In Advances in Neural Information Processing Systems 17, pages: 1489-1496, (Editors: LK, Saul and Y, Weiss and L, Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
We study gender discrimination of human faces using a combination of psychophysical classification and discrimination experiments together with methods from machine learning. We reduce the dimensionality of a set of face images using principal component analysis, and then train a set of linear classifiers on this reduced representation (linear support vector machines (SVMs), relevance vector machines (RVMs), Fisher linear discriminant (FLD), and prototype (prot) classifiers) using human classification data. Because we combine a linear preprocessor with linear classifiers, the entire system acts as a linear classifier, allowing us to visualise the decision-image corresponding to the normal vector of the separating hyperplanes (SH) of each classifier. We predict that the female-to-maleness transition along the normal vector for classifiers closely mimicking human classification (SVM and RVM 1) should be faster than the transition along any other direction. A psychophysical discrimination experiment using the decision images as stimuli is consistent with this prediction.

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PDF Web [BibTex]

PDF Web [BibTex]


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Breaking SVM Complexity with Cross-Training

Bakir, G., Bottou, L., Weston, J.

In Advances in Neural Information Processing Systems 17, pages: 81-88, (Editors: Saul, L.K. , Y. Weiss, L. Bottou), MIT Press, Cambridge, MA, USA, Eighteenth Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
We propose an algorithm for selectively removing examples from the training set using probabilistic estimates related to editing algorithms (Devijver and Kittler82). The procedure creates a separable distribution of training examples with minimal impact on the decision boundary position. It breaks the linear dependency between the number of SVs and the number of training examples, and sharply reduces the complexity of SVMs during both the training and prediction stages.

ei

PDF Web [BibTex]

PDF Web [BibTex]


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Implicit Wiener series for higher-order image analysis

Franz, M., Schölkopf, B.

In Advances in Neural Information Processing Systems 17, pages: 465-472, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
The computation of classical higher-order statistics such as higher-order moments or spectra is difficult for images due to the huge number of terms to be estimated and interpreted. We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals. Since the functionals are estimated implicitly via polynomial kernels, the combinatorial explosion associated with the classical higher-order statistics is avoided. First results show that image structures such as lines or corners can be predicted correctly, and that pixel interactions up to the order of five play an important role in natural images.

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PDF Web [BibTex]

PDF Web [BibTex]


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Limits of Spectral Clustering

von Luxburg, U., Bousquet, O., Belkin, M.

In Advances in Neural Information Processing Systems 17, pages: 857-864, (Editors: Saul, L. K., Y. Weiss, L. Bottou), MIT Press, Cambridge, MA, USA, Eighteenth Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clustering algorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult to handle than the normalized case. Even though recently some first results on the convergence of normalized spectral clustering have been obtained, for the unnormalized case we have to develop a completely new approach combining tools from numerical integration, spectral and perturbation theory, and probability. It turns out that while in the normalized case, spectral clustering usually converges to a nice partition of the data space, in the unnormalized case the same only holds under strong additional assumptions which are not always satisfied. We conclude that our analysis gives strong evidence for the superiority of normalized spectral clustering. It also provides a basis for future exploration of other Laplacian-based methods.

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PDF Web [BibTex]

PDF Web [BibTex]


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Semi-supervised Learning on Directed Graphs

Zhou, D., Schölkopf, B., Hofmann, T.

In Advances in Neural Information Processing Systems 17, pages: 1633-1640, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
Given a directed graph in which some of the nodes are labeled, we investigate the question of how to exploit the link structure of the graph to infer the labels of the remaining unlabeled nodes. To that extent we propose a regularization framework for functions defined over nodes of a directed graph that forces the classification function to change slowly on densely linked subgraphs. A powerful, yet computationally simple classification algorithm is derived within the proposed framework. The experimental evaluation on real-world Web classification problems demonstrates encouraging results that validate our approach.

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PDF Web [BibTex]

PDF Web [BibTex]


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Splines with non positive kernels

Canu, S., Ong, CS., Mary, X.

In 5th International ISAAC Congress, pages: 1-10, (Editors: Begehr, H. G.W., F. Nicolosi), World Scientific, Singapore, 5th International ISAAC Congress, July 2005 (inproceedings)

Abstract
Non parametric regressions methods can be presented in two main clusters. The one of smoothing splines methods requiring positive kernels and the other one known as Nonparametric Kernel Regression allowing the use of non positive kernels such as the Epanechnikov kernel. We propose a generalization of the smoothing spline method to include kernels which are still symmetric but not positive semi definite (they are called indefinite). The general relationship between smoothing spline, Reproducing Kernel Hilbert Spaces and positive kernels no longer exists with indefinite kernel. Instead they are associated with functional spaces called Reproducing Kernel Krein Spaces (RKKS) embedded with an indefinite inner product and thus not directly associated with a norm. Smothing splines in RKKS have many of the interesting properties of splines in RKHS, such as orthogon ality, projection, representer theorem and generalization bounds. We show that smoothing splines can be defined in RKKS as the regularized solution of the interpolation problem. Since no norm is available in a RKKS, Tikhonov regularization cannot be defined. Instead, we proposed to use iterative methods of conjugate gradient type with early stopping as regularization mechanism. Several iterative algorithms were collected which can be used to solve the optimization problems associated with learning in indefinite spaces. Some preliminary experiments with indefinite kernels for spline smoothing are reported revealing the computational efficiency of the approach.

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PDF Web [BibTex]

PDF Web [BibTex]


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Kernel Methods for Implicit Surface Modeling

Schölkopf, B., Giesen, J., Spalinger, S.

In Advances in Neural Information Processing Systems 17, pages: 1193-1200, (Editors: LK Saul and Y Weiss and L Bottou), MIT Press, Cambridge, MA, USA, 18th Annual Conference on Neural Information Processing Systems (NIPS), July 2005 (inproceedings)

Abstract
We describe methods for computing an implicit model of a hypersurface that is given only by a finite sampling. The methods work by mapping the sample points into a reproducing kernel Hilbert space and then determining regions in terms of hyperplanes.

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PDF Web [BibTex]

PDF Web [BibTex]


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Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.

(140), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2005 (techreport)

Abstract
We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

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PDF [BibTex]

PDF [BibTex]


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Active Learning for Parzen Window Classifier

Chapelle, O.

In AISTATS 2005, pages: 49-56, (Editors: Cowell, R. , Z. Ghahramani), Tenth International Workshop on Artificial Intelligence and Statistics (AI & Statistics), January 2005 (inproceedings)

Abstract
The problem of active learning is approached in this paper by minimizing directly an estimate of the expected test error. The main difficulty in this ``optimal'' strategy is that output probabilities need to be estimated accurately. We suggest here different methods for estimating those efficiently. In this context, the Parzen window classifier is considered because it is both simple and probabilistic. The analysis of experimental results highlights that regularization is a key ingredient for this strategy.

ei

Web [BibTex]

Web [BibTex]


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Semi-Supervised Classification by Low Density Separation

Chapelle, O., Zien, A.

In AISTATS 2005, pages: 57-64, (Editors: Cowell, R. , Z. Ghahramani), Tenth International Workshop on Artificial Intelligence and Statistics (AI & Statistics), January 2005 (inproceedings)

Abstract
We believe that the cluster assumption is key to successful semi-supervised learning. Based on this, we propose three semi-supervised algorithms: 1. deriving graph-based distances that emphazise low density regions between clusters, followed by training a standard SVM; 2. optimizing the Transductive SVM objective function, which places the decision boundary in low density regions, by gradient descent; 3. combining the first two to make maximum use of the cluster assumption. We compare with state of the art algorithms and demonstrate superior accuracy for the latter two methods.

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PDF Web [BibTex]

PDF Web [BibTex]


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Kernel Constrained Covariance for Dependence Measurement

Gretton, A., Smola, A., Bousquet, O., Herbrich, R., Belitski, A., Augath, M., Murayama, Y., Pauls, J., Schölkopf, B., Logothetis, N.

In Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics, pages: 112-119, (Editors: R Cowell, R and Z Ghahramani), AISTATS, January 2005 (inproceedings)

Abstract
We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence, with emphasis on constrained covariance (COCO), a novel criterion to test dependence of random variables. We show that COCO is a test for independence if and only if the associated RKHSs are universal. That said, no independence test exists that can distinguish dependent and independent random variables in all circumstances. Dependent random variables can result in a COCO which is arbitrarily close to zero when the source densities are highly non-smooth. All current kernel-based independence tests share this behaviour. We demonstrate exponential convergence between the population and empirical COCO. Finally, we use COCO as a measure of joint neural activity between voxels in MRI recordings of the macaque monkey, and compare the results to the mutual information and the correlation. We also show the effect of removing breathing artefacts from the MRI recording.

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PDF Web [BibTex]

PDF Web [BibTex]