Ante Jukić
Abstract
We present a new method for efficiently approximating the global penetration depth between two rigid objects using machine learning techniques. Our approach consists of two phases: offline learning and performing run-time queries. In the learning phase, we precompute an approximation of the contact space of a pair of intersecting objects from a set of samples in the configuration space. We use active and incremental learning algorithms to accelerate the precomputation and improve the accuracy. During the run-time phase, our algorithm performs a nearest-neighbor query based on translational or rotational distance metrics. The run-time query has a small overhead and computes an approximation to global penetration depth in a few milliseconds. We use our algorithm for collision response computations in Box2D or Bullet game physics engines and complex 3D models and observe more than an order of magnitude improvement over prior PD computation techniques.
- Bader et al., 2012. Bader, B., Kolda, T., and others, 2012. MATLAB Tensor Toolbox Version 2.5. <http://www.sandia.gov/~tgkolda/TensorToolbox/index-2.5.html>.Google Scholar
- Chang and Lin, 2011. LIBSVM: A library for support vector machines. ACM Trans. Intell. Syst. Technol. v2 i3. 27:1-27:27. Google Scholar
- Cichocki et al., 2009. Nonnegative Matrix and Tensor Factorizations. John Wiley & Sons, Chichester, UK.Google Scholar
- Cong et al., 2012. Cong, F., Phan, A. H., Zhao, Q., Wu, Q., Ristaniemi, T., Cichocki, A., 2012. Feature Extraction by Nonnegative Tucker Decomposition from EEG Data Including Testing and Training Observations. In: Proceedings of The International Conference on Neural Information Processing (ICONIP), Doha, Qatar, pp. 166-173. Google Scholar
- Cover and Thomas, 1991. Elements of Information Theory. Wiley, New York, USA.Google Scholar
- Graham and Allison, 1998. Characterizing virtual eigensignatures for general purpose face recognition. In: Wechsler, H., Phillips, P.J., Bruce, V., Fogelman-Soulie, S., Huang, T.S. (Eds.), Face Recognition: From Theory to Applications. NATO ASI Series F, 163. Computer and Systems Sciences. pp. 446-456.Google Scholar
- Hou et al., 2013. Efficient image classification via multiple rank regression. IEEE Trans. Image Process. v22 i1. 340-352.Google Scholar
- Hyvärinen et al., 2001. Independent Component Analysis. Wiley, New York, USA.Google Scholar
-
Kamandar and Ghassemian, 2013. Linear feature extraction for hyperspectral images based on information theoretic learning. IEEE Geosci. Remote Sens. Lett. v10 i4. 702-706.Google Scholar
- Kolda and Bader, 2009. Tensor decompositions and applications. SIAM Rev. v51 i3. 455-500. Google Scholar
- Leiva-Murillo and Artès-Rodrígues, 2007. Maximization of mutual information for supervised linear feature extraction. IEEE Trans. Neural Networks. v18 i5. 1433-1441. Google Scholar
- Nie et al., 2007. Nie, F., Xiang, S., Song, Y., Zhang, C., 2007. Optimal dimensionality discriminant analysis and its application to image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR '07), Minneapolis, Minnesota, USA, pp. 1-8.Google Scholar
- Nie et al., 2009. Extracting the optimal dimensionality for local tensor discriminant analysis. Pattern Recogn. v42. 105-114. Google Scholar
- Petridis and Perantonis, 2004. On the relation between discriminant analysis and mutual information for supervised linear feature extraction. Pattern Recogn. v37. 857-874.Google Scholar
-
Phan, 2012. Phan, A. H., 2012. NFEA: Tensor Toolbox for Feature Extraction and Applications. <http://www.bsp.brain.riken.jp/~phan/nfea/nfea.html>.Google Scholar
- Phan and Cichocki, 2010. Tensor decompositions for feature extraction and classification of high dimensional datasets. IEICE Nonlinear Theory Appl. v1. 37-68.Google Scholar
-
Phan and Cichocki, 2011. Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classfication. Neurocomputing. v74. 1956-1969. Google Scholar
- Signoretto et al., 2011. A kernel-based framework for tensorial data analysis. Neural Networks. v24 i8. 861-874. Google Scholar
- Tao et al., 2007. General tensor discriminant analysis and Gabor features for gait recognition. IEEE Trans. Pattern Anal. Mach. Intell. v29 i10. 1700-1715. Google Scholar
- Torkkola, 2003. Feature extraction by non-parametric mutual information maximization. J. Mach. Learn. Res. v3. 1415-1438. Google Scholar
-
Tucker, 1964. The extension of factor analysis to three-dimensional matrices. In: Gulliksen, H., Frederiksen, N. (Eds.), Contributions to Mathematical Psychology, Holt, Reinhart and Winston, New York. pp. 110-127.Google Scholar
- Tucker, 1966. Some mathematical notes on three-mode factor analysis. Psychometrika. v31. 279-311.Google Scholar
- Wen and Yin, 2012a. A feasible method for optimization with orthogonality constraints. Math. Program.Google Scholar
- Wen and Yin, 2012b. Wen, Z., Yin, W., 2012b. Optimization with Orthogonality Constraints. <http://optman.blogs.rice.edu/>.Google Scholar
- Yan et al., 2005. Yan, S., Xu, D., Yang, Q., Zhang, L., Tang, X. Z.-J., 2005. Discriminant Analysis with Tensor Representation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, San Diego, USA, pp. 526-532. Google Scholar
- Zhang et al., 2009. Tensor linear Laplacian discrimination (TLLD) for feature extraction. Pattern Recogn. v42. 1941-1948. Google Scholar
Index Terms
- Supervised feature extraction for tensor objects based on maximization of mutual information
Recommendations
Supervised tensor learning
Tensor representation is helpful to reduce the small sample size problem in discriminative subspace selection. As pointed by this paper, this is mainly because the structure information of objects in computer vision research is a reasonable constraint ...
Knows what it knows: a framework for self-aware learning
We introduce a learning framework that combines elements of the well-known PAC and mistake-bound models. The KWIK (knows what it knows) framework was designed particularly for its utility in learning settings where active exploration can impact the ...
Empirical usage metadata in learning objects
FIE'09: Proceedings of the 39th IEEE international conference on Frontiers in education conferenceThe iLOG Project (Intelligent Learning Object Guide) is designed to augment multimedia learning objects with information about (1) how a learning object has been used, (2) how it has impacted instruction and learning, and (3) how it should be used. The ...
Comments