Neural networks in non-Euclidean metric spaces

Duch, Włodzisław; Adamczak, Rafał

doi:10.1109/ijcnn.1999.831572

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…When rotational angle is included in the pose space, the appearance manifold possesses the topology of a solid torus S × R 2 . Learning algorithms to estimate non-Euclidean manifolds are still very underdeveloped, and methods that use self-organized maps or neural networks are not particularly efficient with appearance images [12], [5]. We are investigating how a method such as locally linear projection may be extended to handle these more challenging situations.…”

Section: Discussionmentioning

confidence: 99%

Learning nonlinear appearance manifolds for robot localization

Ham

Lin

Lee

2005

2005 IEEE/RSJ International Conference on Intelligent Robots and Systems

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We propose a nonlinear method for learning the low-dimensional pose of a robot from high-dimensional panoramic images. The panoramic images are assumed to lie on a nonlinear low-dimensional appearance manifold that is embedded in a high-dimensional image space. We demonstrate that the local geometry of a point and its nearest neighbors on this manifold can be used to project the point onto a low-dimensional coordinate space. Using this embedding, the unknown camera position can be estimated from a novel panoramic image. We show how the image-based position measurements can be integrated with odometry information in a Bayesian framework to yield an online estimate of a robot's position. Results from simulated data show that the proposed method outperforms other appearance-based models based upon principal components analysis and kernel density estimation.

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Section: Discussionmentioning

confidence: 99%

Learning nonlinear appearance manifolds for robot localization

Ham

Lin

Lee

2005

2005 IEEE/RSJ International Conference on Intelligent Robots and Systems

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“…• Perceptron nodes based on sigmoidal functions with scalar product or distancebased activations [77,78], as in layers of MLP networks, but with targets specified by some criterion (any criterion used for linear transformations is sufficient).…”

Section: Other Non-linear Mappingsmentioning

confidence: 99%

Optimal Support Features for Meta-Learning

Duch

Maszczyk

Grochowski

2011

Studies in Computational Intelligence

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Meta-learning has many aspects, but its final goal is to discover in an automatic way many interesting models for a given data. Our early attempts in this area involved heterogeneous learning systems combined with a complexity-guided search for optimal models, performed within the framework of (dis)similarity based methods to discover "knowledge granules". This approach, inspired by neurocognitive mechanisms of information processing in the brain, is generalized here to learning based on parallel chains of transformations that extract useful information granules and use it as additional features. Various types of transformations that generate hidden features are analyzed and methods to generate them are discussed. They include restricted random projections, optimization of these features using projection pursuit methods, similarity-based and general kernel-based features, conditionally defined features, features derived from partial successes of various learning algorithms, and using the whole learning models as new features. In the enhanced feature space the goal of learning is to create image of the input data that can be directly handled by relatively simple decision processes. The focus is on hierarchical methods for generation of information, starting from new support features that are discovered by different types of data models created on similar tasks and successively building more complex features on the enhanced feature spaces. Resulting algorithms facilitate deep learning, and also enable understanding of structures present in the data by visualization of the results of data transformations and by creating logical, fuzzy and prototype-based rules based on new features. Relations to various machine-learning approaches, comparison of results, and neurocognitive inspirations for meta-learning are discussed.

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“…-Weighted distance-based transformations, a special case of general kernel transformations, that use (optimized) reference vectors [43]. -Perceptron nodes based on sigmoidal functions with scalar product or distancebased activations [42,41], as in layers of MLP networks, but with targets specified by some criterion (any criterion used for linear transformations is sufficient). -Heterogeneous transformations using several types of kernels to capture details at different resolution [57].…”

Section: Extracting Information From All Featuresmentioning

confidence: 99%

Towards Comprehensive Foundations of Computational Intelligence

Duch

2007

Studies in Computational Intelligence

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Abstract. Although computational intelligence (CI) covers a vast variety of different methods it still lacks an integrative theory. Several proposals for CI foundations are discussed: computing and cognition as compression, meta-learning as search in the space of data models, (dis)similarity based methods providing a framework for such meta-learning, and a more general approach based on chains of transformations. Many useful transformations that extract information from features are discussed. Heterogeneous adaptive systems are presented as particular example of transformation-based systems, and the goal of learning is redefined to facilitate creation of simpler data models. The need to understand data structures leads to techniques for logical and prototype-based rule extraction, and to generation of multiple alternative models, while the need to increase predictive power of adaptive models leads to committees of competent models. Learning from partial observations is a natural extension towards reasoning based on perceptions, and an approach to intuitive solving of such problems is presented. Throughout the paper neurocognitive inspirations are frequently used and are especially important in modeling of the higher cognitive functions. Promising directions such as liquid and laminar computing are identified and many open problems presented.

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Neural networks in non-Euclidean metric spaces

Abstract: Abstract.Multilayer Perceptrons (MLPs)

Cited by 5 publications

References 17 publications

Learning nonlinear appearance manifolds for robot localization

Learning nonlinear appearance manifolds for robot localization

Optimal Support Features for Meta-Learning

Towards Comprehensive Foundations of Computational Intelligence

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