In local Principal Component Analysis (PCA), a distribution is approximated by multiple units, each representing a local region by a hyper-ellipsoid obtained through PCA. We present an extension for local PCA which adaptively adjusts both the learning rate of each unit and the potential function which guides the competition between the local units. Our local PCA method is an online neural network method where unit centers and shapes are modified after the presentation of each data point. For several benchmark distributions, we demonstrate that our method improves the overall quality of clustering, especially for high-dimensional distributions where many conventional methods do not perform satisfactorily. Our online method is also well suited for the processing of streaming data: The two adaptive mechanisms lead to a quick reorganization of the clustering when the underlying distribution changes.

Summary Local visual homing methods are a family of algorithms for visually guided navigation on mobile robots. Within this family, the so‐called min‐warping algorithm yields very precise results but is rather compute‐intensive. For this reason, we developed several implementations of this algorithm for different parallel hardware architectures (multi‐core CPUs with SIMD extensions, graphics processing units (GPUs), field‐programmable gate array) to arrive at a fast and energy‐efficient solution which is suited for real‐time performance on mobile platforms with limited battery capacity. Because the min‐warping algorithm is also well suited as a general benchmark, we carried out a comprehensive comparison study which includes both speed and real‐power measurements and covers both low‐power processors and high‐end devices. Our findings suggest that field‐programmable gate arrays offer the most energy‐efficient platform for min‐warping in the area of low‐power processors, while GPUs take the lead in the area of high‐end devices. However, as soon as the full capabilities of modern CPUs (like vector execution units and multiple hardware threads) are used, the speedup advantage of GPUs goes down to the single digit range. Copyright © 2016 John Wiley & Sons, Ltd.

We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as decorrelation method for the estimation of multiple singular vectors and singular values. Experiments on synthetic data show that coupled learning rules converge faster than Hebbian learning rules and that the first-order approximation of Gram-Schmidt orthonormalization produces more precise estimates and better orthonormality than the standard deflation method.

Insects are able to return to important places in their environment by storing an image of the surroundings while at the goal, and later computing a home direction from a matching between this 'snapshot' image and the currently perceived image. Very similar ideas are pursued for the visual navigation of mobile robots. A wide range of different solutions for the matching between the two images have been suggested. This paper explores the application of optical flow techniques for visual homing. The performance of five different flow techniques and a reference method is analysed based on image collections from three different indoor environments. We show that block matching, two simple variants of block matching and two even simpler differential techniques produce robust homing behaviour, despite the simplicity of the matched features. Our analysis reveals that visual homing can succeed even in the presence of many incorrect feature correspondences, and that low-frequency features are sufficient for homing. In particular, the successful application of differential methods opens new vistas on the visual homing problem, both as plausible and parsimonious models of visual insect navigation, and as a starting point for novel robot navigation methods.

The paper reviews single-neuron learning rules for minor component analysis and suggests a novel minor component learning rule. In this rule, the weight vector length is self-stabilizing, i.e., moving towards unit length in each learning step. In simulations with low- and medium-dimensional data, the performance of the novel learning rule is compared with previously suggested rules.

A framework for a class of coupled principal component learning rules is presented. In coupled rules, eigenvectors and eigenvalues of a covariance matrix are simultaneously estimated in coupled equations. Coupled rules can mitigate the stability-speed problem affecting noncoupled learning rules, since the convergence speed in all eigendirections of the Jacobian becomes widely independent of the eigenvalues of the covariance matrix. A number of coupled learning rule systems for principal component analysis, two of them new, is derived by applying Newton's method to an information criterion. The relations to other systems of this class, the adaptive learning algorithm (ALA), the robust recursive least squares algorithm (RRLSA), and a rule with explicit renormalization of the weight vector length, are established.

Insects of several species rely on visual landmarks for returning to important locations in their environment. The "average landmark vector model" is a parsimonious model which reproduces some aspects of the visual homing behavior of bees and ants. To gain insights in the structure and complexity of the neural apparatus that might underly the navigational capabilities of these animals, the average landmark vector model was implemented in analog hardware and used to control a mobile robot. The experiments demonstrate that the apparently complex task of visual homing might be realized by simple and mostly peripheral neural circuits in insect brains.

The computation of shortest paths as a basic task in robotics can be accomplished by graph-searching algorithms. Attempts have been made to accelerate a part of these algorithms-the computation of potential vectors-using fine-grained parallel hardware. As shown in this paper, the complexity of digital path-planning circuits can be enormously reduced, if distances are encoded by hardware time delays.