Heiko Hoffmann

Kernel PCA for novelty detection

Kernel principal component analysis (kernel PCA) is a non-linear extension of PCA. This study introduces and investigates the use of kernel PCA for novelty detection. Training data are mapped into an infinite-dimensional feature space. In this space, kernel PCA extracts the principal components of the data distribution. The squared distance to the corresponding principal subspace is the measure for novelty. This new method demonstrated a competitive performance on two-dimensional synthetic distributions and on two real-world data sets: handwritten digits and breast-cancer cytology.

Perception through visuomotor anticipation in a mobile robot

Several scientists suggested that certain perceptual qualities are based on sensorimotor anticipation: for example, the softness of a sponge is perceived by anticipating the sensations resulting from a grasping movement. For the perception of spatial arrangements, this article demonstrates that this concept can be realized in a mobile robot. The robot first learned to predict how its visual input changes under movement commands. With this ability, two perceptual tasks could be solved: judging the distance to an obstacle in front by mentally simulating a movement toward the obstacle, and recognizing a dead end by simulating either an obstacle-avoidance algorithm or a recursive search for an exit. A simulated movement contained a series of prediction steps. In each step, a multilayer perceptron anticipated the next image, which, however, became increasingly noisy. To denoise an image, it was split into patches, and each patch was projected onto a manifold obtained by modelling the density of the distribution of training patches with a mixture of Gaussian functions.

An extension of neural gas to local PCA

We suggest an extension of the neural gas vector quantization method to local principal component analysis. The distance measure for the competition between local units combines a normalized Mahalanobis distance in the principal subspace and the squared reconstruction error, with the weighting of both measures depending on the residual variance in the minor subspace. A recursive least-squares method performs the local principal component analysis. The method is tested on synthetic two- and three-dimensional data and on the recognition of handwritten digits.

Learning visuomotor transformations for gaze-control and grasping

For reaching to and grasping of an object, visual information about the object must be transformed into motor or postural commands for the arm and hand. In this paper, we present a robot model for visually guided reaching and grasping. The model mimics two alternative processing pathways for grasping, which are also likely to coexist in the human brain. The first pathway directly uses the retinal activation to encode the target position. In the second pathway, a saccade controller makes the eyes (cameras) focus on the target, and the gaze direction is used instead as positional input. For both pathways, an arm controller transforms information on the target’s position and orientation into an arm posture suitable for grasping. For the training of the saccade controller, we suggest a novel staged learning method which does not require a teacher that provides the necessary motor commands. The arm controller uses unsupervised learning: it is based on a density model of the sensor and the motor data. Using this density, a mapping is achieved by completing a partially given sensorimotor pattern. The controller can cope with the ambiguity in having a set of redundant arm postures for a given target. The combined model of saccade and arm controller was able to fixate and grasp an elongated object with arbitrary orientation and at arbitrary position on a table in 94% of trials.

Unsupervised learning of a kinematic arm model

An abstract recurrent neural network trained by an unsupervised method is applied to the kinematic control of a robot arm. The network is a novel extension of the Neural Gas vector quantization method to local principal component analysis. It represents the manifold of the training data by a collection of local linear models. In the kinematic control task, the network learns the relationship between the 6 joint angles of a simulated robot arm, the corresponding 3 end-effector coordinates, and an additional collision variable. After training, the learned approximation of the 10-dimensional manifold of the training data can be used to compute both the forward and inverse kinematics of the arm. The inverse kinematic relationship can be recalled even though it is not a function, but a one-to-many mapping.

Cross-correlation studies with seismic noise

Ocean waves interacting in shallow water at the shore generate land waves propagating inland. To study these waves vertical, horizontal and tilt seismic noise were measured simultaneously at one location. Vibration isolators designed for gravitational wave research were used for detection. Cross-correlation between the above components was calculated. We found correlations between all of them. However, only the correlation between horizontal and vertical motions could be addressed to land waves, and other correlations are thought to be due to local rigid body motion of the large building in which the experiments were located.