Publications

Similarity ratings are a widely used tool for the assessment of high-level perceptual similarity. Several approaches to conceptualizing similarity exist. We are concerned with the featural approach which was developed by [Tversky, 1977, Psychological Review 84:327-352] and mathematically formalized in [Lengnink, 1996, PhD Dissertation, TU Darmstadt]. This formalization posits a partial order between pairs of objects (stimuli) as the fundamental mathematical structure of similarity, traditional similarity measures (e.g. Russell-Rao, Jaccard etc.) are conceived as order-preserving mappings from the partial order between pairs into the (real) numbers. This approach preserves the main structural features of Tversky's model, and makes additional predictions about the (non-)comparability of similarity between pairs of objects. We tested these predictions experimentally: a) subjects rated the similarity between natural images on a 7-point Likert scale, and b) they ordered pairs of images by their perceived similarity. We find that the ordering predictions of ratings are well preserved (>85%). One drawback of similarity ratings is that they provide only an implicit measure of “relatedness”. We employ theoretical framework of Formal Concept Analysis [Ganter {{&}} Wille, 1996, Formal Concept Analysis, Springer, New York] to make the relationships explicit as concept lattices, which generalizes traditional approaches based on hierarchical clustering. [Support from EU Commission, EC FP7-ICT-248311 AMARSi, ABC PITN-GA-011-290011: DFG GI 305/4-1, DFG GZ: KA 1258/15-1, BMBF, FKZ: 01GQ1002A]

A wide range of blind source separation methods have been used in motor control research for the extraction of movement primitives from EMG and kinematic data. Popular examples are principal component analysis (PCA),independent component analysis (ICA), anechoic demixing, and the time-varying synergy model. However, choosing the parameters of these models, or indeed choosing the type of model, is often done in a heuristic fashion, driven by result expectations as much as by the data. We propose an objective criterion which allows to select the model type, number of primitives and the temporal smoothness prior. Our approach is based on a Laplace approximation to the posterior distribution of the parameters of a given blind source separation model, re-formulated as a Bayesian generative model.We first validate our criterion on ground truth data, showing that it performs at least as good as traditional model selection criteria (Bayesian information criterion, BIC and the Akaike Information Criterion (AIC)). Then, we analyze human gait data, finding that an anechoic mixture model with a temporal smoothness constraint on the sources can best account for the data.

The endpoint trajectories of human movements fulfill characteristic power laws linking velocity and curvature. The parameters of these power laws typically vary between different segments of longer action sequences. These parameters might thus be exploited for the unsupervised segmentation of actions into movement primitives. For the example of sign language we investigate whether such segments can be identified by Bayesian binning, using a Gaussian observation model whose mean has a polynomial time dependence. We show that this method yields good segmentation and correctly models ground-truth data composed of segments obeying power laws correctly models ground truth kinematics composed of consecutive segments derived from wrist trajectories recorded from users of Israeli Sign Language. Importantly, polynomial orders between 3 and 5 yield an optimal trade-off between complexity and accuracy of the trajectory approximation, in accordance with the minimum acceleration and minimum jerk models. Comparing the orders of the polynomials best approximating natural kinematics against those needed to fit the power law ground truth data suggests that kinematic properties not compatible with power laws are also not adequately represented by low order polynomials and require higher order polynomials for a good approximation.