Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data

In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrap$632+$and k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead to$sim 96$correct classification rates with less than 10% of the original features

Large-scale simultaneous inference under dependence

Simultaneous, post-hoc inference is desirable in large-scale hypotheses testing as it allows for exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post-hoc inference methods for the number of true discoveries must be based on closed testing. In this paper we investigate tractable and efficient closed testing with local tests of different properties, such as monotonicty, symmetry and separability, meaning that the test thresholds a monotonic or symmetric function or a function of sums of test scores for the individual hypotheses. This class includes well-known global null tests by Fisher, Stouffer and Ruschendorf, as well as newly proposed ones based on harmonic means and Cauchy combinations. Under monotonicity, we propose a new linear time statistic ("coma") that quantifies the cost of multiplicity adjustments. If the tests are also symmetric and separable, we develop several fast (mostly linear-time) algorithms for post-hoc inference, making closed testing tractable. Paired with recent advances in global null tests based on generalized means, our work immediately instantiates a series of simultaneous inference methods that can handle many complex dependence structures and signal compositions. We provide guidance on choosing from these methods via theoretical investigation of the conservativeness and sensitivity for different local tests, as well as simulations that find analogous behavior for local tests and full closed testing. One result of independent interest is the following: if $P_1,\dots,P_d$ are $p$-values from a multivariate Gaussian with arbitrary covariance, then their arithmetic average P satisfies $Pr(P \leq t) \leq t$ for $t \leq \frac{1}{2d}$.Comment: 40 page

Modeling differences in the time-frequency representation of EEG signals through HMM’s for classification of imaginary motor tasks

Brain Computer interfaces are systems that allow the control of external devices using the information extracted from the brain signals. Such systems find applications in rehabilitation, as an alternative communication channel and in multimedia applications for entertainment and gaming. In this work, a new approach based on the Time-Frequency (TF) distribution of the signal power, obtained by autoregressive methods and the use Hidden Markov models (HMM) is developed. This approach take into account the changes of power on different frequency bands with time. For that purpose HMM’s are used to modeling the changes in the power during the execution of two different motor tasks. The use of TF methods involves a problem related to the selection of the frequency bands that can lead to over fitting (due to the course of dimensionality) as well as problems related to the selection of the model parameters. These problems are solved in this work by combining two methods for feature selection: Fisher Score and Sequential Floating Forward Selection. The results are compared to the three top results of the BCI competition IV. It is shown here that the proposed method over perform those other methods in four subjects and the average over all the subjects equals the one obtained by the winner algorithm of the competition