PARAMETRIC AND KERNEL DENSITY METHODS IN DISCRIMINANT ANALYSIS: ANOTHER COMPARISON

Author(s):  
B.J. MURPHY ◽  
M.A. MORAN
2005 ◽  
Vol 127 (6) ◽  
pp. 1020-1024 ◽  
Author(s):  
J. Y. Goulermas ◽  
D. Howard ◽  
C. J. Nester ◽  
R. K. Jones ◽  
L. Ren

This work presents a novel and extensive investigation of mathematical regression techniques, for the prediction of laboratory-type kinematic measurements during human gait, from wearable measurement devices, such as gyroscopes and accelerometers. Specifically, we examine the hypothesis of predicting the segmental angles of the legs (left and right foot, shank and thighs), from rotational foot velocities and translational foot accelerations. This first investigation is based on kinematic data emulated from motion-capture laboratory equipment. We employ eight established regression algorithms with different properties, ranging from linear methods and neural networks with polynomial support and expanded nonlinearities, to radial basis functions, nearest neighbors and kernel density methods. Data from five gait cycles of eight subjects are used to perform both inter-subject and intra-subject assessments of the prediction capabilities of each algorithm, using cross-validation resampling methods. Regarding the algorithmic suitability to gait prediction, results strongly indicate that nonparametric methods, such as nearest neighbors and kernel density based, are particularly advantageous. Numerical results show high average prediction accuracy (ρ=0.98∕0.99,RMS=5.63°∕2.30°,MAD=4.43°∕1.52° for inter∕intra-subject testing). The presented work provides a promising and motivating investigation on the feasibility of cost-effective wearable devices used to acquire large volumes of data that are currently collected only from complex laboratory environments.


2000 ◽  
Vol 24 (2-7) ◽  
pp. 835-840 ◽  
Author(s):  
P.R. Goulding ◽  
B. Lennox ◽  
Q. Chen ◽  
D.J. Sandoz

2016 ◽  
Vol 33 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Thomas Ledl

Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descriptive application, the model seems to be quite suitable for application in discriminant analysis, where (multivariate) class densities are the basis for the assignment of a vector to a given class. Thisarticle gives insight to most popular bandwidth parameter selectors as well as to the performance of the kernel density estimator as a classification method compared to the classical linear and quadratic discriminant analysis, respectively. Both a direct estimation in a multivariate space as well as an application of the concept to marginal normalizations of the single variables will be taken into consideration. From this report the gap between theory and application is going to be pointed out.


Author(s):  
George Sakellaropoulos ◽  
Antonis Daskalakis ◽  
George Nikiforidis ◽  
Christos Argyropoulos

The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be problematic due to their featureless, dense nature. Furthermore microarray images are characterized by significant background noise, but the effects of the latter on the holistic interpretation of gene expression profiles remains under-explored. We hypothesize that a framework combining (a) Bayesian methodology for background adjustment in microarray images with (b) model-free modeling tools, may serve the dual purpose of data and model reduction, exposing hitherto hidden features of gene expression profiles. Within the proposed framework, microarray image restoration and noise adjustment is facilitated by a class of prior Maximum Entropy distributions. The resulting gene expression profiles are non-parametrically modeled by kernel density methods, which not only normalize the data, but facilitate the generation of reduced mathematical descriptions of biological variability as mixture models.


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