12,494 research outputs found
A Bonferroni Mean Based Fuzzy K Nearest Centroid Neighbor Classifier
K-nearest neighbor (KNN) is an effective nonparametric classifier that determines the neighbors of a point based only on distance proximity. The classification performance of KNN is disadvantaged by the presence of outliers in small sample size datasets and its performance deteriorates on datasets with class imbalance. We propose a local Bonferroni Mean based Fuzzy K-Nearest Centroid Neighbor (BM-FKNCN) classifier that assigns class label of a query sample dependent on the nearest local centroid mean vector to better represent the underlying statistic of the dataset. The proposed classifier is robust towards outliers because the Nearest Centroid Neighborhood (NCN) concept also considers spatial distribution and symmetrical placement of the neighbors. Also, the proposed classifier can overcome class domination of its neighbors in datasets with class imbalance because it averages all the centroid vectors from each class to adequately interpret the distribution of the classes. The BM-FKNCN classifier is tested on datasets from the Knowledge Extraction based on Evolutionary Learning (KEEL) repository and benchmarked with classification results from the KNN, Fuzzy-KNN (FKNN), BM-FKNN and FKNCN classifiers. The experimental results show that the BM-FKNCN achieves the highest overall average classification accuracy of 89.86% compared to the other four classifiers
Optimal Bayes Classifiers for Functional Data and Density Ratios
Bayes classifiers for functional data pose a challenge. This is because
probability density functions do not exist for functional data. As a
consequence, the classical Bayes classifier using density quotients needs to be
modified. We propose to use density ratios of projections on a sequence of
eigenfunctions that are common to the groups to be classified. The density
ratios can then be factored into density ratios of individual functional
principal components whence the classification problem is reduced to a sequence
of nonparametric one-dimensional density estimates. This is an extension to
functional data of some of the very earliest nonparametric Bayes classifiers
that were based on simple density ratios in the one-dimensional case. By means
of the factorization of the density quotients the curse of dimensionality that
would otherwise severely affect Bayes classifiers for functional data can be
avoided. We demonstrate that in the case of Gaussian functional data, the
proposed functional Bayes classifier reduces to a functional version of the
classical quadratic discriminant. A study of the asymptotic behavior of the
proposed classifiers in the large sample limit shows that under certain
conditions the misclassification rate converges to zero, a phenomenon that has
been referred to as "perfect classification". The proposed classifiers also
perform favorably in finite sample applications, as we demonstrate in
comparisons with other functional classifiers in simulations and various data
applications, including wine spectral data, functional magnetic resonance
imaging (fMRI) data for attention deficit hyperactivity disorder (ADHD)
patients, and yeast gene expression data
k-nearest neighbors prediction and classification for spatial data
We propose a nonparametric predictor and a supervised classification based on
the regression function estimate of a spatial real variable using k-nearest
neighbors method (k-NN). Under some assumptions, we establish almost complete
or sure convergence of the proposed estimates which incorporate a spatial
proximity between observations. Numerical results on simulated and real fish
data illustrate the behavior of the given predictor and classification method
Nonparametrically consistent depth-based classifiers
We introduce a class of depth-based classification procedures that are of a
nearest-neighbor nature. Depth, after symmetrization, indeed provides the
center-outward ordering that is necessary and sufficient to define nearest
neighbors. Like all their depth-based competitors, the resulting classifiers
are affine-invariant, hence in particular are insensitive to unit changes.
Unlike the former, however, the latter achieve Bayes consistency under
virtually any absolutely continuous distributions - a concept we call
nonparametric consistency, to stress the difference with the stronger universal
consistency of the standard NN classifiers. We investigate the finite-sample
performances of the proposed classifiers through simulations and show that they
outperform affine-invariant nearest-neighbor classifiers obtained through an
obvious standardization construction. We illustrate the practical value of our
classifiers on two real data examples. Finally, we shortly discuss the possible
uses of our depth-based neighbors in other inference problems.Comment: Published at http://dx.doi.org/10.3150/13-BEJ561 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The DD-classifier in the functional setting
The Maximum Depth was the first attempt to use data depths instead of
multivariate raw data to construct a classification rule. Recently, the
DD-classifier has solved several serious limitations of the Maximum Depth
classifier but some issues still remain. This paper is devoted to extending the
DD-classifier in the following ways: first, to surpass the limitation of the
DD-classifier when more than two groups are involved. Second to apply regular
classification methods (like NN, linear or quadratic classifiers, recursive
partitioning,...) to DD-plots to obtain useful insights through the diagnostics
of these methods. And third, to integrate different sources of information
(data depths or multivariate functional data) in a unified way in the
classification procedure. Besides, as the DD-classifier trick is especially
useful in the functional framework, an enhanced revision of several functional
data depths is done in the paper. A simulation study and applications to some
classical real datasets are also provided showing the power of the new
proposal.Comment: 29 pages, 6 figures, 6 tables, Supplemental R Code and Dat
Wavelet Shrinkage and Thresholding based Robust Classification for Brain Computer Interface
A macaque monkey is trained to perform two different kinds of tasks, memory
aided and visually aided. In each task, the monkey saccades to eight possible
target locations. A classifier is proposed for direction decoding and task
decoding based on local field potentials (LFP) collected from the prefrontal
cortex. The LFP time-series data is modeled in a nonparametric regression
framework, as a function corrupted by Gaussian noise. It is shown that if the
function belongs to Besov bodies, then using the proposed wavelet shrinkage and
thresholding based classifier is robust and consistent. The classifier is then
applied to the LFP data to achieve high decoding performance. The proposed
classifier is also quite general and can be applied for the classification of
other types of time-series data as well, not necessarily brain data
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