12,297 research outputs found
A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination
By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks
A CASE STUDY ON SUPPORT VECTOR MACHINES VERSUS ARTIFICIAL NEURAL NETWORKS
The capability of artificial neural networks for pattern recognition of real world problems is well known. In recent years, the support vector machine has been advocated for its structure risk minimization leading to tolerance margins of decision boundaries. Structures and performances of these pattern classifiers depend on the feature dimension and training data size. The objective of this research is to compare these pattern recognition systems based on a case study. The particular case considered is on classification of hypertensive and normotensive right ventricle (RV) shapes obtained from Magnetic Resonance Image (MRI) sequences. In this case, the feature dimension is reasonable, but the available training data set is small, however, the decision surface is highly nonlinear.For diagnosis of congenital heart defects, especially those associated with pressure and volume overload problems, a reliable pattern classifier for determining right ventricle function is needed. RV¡¦s global and regional surface to volume ratios are assessed from an individual¡¦s MRI heart images. These are used as features for pattern classifiers. We considered first two linear classification methods: the Fisher linear discriminant and the linear classifier trained by the Ho-Kayshap algorithm. When the data are not linearly separable, artificial neural networks with back-propagation training and radial basis function networks were then considered, providing nonlinear decision surfaces. Thirdly, a support vector machine was trained which gives tolerance margins on both sides of the decision surface. We have found in this case study that the back-propagation training of an artificial neural network depends heavily on the selection of initial weights, even though randomized. The support vector machine where radial basis function kernels are used is easily trained and provides decision tolerance margins, in spite of only small margins
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
The recovery of the intrinsic geometric structures of data collections is an
important problem in data analysis. Supervised extensions of several manifold
learning approaches have been proposed in the recent years. Meanwhile, existing
methods primarily focus on the embedding of the training data, and the
generalization of the embedding to initially unseen test data is rather
ignored. In this work, we build on recent theoretical results on the
generalization performance of supervised manifold learning algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
Sparse multinomial kernel discriminant analysis (sMKDA)
Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets
The Geometry of Nonlinear Embeddings in Kernel Discriminant Analysis
Fisher's linear discriminant analysis is a classical method for
classification, yet it is limited to capturing linear features only. Kernel
discriminant analysis as an extension is known to successfully alleviate the
limitation through a nonlinear feature mapping. We study the geometry of
nonlinear embeddings in discriminant analysis with polynomial kernels and
Gaussian kernel by identifying the population-level discriminant function that
depends on the data distribution and the kernel. In order to obtain the
discriminant function, we solve a generalized eigenvalue problem with
between-class and within-class covariance operators. The polynomial
discriminants are shown to capture the class difference through the population
moments explicitly. For approximation of the Gaussian discriminant, we use a
particular representation of the Gaussian kernel by utilizing the exponential
generating function for Hermite polynomials. We also show that the Gaussian
discriminant can be approximated using randomized projections of the data. Our
results illuminate how the data distribution and the kernel interact in
determination of the nonlinear embedding for discrimination, and provide a
guideline for choice of the kernel and its parameters
Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant
Subsidy food is government program for social protection to poor households. The aims of this program are to effort households from starve and to decrease poverty. Less precisely target of this program has negative impact. So that to successful program, it’s important to know accuracy classification of admission subsidy food. The variables classification are number of household members, number of household member in work, average expenditure capita, weighted household, and floor area. Discriminant analysis is a multivariate statistical technique which can be used to classify the new observation into a specific group. Kernel discriminant analysis is a non-parametric method which is flexible because it does not have to concern about assumption from certain distribution and equal variance matrices as in parametric discriminant analysis. The classification using the kernel discriminant analysis with the normal kernel function with optimum bandwidth 0.6 gives accurate classification 75.35%
Neural Class-Specific Regression for face verification
Face verification is a problem approached in the literature mainly using
nonlinear class-specific subspace learning techniques. While it has been shown
that kernel-based Class-Specific Discriminant Analysis is able to provide
excellent performance in small- and medium-scale face verification problems,
its application in today's large-scale problems is difficult due to its
training space and computational requirements. In this paper, generalizing our
previous work on kernel-based class-specific discriminant analysis, we show
that class-specific subspace learning can be cast as a regression problem. This
allows us to derive linear, (reduced) kernel and neural network-based
class-specific discriminant analysis methods using efficient batch and/or
iterative training schemes, suited for large-scale learning problems. We test
the performance of these methods in two datasets describing medium- and
large-scale face verification problems.Comment: 9 pages, 4 figure
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