9,425 research outputs found
Statistical Mechanics of Support Vector Networks
Using methods of Statistical Physics, we investigate the generalization
performance of support vector machines (SVMs), which have been recently
introduced as a general alternative to neural networks. For nonlinear
classification rules, the generalization error saturates on a plateau, when the
number of examples is too small to properly estimate the coefficients of the
nonlinear part. When trained on simple rules, we find that SVMs overfit only
weakly. The performance of SVMs is strongly enhanced, when the distribution of
the inputs has a gap in feature space.Comment: REVTeX, 4 pages, 2 figures, accepted by Phys. Rev. Lett (typos
corrected
Disturbance Grassmann Kernels for Subspace-Based Learning
In this paper, we focus on subspace-based learning problems, where data
elements are linear subspaces instead of vectors. To handle this kind of data,
Grassmann kernels were proposed to measure the space structure and used with
classifiers, e.g., Support Vector Machines (SVMs). However, the existing
discriminative algorithms mostly ignore the instability of subspaces, which
would cause the classifiers misled by disturbed instances. Thus we propose
considering all potential disturbance of subspaces in learning processes to
obtain more robust classifiers. Firstly, we derive the dual optimization of
linear classifiers with disturbance subject to a known distribution, resulting
in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into
two kinds of disturbance, relevant to the subspace matrix and singular values
of bases, with which we extend the Projection kernel on Grassmann manifolds to
two new kernels. Experiments on action data indicate that the proposed kernels
perform better compared to state-of-the-art subspace-based methods, even in a
worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to
SIGKDD'1
A robust morphological classification of high-redshift galaxies using support vector machines on seeing limited images. I Method description
We present a new non-parametric method to quantify morphologies of galaxies
based on a particular family of learning machines called support vector
machines. The method, that can be seen as a generalization of the classical CAS
classification but with an unlimited number of dimensions and non-linear
boundaries between decision regions, is fully automated and thus particularly
well adapted to large cosmological surveys. The source code is available for
download at http://www.lesia.obspm.fr/~huertas/galsvm.html To test the method,
we use a seeing limited near-infrared ( band, ) sample observed
with WIRCam at CFHT at a median redshift of . The machine is trained
with a simulated sample built from a local visually classified sample from the
SDSS chosen in the high-redshift sample's rest-frame (i band, ) and
artificially redshifted to match the observing conditions. We use a
12-dimensional volume, including 5 morphological parameters and other
caracteristics of galaxies such as luminosity and redshift. We show that a
qualitative separation in two main morphological types (late type and early
type) can be obtained with an error lower than 20% up to the completeness limit
of the sample () which is more than 2 times better that what would
be obtained with a classical C/A classification on the same sample and indeed
comparable to space data. The method is optimized to solve a specific problem,
offering an objective and automated estimate of errors that enables a
straightforward comparison with other surveys.Comment: 11 pages, 7 figures, 3 tables. Submitted to A&A. High resolution
images are available on reques
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
- …