103,460 research outputs found
Discrimination on the Grassmann Manifold: Fundamental Limits of Subspace Classifiers
We present fundamental limits on the reliable classification of linear and
affine subspaces from noisy, linear features. Drawing an analogy between
discrimination among subspaces and communication over vector wireless channels,
we propose two Shannon-inspired measures to characterize asymptotic classifier
performance. First, we define the classification capacity, which characterizes
necessary and sufficient conditions for the misclassification probability to
vanish as the signal dimension, the number of features, and the number of
subspaces to be discerned all approach infinity. Second, we define the
diversity-discrimination tradeoff which, by analogy with the
diversity-multiplexing tradeoff of fading vector channels, characterizes
relationships between the number of discernible subspaces and the
misclassification probability as the noise power approaches zero. We derive
upper and lower bounds on these measures which are tight in many regimes.
Numerical results, including a face recognition application, validate the
results in practice.Comment: 19 pages, 4 figures. Revised submission to IEEE Transactions on
Information Theor
Meta learning of bounds on the Bayes classifier error
Meta learning uses information from base learners (e.g. classifiers or
estimators) as well as information about the learning problem to improve upon
the performance of a single base learner. For example, the Bayes error rate of
a given feature space, if known, can be used to aid in choosing a classifier,
as well as in feature selection and model selection for the base classifiers
and the meta classifier. Recent work in the field of f-divergence functional
estimation has led to the development of simple and rapidly converging
estimators that can be used to estimate various bounds on the Bayes error. We
estimate multiple bounds on the Bayes error using an estimator that applies
meta learning to slowly converging plug-in estimators to obtain the parametric
convergence rate. We compare the estimated bounds empirically on simulated data
and then estimate the tighter bounds on features extracted from an image patch
analysis of sunspot continuum and magnetogram images.Comment: 6 pages, 3 figures, to appear in proceedings of 2015 IEEE Signal
Processing and SP Education Worksho
A Theoretical Analysis of Deep Neural Networks for Texture Classification
We investigate the use of Deep Neural Networks for the classification of
image datasets where texture features are important for generating
class-conditional discriminative representations. To this end, we first derive
the size of the feature space for some standard textural features extracted
from the input dataset and then use the theory of Vapnik-Chervonenkis dimension
to show that hand-crafted feature extraction creates low-dimensional
representations which help in reducing the overall excess error rate. As a
corollary to this analysis, we derive for the first time upper bounds on the VC
dimension of Convolutional Neural Network as well as Dropout and Dropconnect
networks and the relation between excess error rate of Dropout and Dropconnect
networks. The concept of intrinsic dimension is used to validate the intuition
that texture-based datasets are inherently higher dimensional as compared to
handwritten digits or other object recognition datasets and hence more
difficult to be shattered by neural networks. We then derive the mean distance
from the centroid to the nearest and farthest sampling points in an
n-dimensional manifold and show that the Relative Contrast of the sample data
vanishes as dimensionality of the underlying vector space tends to infinity.Comment: Accepted in International Joint Conference on Neural Networks, IJCNN
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