5,204 research outputs found
Testing and Learning on Distributions with Symmetric Noise Invariance
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD),
the resulting distance between distributions, are useful tools for fully
nonparametric two-sample testing and learning on distributions. However, it is
rarely that all possible differences between samples are of interest --
discovered differences can be due to different types of measurement noise, data
collection artefacts or other irrelevant sources of variability. We propose
distances between distributions which encode invariance to additive symmetric
noise, aimed at testing whether the assumed true underlying processes differ.
Moreover, we construct invariant features of distributions, leading to learning
algorithms robust to the impairment of the input distributions with symmetric
additive noise.Comment: 22 page
Out-of-sample generalizations for supervised manifold learning for classification
Supervised manifold learning methods for data classification map data samples
residing in a high-dimensional ambient space to a lower-dimensional domain in a
structure-preserving way, while enhancing the separation between different
classes in the learned embedding. Most nonlinear supervised manifold learning
methods compute the embedding of the manifolds only at the initially available
training points, while the generalization of the embedding to novel points,
known as the out-of-sample extension problem in manifold learning, becomes
especially important in classification applications. In this work, we propose a
semi-supervised method for building an interpolation function that provides an
out-of-sample extension for general supervised manifold learning algorithms
studied in the context of classification. The proposed algorithm computes a
radial basis function (RBF) interpolator that minimizes an objective function
consisting of the total embedding error of unlabeled test samples, defined as
their distance to the embeddings of the manifolds of their own class, as well
as a regularization term that controls the smoothness of the interpolation
function in a direction-dependent way. The class labels of test data and the
interpolation function parameters are estimated jointly with a progressive
procedure. Experimental results on face and object images demonstrate the
potential of the proposed out-of-sample extension algorithm for the
classification of manifold-modeled data sets
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