26,303 research outputs found
A Multiscale Approach for Statistical Characterization of Functional Images
Increasingly, scientific studies yield functional image data, in which the observed data consist of sets of curves recorded on the pixels of the image. Examples include temporal brain response intensities measured by fMRI and NMR frequency spectra measured at each pixel. This article presents a new methodology for improving the characterization of pixels in functional imaging, formulated as a spatial curve clustering problem. Our method operates on curves as a unit. It is nonparametric and involves multiple stages: (i) wavelet thresholding, aggregation, and Neyman truncation to effectively reduce dimensionality; (ii) clustering based on an extended EM algorithm; and (iii) multiscale penalized dyadic partitioning to create a spatial segmentation. We motivate the different stages with theoretical considerations and arguments, and illustrate the overall procedure on simulated and real datasets. Our method appears to offer substantial improvements over monoscale pixel-wise methods. An Appendix which gives some theoretical justifications of the methodology, computer code, documentation and dataset are available in the online supplements
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science
volume "Pattern Recognition Applications and Methods 2013", part of series on
Advances in Intelligent and Soft Computin
EC3: Combining Clustering and Classification for Ensemble Learning
Classification and clustering algorithms have been proved to be successful
individually in different contexts. Both of them have their own advantages and
limitations. For instance, although classification algorithms are more powerful
than clustering methods in predicting class labels of objects, they do not
perform well when there is a lack of sufficient manually labeled reliable data.
On the other hand, although clustering algorithms do not produce label
information for objects, they provide supplementary constraints (e.g., if two
objects are clustered together, it is more likely that the same label is
assigned to both of them) that one can leverage for label prediction of a set
of unknown objects. Therefore, systematic utilization of both these types of
algorithms together can lead to better prediction performance. In this paper,
We propose a novel algorithm, called EC3 that merges classification and
clustering together in order to support both binary and multi-class
classification. EC3 is based on a principled combination of multiple
classification and multiple clustering methods using an optimization function.
We theoretically show the convexity and optimality of the problem and solve it
by block coordinate descent method. We additionally propose iEC3, a variant of
EC3 that handles imbalanced training data. We perform an extensive experimental
analysis by comparing EC3 and iEC3 with 14 baseline methods (7 well-known
standalone classifiers, 5 ensemble classifiers, and 2 existing methods that
merge classification and clustering) on 13 standard benchmark datasets. We show
that our methods outperform other baselines for every single dataset, achieving
at most 10% higher AUC. Moreover our methods are faster (1.21 times faster than
the best baseline), more resilient to noise and class imbalance than the best
baseline method.Comment: 14 pages, 7 figures, 11 table
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