LFGPC: Learning Optimal Filters for Gaussian Process Classification
P. Ruiz, R. Molina, and A.K. Katsaggelos, “Joint Data Filtering and Labeling using Gaussian Processes and Alternating Direction Method of Multipliers”, IEEE Transactions on Image Processing, vol. 25, no. 7, 3059-3072, July 2016. [BibTeX entry][Abstract][ (1614 KB.)]
Sequence labeling aims at assigning a label to every sample of a signal (or pixel of an image) while taking into account the sequentiality (or vicinity) of the samples. To perform this task, many works in the literature first filter and then label the data. Unfortunately, the filtering, which is performed independently from the labeling, is far from optimal and frequently makes the latter task harder. In this work, a novel approach which trains a Gaussian Process (GP) classifier and estimates the coefficients of an optimal filter jointly is presented. The new approach, based on Bayesian modeling and Alternating Direction Method of Multipliers (ADMM) optimization, performs both tasks simultaneously. All unknowns are treated as stochastic variables which are estimated using Variational Inference and filtering and labeling are linked with the use of ADMM. In the experimental section synthetic and real experiments are presented to compare the proposed method with other existing approaches.
Representation of joint filtering and GP classification system
Original Signal Coefficients
Filter Coefficients Filtered Features Labels
A synthetic example
Our groundtruth is a checkerboard. We generate the observations adding Gaussian noise of variance 0.16, and means 0.25 and 0.75 for Black and White classes, respectively. Here we show the original groundtruth and the noisy observations:
Applying the proposed method, the following results are obtained:
Filter sizes 3 x 3 5 x 5 7 x 7 9 x 9 Obtained filters Filtered observations Classification maps
Matlab Code and Synthetic Dataset
MATLAB code and synthetic dataset can be downloaded here.
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