Improved Estimation of Water Chlorophyll Concentration With Semisupervised Gaussian Process Regression

This paper proposes a novel semisupervised regression framework for estimating chlorophyll concentrations in subsurface waters from remotely sensed imagery. This framework integrates multiobjective optimization and Gaussian processes (GPs) for boosting the accuracy of the estimation process when conditioned by limited labeled-sample availability. To this end, the labeled samples are exploited in conjunction with unlabeled ones (available at zero cost from the image under analysis) for learning the regression model. The estimation of the target of these unlabeled samples is handled by the simultaneous optimization of two different criteria expressing the generalization capabilities of the GP estimator. The first is the empirical risk quantified in terms of the mean square error measure, and the second is the log marginal likelihood, which merges two terms expressing the model complexity and the data fit capability, respectively. In order to alleviate the computational burden and, possibly, to improve the estimation process accuracy, two different selection strategies of unlabeled samples are compared to the simple random-sampling procedure. They are based on the estimated variance provided by the GP estimator and the differential entropy measure, respectively. Experimental results obtained on simulated and real data sets are reported and discussed.

[1]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[2]  Marco Diani,et al.  Retrieval of sea water optically active parameters from hyperspectral data by means of generalized radial basis function neural networks , 2001, IEEE Trans. Geosci. Remote. Sens..

[3]  Zhi-Hua Zhou,et al.  Semisupervised Regression with Cotraining-Style Algorithms , 2007, IEEE Transactions on Knowledge and Data Engineering.

[4]  Ishwar K. Sethi,et al.  Confidence-based active learning , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Farid Melgani,et al.  Active Learning Methods for Electrocardiographic Signal Classification , 2010, IEEE Transactions on Information Technology in Biomedicine.

[6]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[7]  Wei Yang,et al.  An Enhanced Three-Band Index for Estimating Chlorophyll-a in Turbid Case-II Waters: Case Studies of Lake Kasumigaura, Japan, and Lake Dianchi, China , 2010, IEEE Geoscience and Remote Sensing Letters.

[8]  Carl E. Rasmussen,et al.  Assessing Approximate Inference for Binary Gaussian Process Classification , 2005, J. Mach. Learn. Res..

[9]  Farid Melgani,et al.  Support Vector Machine Active Learning Through Significance Space Construction , 2011, IEEE Geoscience and Remote Sensing Letters.

[10]  David J. C. MacKay,et al.  Variational Gaussian process classifiers , 2000, IEEE Trans. Neural Networks Learn. Syst..

[11]  Tom Minka,et al.  A family of algorithms for approximate Bayesian inference , 2001 .

[12]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[13]  Bertrand Saulquin,et al.  Regional Objective Analysis for Merging High-Resolution MERIS, MODIS/Aqua, and SeaWiFS Chlorophyll- a Data From 1998 to 2008 on the European Atlantic Shelf , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[14]  Hyun-Chul Kim,et al.  Bayesian Gaussian Process Classification with the EM-EP Algorithm , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[16]  Ping Shi,et al.  Retrieval of oceanic chlorophyll concentration using support vector machines , 2003, IEEE Trans. Geosci. Remote. Sens..

[17]  Janet W. Campbell,et al.  The lognormal distribution as a model for bio‐optical variability in the sea , 1995 .

[18]  David Barber,et al.  Bayesian Classification With Gaussian Processes , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Christopher K. I. Williams Computation with Infinite Neural Networks , 1998, Neural Computation.

[20]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[21]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[22]  Junsheng Li,et al.  Modeling Remote-Sensing Reflectance and Retrieving Chlorophyll-a Concentration in Extremely Turbid Case-2 Waters (Lake Taihu, China) , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[23]  Lorenzo Bruzzone,et al.  Robust multiple estimator systems for the analysis of biophysical parameters from remotely sensed data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[24]  Frédéric Mélin,et al.  Global Distribution of the Random Uncertainty Associated With Satellite-Derived Chl a , 2010, IEEE Geoscience and Remote Sensing Letters.

[25]  P. J. Werdell,et al.  An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation , 2005 .

[26]  Anatoly A. Gitelson,et al.  Satellite Estimation of Chlorophyll-$a$ Concentration Using the Red and NIR Bands of MERIS—The Azov Sea Case Study , 2009, IEEE Geoscience and Remote Sensing Letters.

[27]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[28]  Farid Melgani,et al.  Semisupervised PSO-SVM Regression for Biophysical Parameter Estimation , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[29]  Vincenzo Cutello,et al.  A Class of Pareto Archived Evolution Strategy Algorithms Using Immune Inspired Operators for Ab-Initio Protein Structure Prediction , 2005, EvoWorkshops.

[30]  Menghua Wang,et al.  Seawifs Postlaunch Calibration and Validation Analyses , 2013 .

[31]  Farid Melgani,et al.  Gaussian Process Regression for Estimating Chlorophyll Concentration in Subsurface Waters From Remote Sensing Data , 2010, IEEE Geoscience and Remote Sensing Letters.

[32]  Farid Melgani,et al.  Gaussian Process Approach to Remote Sensing Image Classification , 2010, IEEE Transactions on Geoscience and Remote Sensing.