co-clustering method using spatial generalized linear ...asa-qprc.org/2013/€¦ · integrated pest...

Co-Clustering method using Spatial Generalized LinearMixed Models

Fei He

Department of StatisticsUniversity of Statistics - Riverside

June 6, 2013

Fei He (UCR) QPRC 2013 June 6, 2013 1 / 21

Outline of the Talk

1 MotivationCo-clustering and its application to the Integrated Pest Management

2 MethodologySpatial Clustering using SADIEGeneralized Linear Mixed Model based Co-clusteringHeuristic Searching Algorithm for Co-clusters

3 Application Examples

4 Summary and Future work


Motivation

Integrated Pest Management (IPM): is an approach to managepests by combining biological, cultural, physical and chemicaltools in a way that minimizes economic loss associated withcrops, while simultaneously minimizing human health andenvironmental risks.

Current Approach to Pest AssessmentFor a given pre-determined critical economic threshold ◊c , testH0 : ◊ Æ ◊c vs. Ha : ◊ > ◊cRejecting H0 would call for treatment that is applied to the entire orchard


Goal

Hot SpotThe haphazard and often di�use initial settlements of high densitypopulations in small areas are referred to by pest management specialistsas hot spots.


Co-clustering

Co-Clustering: also called biclustering, bivariate clustering, ortwo-mode clustering.

Method such as Heat map is to construct dendrograms forcolums and rows independently. Oftenly used inbioinformatics and text mining.

Figure : Heat map generated from DNA microarray data reflecting geneexpression values in several conditions (Andrade, M. 2007)


Spatial Analysis by Distance IndicEs (SADIE)

Distance to Regularity measures the minimum e�ort that theindividuals in a sample would need to expend to move to anarrangement where there was an equal number in each sampleunit.

Figure : Counts of cereal aphid in a field of winter wheat nearWimborne, UK (Winder et al. 1998)


Clustering using SADIERed-Blue Plot

Clustering IndexRed (patches) when v > 1.5Blue (gaps) when v < ≠1.5White when ≠1.5 < v < 1.5


Checkerboard Structure of the Grid

An r ◊ c spatial grid in which each grid point is a potential sampling site

Yj(i) | s ≥ Negative Binomial (◊i , Ÿ) , (i = 1, 2, · · · nm; j = 1, 2, · · · , ni)

log (◊i) = µ + si ; s = (s1, s2, · · · , snm)Õs MVN (0, D)


Heuristic Search Algorithm for the Optimal Design(ref: Zhang, Jeske, and Cui - 2011, Journal of Agricultural and Environmental Statistics)

Starting with the original spatial grid, fit GLMM to each of the designassociatied with the 1 ◊ 2 and 2 ◊ 1 nomenclature. “Current OptimalDesign” is the one with maximum Likelihood.


Heuristic Search Algorithm for the Optimal Design

Starting with the “Current Optimal Design”, fit GLMM to each of thedesigns with the nomenclature with either one more horizontal orvertical divider. “Potential Optimal Design” is the one with maximumLikelihood.


Heuristic Search Algorithm for the Optimal Design

If the likelihood of “Potential Optimal Design” is greater than“Current Optimal Design”, then promote it to the “Current OptimalDesign”, and repeat step 2; otherwise, stop the searching.


Application Example 1Cottony Cushion Scale Counts on Mandarin-Delite trees in Reedley, CA

Counts of adult female scales on 8 branches per tree for 30 trees eachrow, total 21 rows


SADIE ClusteringCottony Cushion Scale Counts on Mandarin-Delite trees in Reedley, CA

Clustering using SADIE plot on a Red-Blue Plot


Model-based Co-clusteringCottony Cushion Scale Counts on Mandarin-Delite orange trees in Reedley, CA

Model-based Co-clustering (with minimum co-cluster size 5 ◊ 5)using Independent GLMM with covariance matrix D = ‡2Iusing Spatially correlated GLMM with the covariance matrixD = ‡2

Ëe≠

dij◊

È

ij


Application Example 2Cottony Cushion Scale Counts on Mandarin-Delite orange trees in Visalia ranch, CA

Counts of cottony cushion scales on 8 branches per tree for 41 treeseach row, total 24 rows (20% sampling from 6 strata)


SADIE ClusteringCottony Cushion Scale Counts on Mandarin-Delite orange trees in Visalia ranch, CA


Model-based Co-clusteringCottony Cushion Scale Counts on Mandarin-Delite orange trees in Visalia ranch, CA


Parameter estimatesCottony Cushion Scale Counts on orange trees in Visalia

µ̂ ‡̂2 Ÿ̂ ◊̂Independent model 1.6415 1.8138 1.6306

(0.4114) (0.8707) (0.1934)Correlated model 1.8619 1.5675 1.2029 1.5081

(0.3621) (0.6543) (0.1358) (1.3330)


Summary on three methods

SADIE vs. model-basedSADIE is “Empirical”, other two methods are model-basedDi�erent thresholds yield di�erent clusteringSADIE gets clusters with irregular shape

Independent vs. Spatial correlated GLMM co-clusteringFrom our examples, correlated GLMM based co-clustering gets nobetter answer than independent GLMMFrom simulation studies, need fairly large size of grid to get betterparameter estimatesComputationally di�cult using spatial correlated GLMM basedco-clustering


Future Work

More general spatial co-cluster techniquesAlternative Spatial structure, e.g. anisotropicAlternative distribution of data, e.g. absence/presence data to fitlogistic GLMMs

Bayesian Approach of Cluster DetectionLarge spatially correlated datasetData is not on a grid


Thank you!

co-clustering method using spatial generalized linear ...asa-qprc.org/2013/€¦ · integrated pest...

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