1

Particle Swarm Optimization-based Particle Swarm Optimization-based Dimensionality Reduction for Dimensionality Reduction for

Hyperspectral Image ClassificationHyperspectral Image Classification

He Yang, Jenny Q. DuDepartment of Electrical and Computer Engineering

Mississippi State University, MS 39762, USA

OutlineOutline

Motivation

Existing band selection approaches Unsupervised band selection

Supervised band selection

Particle swarm optimization (PSO)

PSO for hyperspectral band selection

Experimental results

Conclusion

MotivationMotivation

The vast data volume of hyperspectral imagery brings about problems in data transmission and storage. In particular, the very high data dimensionality presents a challenge to many traditional image analysis algorithms.

One approach of reducing the data dimensionality is to transform the data onto a low-dimensional space using certain criteria (e.g., PCA, LDA). But these methods usually change the physical meaning of the original data since the channels in the low-dimensional space do not correspond to individual original bands but their linear combinations.

Another dimensionality reduction approach is band selection. It is to select a subset of the original bands without losing their physical meaning.

Motivation (Cont’d)Motivation (Cont’d) In terms of object information availability, band selection

techniques can be divided into two categories: supervised and unsupervised. Supervised methods are to preserve the desired object information, which is known a priori; while unsupervised methods do not assume any object information.

Supervised techniques clearly aim at selecting the bands that include important object information and the selected bands can provide better detection or classification than those from unsupervised techniques. When the prior knowledge is unavailable, we have to apply an unsupervised method that can generally offer good performance regardless of the objects to be detected or classified in the following step.

In this research, dimensionality reduction is achieved by supervised band selection, and we propose to use particle swarm optimization (PSO) in conjunction with simple but effective objective functions for optimal band searching.

We will demonstrate that using data dimensionality reduction as a pre-processing step, support vector machine (SVM)-based classification accuracy (either before or after decision fusion) can be greatly improved.

Motivation (Cont’d)Motivation (Cont’d)

Unsupervised Band SelectionUnsupervised Band Selection

The basic idea of an unsupervised band selection is to select distinctive and informative bands. Information Entropy First Spectral Derivative Second Spectral Derivative Spectral Angle Spectral Correlation Uniform Spectral Spacing

Unsupervised band selection can be achieved by evaluating band similarity.

● ● Q. Du and H. Yang, “Similarity-based unsupervised band selection for hyperspectral image analysis,” IEEE Geoscience and Remote Sensing Letters, vol. 5, no. 4, pp. 564-568, Oct. 2008.

● ● H. Yang, Q. Du, and G. Chen, “Unsupervised hyperspectral band selection using graphics processing units,” IEEE Journal of Selected Topics in Earth Observation and Remote Sensing, vol. 4, no. 3, July 2011.

Supervised Band SelectionSupervised Band Selection

When class information is known, supervised band selection is applied to preserve the desired object information. A supervised band selection algorithm maximizes class

separability when a subset of bands is selected.

Class separability may be measured with −− Divergence

−− Transformed divergence

−− Bhattacharyya distance

−− Jeffries-Matusita (JM) distance

Recently, we proposed a new metric based on minimum endmember abundance covariance (MEAC).

● ● H. Yang, Q. Du, H. Su, and Y. Sheng, “An efficient method for supervised hyperspectral band selection,” IEEE Geoscience and Remote Sensing Letters, vol. 8, no. 1, pp. 138-142, Jan. 2011.

Band SearchingBand Searching

To avoid testing all the possible band combinations, subset searching strategies can be used:

Sequential forward selection (SFS)

Sequential forward floating selection (SFFS)

Branch and Bound

An advanced but simple searching strategy is particle swarm optimization (PSO).

Particle Swarm OptimizationParticle Swarm Optimization

PSO is a computational optimization technique developed by Kennedy and Eberhart in 1995. It uses a simple mechanism that mimics swarm behavior in birds flocking and fish schooling to guide the particles to search for global optimal solutions.

PSO is proved to be a very efficient optimization algorithm by searching an entire high-dimensional problem space.

PSO does not use the gradient of the problem being optimized, so it does not require that the optimization problem be differential as required by classic optimization methods. PSO can be useful for optimization of irregular problems.

● ● PSO is used to search the solution of . ● ● The initial particles are spread sparsely in the whole problem space in iteration 1.● ● The particles start to be pulled by the update procedure to the optimal regions

from iteration 25 to iteration 75. ● ● All the particles are gathered at the optimum point by the updating procedure.

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-8

-6

-4

-2

0

2

4

6

8

10

X1

X2

Particles

gBeset

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-8

-6

-4

-2

0

2

4

6

8

10

X1

X2

Particles

gBeset

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-8

-6

-4

-2

0

2

4

6

8

10

X1

X2

Particles

gBeset

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-8

-6

-4

-2

0

2

4

6

8

10

X1

X2

Particles

gBeset

Iteration 1 Iteration 25

Iteration 50 Iteration 752

22

121 )5()5(),( xxxxf

PSO for Band SelectionPSO for Band Selection Assume p bands are to be selected. Let a particle xid (of size p×1)

denote the selected band indices, and vid the update for selected band indices. The historically best local solution is vid, and the historically best global solution among all the particles is pgd.

Particle update:

It calculates the new velocity for each particle based on the previous velocity vid, the particle’s location (pid) that it has reached so far so best for the objective function, and the particle’s location among the global searched solutions (pgd) that has reached so far so best.

Particles are updated as:

c1 and c2 control the contributions from local and global solutions respectively, r1 and r2 are independent random variables; and w is used as the scalar of previous velocity vid in particle update.

)()( 2211 idgdidididid rcrcw xpxpvv

ididid vxx

PSO for Band SelectionPSO for Band Selection Algorithm: 1. Assume p bands are to be selected. Randomly initialize M particles xid,

and each particle includes p indices of the bands to be selected. 2. Evaluate the objective function for each particle, and determine the local

and global optimal solution pid and pgd respectively.

3. Update all the particles.4. If the algorithm is converged, then stop; otherwise, go to step 2.5. The particle yielding the global optimum solution pgd is the final result.

11 ˆˆˆ SΣSTtrace

2/12/1

1 2/ln

2

1

28

1

ji

jiji

jiTji

ΣΣ

ΣΣμμ

ΣΣμμ

MEAC:

JM distance:

Objective function:

Illustration of PSO-based band selection(Selecting 6 bands from L bands)

0 50 100 150 200 250 300 350 4000.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

Iterations

ME

AC

Va

lue

Convergence Curve of PSO Band Selection use MEAC

Convergence curves of PSO-based band selection (MEAC)

0 50 100 150 200 250 300 350 400 450-21.19

-21.185

-21.18

-21.175

-21.17

-21.165

-21.16

-21.155

-21.15

number of iterations

Neg

ativ

e J

M D

ista

nce

Convergence Curve of PSO Band Selection use JM Distance

Convergence curve of PSO-based band selection (JM distance)

Decision FusionDecision FusionHyperspectral Image Data

Supervised classifier(SVM)

Use unsupervised result to segment supervised result

Unsupervised classifier(Kmeans, Mean-Shift)

(Weighted) Majority Voting

Final Decision

● ● H. Yang, Q. Du, and B. Ma, “Decision fusion on supervised and unsupervised classifiers for hyperspectral imagery,” IEEE Geoscience and Remote Sensing Letters, vol. 7, no. 4, pp. 875-879, Oct. 2010.

ExperimentsExperiments

The hyperspectral data used in the experiments was taken by the airborne Hyperspectral Digital Imagery Collection Experiment (HYDICE) sensor. It was collected for the Mall in Washington, DC with 210 bands covering 0.4-2.4 µm spectral region. The water-absorption bands were deleted, resulting in 191 bands. The original data has 1280×307 pixels.

Another hyperspectral data used in the experiments was the 126-band HyMap data about a residential area near the campus of Purdue University. The image size is 377×512.

HYDICE ExperimentHYDICE Experiment

six classes: road, grass, shadow, trail, tree, roof

HYDICE ExperimentHYDICE Experiment

Training Test

Road 55 892Grass 57 910

Shadow 50 567Trail 46 624Tree 49 656Roof 52 1123

SVM classification accuracy using MEAC-selected bands in the HYDICE experiment

SVM classification accuracy using JM-selected bands in the HYDICE experiment

SVM Mean-Shift

Road Grass Shadow Trail Tree Roof

Majority-voting Fused result

Road Grass Shadow Trail Tree Roof OA AA Kappa

svm(pca) 99.0 98.6 82.0 92.3 98.8 84.8 92.6 92.6 91.1

svm(pso) 98.1 98.9 94.7 92.5 99.4 95.4 96.6 96.5 95.9

svm(pca)+ms 100.0 99.0 81.3 94.9 98.9 89.3 94.3 93.9 93.0

svm(pso)+ms 90.7 99.0 100.0 100.0 98.9 98.9 97.5 97.9 97.0

svm(pca)+kmeans 99.9 96.9 75.7 96.6 98.8 95.3 94.8 93.9 93.6

svm(pso)+kmeans 94.8 99.2 98.9 99.7 95.9 99.3 97.9 98.0 97.5

Classification accuracy from different methods in HYDICE experiment(with 6 bands or 6 PCs)

HyMap ExperimentHyMap Experiment

six classes: road, grass, shadow, soil, tree, roof

HyMap ExperimentHyMap Experiment

Training Test

Road 73 1231Grass 72 1072

Shadow 49 215Soil 69 380Tree 67 1321Roof 74 1244

SVM classification accuracy using MEAC-selected bands in the HyMap experiment

SVM classification accuracy using JM-selected bands in the HyMap experiment

SVM Mean-Shift

Road Grass Shadow Soil Tree Roof

Majority-volting Fused result

Road Grass Shadow Soil Tree Roof OA AA Kappa

svm(pca) 92.4 98.9 97.2 90.8 96.4 81.4 92.2 92.8 90.3

svm(pso) 94.9 98.3 98.1 85.2 93.9 89.6 93.6 93.3 91.9

svm(pca)+ms 96.3 100.0 98.1 100.0 97.7 85.5 95.2 96.3 94.0

svm(pso)+ms 97.3 96.0 100.0 98.7 98.9 100.0 98.2 98.5 97.7

svm(pca)+kmeans 99.2 99.7 86.9 71.7 98.7 81.8 92.9 89.7 91.0

svm(pso)+kmeans 96.1 96.6 95.9 98.1 99.5 98.2 97.6 97.4 96.9

Classification accuracy from different methods in HyMap experiment(with 6 bands or 6 PCs)

ConclusionConclusion

The experimental results demonstrate that PSO can greatly improve band selection performance in terms of SVM classification accuracy, compared to the frequently used SFS and SFFS searching strategies. The classification improvement can be magnified through decision fusion.

The searching criterion called MEAC without requiring training samples is considered more advanced than the JM distance. In the SFS searching, the JM performance is much worse than MEAC; however, after using PSO searching, its performance can be as good as MEAC. This means the employed searching strategy does play an important role in band selection performance.