Particle Swarm Optimization-based
Dimensionality Reduction for
Hyperspectral Image Classification
He Yang, Jenny Q. Du
Department of Electrical and Computer Engineering
Mississippi State University, MS 39762, USA
1
Outline
 Motivation
 Existing band selection approaches
 Unsupervised band selection
 Supervised band selection
 Particle swarm optimization (PSO)
 PSO for hyperspectral band selection
 Experimental results
 Conclusion
Motivation
 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)
 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.
Motivation (Cont’d)
 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.
Unsupervised 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 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 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 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.
10
10
Particles
gBeset
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-8
-6
-4
-2
0
X1
2
4
6
8
Particles
gBeset
8
X2
X2
8
-10
-10
10
-8
-6
-4
Iteration 1
2
4
6
8
10
10
Particles
gBeset
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-8
-6
-4
-2
0
X1
2
Iteration 50
4
6
8
Particles
gBeset
8
X2
X2
0
X1
Iteration 25
10
-10
-10
-2
10
-10
-10
-8
-6
-4
-2
0
X1
2
4
6
8
10
Iteration 75
● PSO is used to search the solution of f ( x1, x2 )  ( x1  5) 2  ( x2  5) 2.
● 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.
PSO 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: v id  w  v id  c1  r1  (p id  x id )  c2  r2  (p gd  x id )
 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: x id  x id  v id
 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.
PSO 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.
 Objective function:


ˆ 1Sˆ 1 
trace Sˆ T Σ


1
T  Σi  Σ j
μ i  μ j 
 JM distance:
8
2

 MEAC:






1




1  Σi  Σ j / 2 
μ i  μ j  ln

2  Σ 1/ 2 Σ 1/ 2 
j
 i



v1
1
v3
……
B1
Iteration i
……
……
……
B2
B3
……
B1'
……
B5
B2'
B6
……
……
……
B3'
B4'
……
v5
v4
……
L
……
……
1
……
v6
……
B4
v2
Iteration i+1
……
……
……
L
……
B5'
……
Illustration of PSO-based band selection
(Selecting 6 bands from L bands)
B6'
……
……
Convergence Curve of PSO Band Selection use MEAC
0.022
0.02
0.018
MEAC Value
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0
50
100
150
200
Iterations
250
300
350
400
Convergence curves of PSO-based band selection (MEAC)
Convergence Curve of PSO Band Selection use JM Distance
-21.15
-21.155
Negative JM Distance
-21.16
-21.165
-21.17
-21.175
-21.18
-21.185
-21.19
0
50
100
150
300
250
200
number of iterations
350
400
450
Convergence curve of PSO-based band selection (JM distance)
Decision Fusion
Hyperspectral Image Data
Supervised classifier
(SVM)
Unsupervised classifier
(Kmeans, Mean-Shift)
Use unsupervised result to
segment supervised result
(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.
Experiments
 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 Experiment
six classes: road, grass, shadow, trail, tree, roof
HYDICE Experiment
Road
Grass
Shadow
Trail
Tree
Roof
Training
55
57
50
46
49
52
Test
892
910
567
624
656
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
Majority-voting Fused result
Road
Grass
Shadow
Trail
Tree
Roof
Classification accuracy from different methods in HYDICE experiment
(with 6 bands or 6 PCs)
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
HyMap Experiment
six classes: road, grass, shadow, soil, tree, roof
HyMap Experiment
Road
Grass
Shadow
Soil
Tree
Roof
Training
73
72
49
69
67
74
Test
1231
1072
215
380
1321
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
Majority-volting Fused result
Road
Grass
Shadow
Soil
Tree
Roof
Classification accuracy from different methods in HyMap experiment
(with 6 bands or 6 PCs)
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
Conclusion
 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.