A Novel Approach for Dimensionality Reduction and Classification of Hyperspectral Images based on Normalized Synergy

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(IJACSA) International Journal of Advanced Computer Science and Applications,

Vol. 10, No. 8, 2019

248 | P a g e

www.ijacsa.thesai.org

A Novel Approach for Dimensionality Reduction and

Classification of Hyperspectral Images based on

Normalized Synergy

Asma Elmaizi1*, Hasna Nhaila2, Elkebir Sarhrouni3, Ahmed Hammouch4, Nacir Chafik5

Research Laboratory in Electrical Engineering LRGE,

Mohammed V University, Rabat, Morocco

Abstract—During the last decade, hyperspectral images have

attracted increasing interest from researchers worldwide. They

provide more detailed information about an observed area and

allow an accurate target detection and precise discrimination of

objects compared to classical RGB and multispectral images.

Despite the great potentialities of hyperspectral technology, the

analysis and exploitation of the large volume data remain a

challenging task. The existence of irrelevant redundant and noisy

images decreases the classification accuracy. As a result,

dimensionality reduction is a mandatory step in order to select a

minimal and effective images subset. In this paper, a new filter

approach normalized mutual synergy (NMS) is proposed in

order to detect relevant bands that are complementary in the

class prediction better than the original hyperspectral cube data.

The algorithm consists of two steps: images selection through

normalized synergy information and pixel classification. The

proposed approach measures the discriminative power of the

selected bands based on a combination of their maximal

normalized synergic information, minimum redundancy and

maximal mutual information with the ground truth. A

comparative study using the support vector machine (SVM)

and k-nearest neighbor (KNN) classifiers is conducted to evaluate

the proposed approach compared to the state of art band

selection methods. Experimental results on three benchmark

hyperspectral images proposed by the NASA “Aviris Indiana

Pine”, “Salinas” and “Pavia University” demonstrated the

robustness, effectiveness and the discriminative power of the

proposed approach over the literature approaches.

Keywords—Hyperspectral images; target detection; pixel

classification; dimensionality reduction; band selection;

information theory; mutual information; normalized synergy

I. INTRODUCTION

In the next decade, the exploitation of hyperspectral

imaging [1] will experience a spectacular development thanks

to the technological imaging evolution growing in many areas.

The current generation of hyperspectral sensors provides large

quantities of precise information on the nature and spatial-

temporal evolution of the analyzed areas. The maturity and

accessibility of this technology make it possible to address new

applications in the fields of agronomy, environment, military,

industrial and health security, etc. In remote sensing [2], the

rich and detailed spectral information provided by

hyperspectral images helped in detecting the composition of

imaged materials and classifying targets with high spectral and

spatial accuracy [3]. Embedded on an aircraft, a hyperspectral

sensor operating in the visible near-infrared range (400-1000

nm) can simultaneously record several tens, even hundreds of

narrow spectral bands. The volumes of data (data cubes)

acquired often reach gigabytes for a single scene observed. As

a result, their exploitation with classical methods developed for

monochrome or color is very limited. In many cases, it is

unnecessary to process all the spectral bands of an HSI [4][5]

(Hughes phenomenon).

Most materials have specific characteristics only at certain

bands, which makes the remaining spectral bands somewhat

redundant. Additionally, some noisy bands [6] are influenced

by various atmospheric effects. To overcome these challenges

and respond quickly to the needs arising from the different

potential applications, dimensionality reduction is an essential

pre-processing step. Methods of bands selection must be

developed to achieve the best compromise between reducing

and preserving the amount of information acquired.

The selection approaches [7] consist of retaining the dataset

physical meaning by selecting the most relevant bands. The

hyperspectral band‟s selection will be the main topic of the

work presented in this paper. Currently, selection algorithms

can be categorized into two common approaches: wrapper and

filters [8].

 The wrapper methods are classifier-dependent. They

evaluate the band‟s relevance based on the

classification accuracy and generally reach promising

results. However, these approaches are very expensive

in terms of computational complexity and may suffer

from over-fitting to the learning algorithm.

 The filter methods are classifier-independent. They are

based on the maximization of a certain evaluation

function. The main advantages of these methods are

their computational efficiency, simplicity and

independence from the classifier. A common drawback

shared by these approaches in literature is the lack of

information about the synergy and interaction

correlation between the picked bands and the ground

truth.

In literature, many filter-selection methods have been

developed using different evaluation measures. The evaluation

function is generally based on distance, information,

correlation and different consistency measures.

*Corresponding Authors

(IJACSA) International Journal of Advanced Computer Science and Applications,

Vol. 10, No. 8, 2019

249 | P a g e

www.ijacsa.thesai.org

Information theory introduced by “Cover & Thomas” [9]

has been widely applied in filter methods, where information

measures are used to evaluate the band‟s relevance and

quantify the amount of information contained on images. This

paper contributes to the knowledge in the area of hyperspectral

dimensionality reduction by proposing a new approach based

on normalized synergic correlation. The proposed method aims

to overcome the limitations of the current state of the art filter

band selection methods such as overestimation of the band

significance, which causes selection of redundant and

irrelevant bands. The new evaluation method selects the band

that has maximum relevance, minimum redundancy and

maximum normalized synergy with the previously selected

bands. This paper reviews the state of art band selection

methods highlighting their common limitations and comparing

their performance versus the proposed algorithm. Experimental

results are carried out using three benchmark hyperspectral

images proposed by the NASA “AVIRIS Indiana Pine” [10],

“Pavia University” and “ROSIS Salinas” [11]. Classification

results are generated using the SVM [12][13] and KNN [14] to

demonstrate the effectiveness and classification accuracy

improvement of the proposed approach.

The rest of the paper is structured as follows. Section 2

describes the fundamentals of information theory and reviews

the state of art band selection methods. Section 3 presents the

proposed normalized max synergy (NMS) algorithm. Section 4

outlines the experiment conducted on the three datasets and

analysis the achieved results. Finally, Section 5 concludes the

paper.

II. BACKGROUND ON INFORMATION THEORY BASED

APPROACHES

In this section, we describe some basic concepts about

information theory and feature selection, which will be used to

build the proposed hyperspectral band selection algorithm.

The information theory proposed by "Cover & Thomas" [9]

has been widely applied in filtering methods, where

information measures are used to assess the relevance and

discrimination of the characteristic.

Definition 1: The Shannon entropy introduced in (1) is

defined as the quantification of the amount of information

contained in variable X.



 (1)

Since, Shannon entropy H(X) is defined for a single

variable and it is independent of the class, the mutual

information between two random variables was introduced in

order to measure the statistical dependence between the

features and between the features and the class.

Definition 2: The mutual information (MI) of a pair of

variables in (2) represents their degree of dependence in the

probabilistic sense. It is the reduction of uncertainty on a

random variable through the knowledge of another.

  

 

 (2)

      (3)

     (4)

The P(X,Y) in (2) is the joint probability function and P(X)

, P(Y) represent the marginal probabilities.

In the equation (3), H(X) and H(Y) are the Shannon

entropies of two variables X, Y respectively and H(X, Y) is the

joint entropy between the variables. The mutual information

can also be formulated using the conditional entropy as

presented in (4).

Mutual information has the following properties.

 Mutual information is positive or zero.

 The mutual information is symmetrical.

In a wide survey of the feature selection literature, we have

identified different information theory-based filters [15] and

we will be presenting a selection of the most well-known

criteria.

In the results section, the selected relevant methods will be

applied to hyperspectral data to compare it with our proposed

approach.

Battiti [16] proposed to use mutual information for variable

selection in the Mutual Information-based Feature Selection

(MIFS) algorithm. In this approach, the number of variables is

fixed in advance and at each step, the variable that maximizes

the mutual information between all the variables already

selected is chosen. Formally, the variable selected by the MIFS

algorithm is the one that maximizes the following goal

function:

     

 (5)

The factor „‟ in (5) allows to control the redundancy term

MI(Fi,Fs) and has a great influence on the selection algorithm.

Several authors like Bollacker and Ghosh [17] that use

different values for the parameter  without any justification.

The value of  is often determined experimentally and depends

on the data used. The problem is highlighted when the subset is

very large and the redundancy term becomes larger than the

relevance term. The algorithm will then select irrelevant

features because they are not redundant, but not because they

are relevant to the class.

As a consequence, several variants of the MIFS algorithm

have been proposed in recent years in order to overcome its

limitations. Kwak and Choi [18] proposed the algorithm MIFS-

U as an improvement of MIFS.

     



 (6)

Peng [19] analyzed as well the limitations of the previous

selection approach and proposed a robust approach minimum

redundancy maximum relevance (mRMR) where the

redundancy term in (7) is divided over the cardinality of the

subset.

   



 (7)

Asma et al. [20] proposed a hybrid strategy combining the

filter mRMR with the Fanno based wrapper strategy in order to

select the relevant hyperspectral bands. Yang and Moody [21]

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(IJACSA)InternationalJournalofAdvancedComputerScienceandApplications,Vol.10,No.8,2019248|Pagewww.ijacsa.thesai.orgANovelApproachforDimensionalityReductionandClassificationofHyperspectralImagesbasedonNormalizedSynergyAsmaElmaizi1*,HasnaNhaila2,ElkebirSarhrouni3,AhmedHammouch4,NacirChafik5ResearchLabo...

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