IEEE Geoscience and Remote Sensing Magazine - June 2019 - 128

EMBEDDING LEARNING-BASED METHODS
Embedding learning-based methods incorporate band selection into the optimization of specific application models
(e.g., classification, target detection, and spectral unmixing).
CLASSIFIER LEARNING-BASED METHODS
Because of low sensitivity to imbalanced training samples,
the SVM classifier is a very popular method used in hyperspectral image analysis. The recursive-feature elimination (RFE)-SVM can provide superior performance in
hyperspectral band selection; here, the weight value calculated in the SVM training stage was used as the ranking criterion to remove redundant bands and optimize the
SVM classifier. RFE focuses on minimizing the generalization error by eliminating features that maximize the margin. The predictive ability measurement s REF is inversely
proportional to the margin and is given by
D

D

s REF = / / a i a j y i y j U (x i, x j),

(19)

i =1 j =1

where x i and y i ! " -1, 1 , are the ith training sample and
its class label, respectively, and U (x i, x j) is the kernel function (e.g., polynomial and Gaussian) in the SVM classifier. In [123], the embedded feature-selection algorithm
adopted logistic voting to improve the convergence speed
of RFE and automatically eliminated redundant bands
without having prior knowledge of the fixed band number. In [124], the modified recursive SVM implemented a
new ranking criterion in the RFE-SVM training process to
achieve higher classification accuracy and reduce processing time. In [125], the RFE-SVM was modified into the
kernel-based feature-selection algorithm, which used the
magnitude of the SVM coefficients as a ranking criterion
to select the important bands and better train the SVM
classifier. A convolutional neural network (CNN) was
used to exploit deep features of HSI classification and
then combined with an AdaBoost SVM classifier to select
discriminative and complementary spectral bands [126].
Another typical model widely utilized in classifierlearning based methods is the multinomial linear regression (MLR) classifier [127], which reports the probability p
of a given sample x i belonging to class c given by
p ^ y ci =1 x i, wh =

exp (w Tc x i)
C

/ exp (w Tj x i)

,

(20)

j =1

where w j =[W 1j , g, W Nj ] is the weight vector corresponding to the jth class label, C is the number of classes, and
y ci = 1 refers to the training sample x i belonging to class c.
To achieve an acceptable level of sparsity, a Laplacian prior
was incorporated to estimate the weight w using the maximum a posteriori (MAP) criterion. The objective function
of sparse MLR (SMLR) [128] is defined as
u MAP = argmax 6L ^ w h + log p (w)@,
w
w

128

(21)

where p (w) is the sparsity-promoting Laplacian prior
with p ^ w h ? exp (-m w 1) and Log ^ w h is the log-likelihood function
Log ^ w h = / < / y Tj w Tj x i - log d / exp ^ w Tj x i hnF . (22)
C -1

C -1

i =1 j =1

j =1

n

The SMLR adopts a dynamic training scheme to integrate
band selection and SMLR training into a unified framework, and nonzero logistic regression coefficients correspond to the selected bands. Later, the SMLR was tested
to improve the accuracy of pine, spruce, and birch tree
species classification in the hyperspectral data of a boreal
forest [129].
OTHER LEARNING-BASED METHODS
Band selection models can also be embedded in the learning models of target detection and endmember extraction.
In [130], a band sparsity term along with a sparsity-promoting prior was incorporated to extend the sparsity-promoting
iterated-constrained endmember into the objective function
RSS
J = h N B + bSSD B + SPT + BST,

(23)

where RSS B is the residual sum of squares based on the convex geometry model, SSD B is the term that describes the
sum of squared distances, SPT is the band sparsity-promoting term, and the BST term describes the weighted sum of
band weights. Here, h and b are regularization parameters
that balance RSS B and SSD B in the objective function. The
iterative-update scheme was implemented to autonomously
determine the number of spectral bands required and to select bands while performing endmember determination and
unmixing. Using a similar idea, band selection was embedded in the target detection model by adding a sparse regularization item into the CEM detector. The formulated sparse
CBS [131] was solved by optimizing a continuous convex
quadratic programming problem, and the proper bands and
sparse CEM detector were simultaneously obtained.
A few researchers have investigated band selection using
deep NNs. In [132], a subspace-partitioning band selection
of distance density was proposed to optimize a pretrained
CNN model. After that, an autoencoder NN was utilized to
replace the CNNs, and the segmented autoencoder method
[133] was presented to select the most significant bands.
Attention-based CNNs in [134] selected the most informative bands with trained deep networks. The contribution
map (CM) in [135], recorded discriminative band locations
of each class, was incorporated into CNNs, and the formulated CM-CNNs selected more discriminative bands.
HYBRID SCHEME-BASED METHODS
Hybrid scheme-based methods implement multiple schemes
to select appropriate bands. In particular, a clustering scheme
was more widely combined with a ranking scheme to form
hybrid algorithms. In [136], the spectral separability index
(SSI) algorithm integrated clustering, ranking, and searching
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2019
IEEE Geoscience and Remote Sensing Magazine - June 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2019
