IEEE Geoscience and Remote Sensing Magazine - June 2019 - 123

SUPERVISED SEARCHING
Supervised incremental searching-based methods use prior
knowledge of HSI data to maximize class separability. In
[48], employing the exact decomposition of SAM, the band
add-on (BAO) algorithm was presented to iteratively select
bands that increase the angular separation between two
spectra in a spectral library. To address more the practical
problem of discriminating two classes of spectra, the BAO
was extended to two band selection approaches, i.e., the average distance and minimum distance methods (MDMs),
and the selected bands increased the angular separability
of the two classes. Similarly, in [49], using class spectral
signatures, the minimum estimation abundance covariance (MEAC) algorithm incrementally selected dissimilar
bands to preserve the desired information for classification
through minimization of the trace of abundance covariance
matrix as
-1
argmin ( trace 6^St T St h @ 2 ,
MS

(7)

where M S is the selected band subset and St is the matrix
containing class spectral signatures in the selected subset.
Using fast SFS searching, the nonlinear parsimonious feature selection algorithm in [50] iteratively selected spectral
bands that maximized an estimate of the classification rate
from the Gaussian mixture model classifier.
Cramer's V (CV) is the most popular nominal association
used to measure the strength of the relationship between
variables regardless of table size. Based on CV-test theory,
the maximal minimal associated index (MMAIQ) [51] was
proposed to incrementally select bands that yield statistically maximal associations between target labels/features and
minimal associations among selected features. However, the
MMAIQ suffers from the discretization problem and does
not consider class labels in calculating the CV-test value.
Therefore, in [52], the CV-test discretization-based association index and the class-attribution interdependence maximization-based association index were proposed to refine
the band selection result of the MMAIQ. The two derived
algorithms implemented the CV-test discretization scheme
and incrementally selected the optimal spectral bands using the greedy algorithm. Later, a simple equal-width interval-binning approach [53] was implemented in a rough
set-based band selection algorithm, which quantified the
relevance and significance of each band based on the rough
set theory and iteratively selected informative bands with
higher relevance and significance values.
Also inspired by the rough set theory, the variable-precision neighborhood rough set (VPNRS)-based algorithm
[54] measured the significance of each band using dependency and implemented the forward greedy algorithm to
select informative bands. A sequential band subset selection algorithm [55] was put forward to select proper
bands for anomaly detection, inspired by the N-FINDER
and iteratively added new bands by comparing the performance of anomaly detection with that of all bands using
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

the averaged least-squares error and 3D receiver operating
characteristic curves. A new index was proposed for target detection using selected bands in [56] by comparing
the largest outputs in the detection map using all of the
original bands.
UPDATED SEARCHING-BASED METHODS
The updated searching-based methods iteratively replace
elements of the current band subset with new ones as
needed during the searching procedure to ensure that the
predefined evaluation criterion is optimized. Aside from
simple searching strategies such as the sequential forwardfloating search [21], the branch-and-bound search [57],
the steep ascent search, and the constrained search [58],
[59], evolutionary algorithms have been adopted for band
searching, such as particle swarm optimization (PSO) [21],
[56], adaptive simulated annealing [60], [61], genetic algorithms (GAs) [62], firefly algorithms (FAs) [63], differential
evolutionary algorithms [64], and ant colony optimization
[65], [66]. Similar to incremental searching-based methods,
similarity or information measurements can be used as an
objective function. In [67], a maximum-information and
minimum-redundancy (MIMR) criterion was derived as
the low-order approximation of maximum joint-MI criterion. The clonal-selection algorithm in an artificial immune
system was devised to optimize the objective function of
MIMR. In [68], the conflicting relationships between information entropy and the number of selected bands was examined, and a multiobjective optimization band selection
algorithm was designed to find the best tradeoff solution.
Some objective functions utilize the prior knowledge of HSI
data (e.g., labeled training samples and class signatures) to
formulate supervised or semisupervised band selection
methods for HSI classification. According to whether a classifier is involved during band searching, these approaches
can be grouped into classifier-independent or classifierdependent methods.
CLASSIFIER-INDEPENDENT METHODS
The objective function is independent of classification
accuracy from a true-classifier and estimates-only class
separability perspective, based on specific metrics. In [69],
the clonal-selection, feature-selection algorithm adopted
the averaged JM distance among different classes as the
criterion function, and the clonal-selection strategy was
implemented to search for a band subset that optimizes
the criterion function. In [70], band selection was converted into an optimization problem for maximizing class
separability using certain criteria, i.e., ED, SAM, spectral
correlation mapper, and BC, and the immune clonal-strategy algorithm was adopted for band searching. In [71], the
PSO algorithm was used to search for a band subset that
optimizes the criterion function of MEAC or JM distance
among different classes. In [72], the GA was introduced to
search the optimal band combination and coordinate the
potential conflicts in the objective function constituted of
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