IEEE Geoscience and Remote Sensing Magazine - December 2017 - 46

Graph embedding and manifold-based SR were combined
in a semisupervised framework for hyperspectral DR [75],
where the sparse coefficients were exploited to construct the
graph. Semisupervised manifold alignment [76] and semisupervised transfer component analysis [77] were proposed to
find a transformation matrix to project high-dimensional
multimodal images into a lower-dimensional feature space,
where the geometry of each modality could be preserved.
These semisupervised DR methods try to build a similar
objective function, i.e., maximizing class discrimination
while at the same time preserving the intrinsic geometric
structure of the data. The optimal solutions are acquired by
solving generalized eigenvalue problems in the same manner [78]. These methods can be further expanded to shape a
manifold learning method by using the kernel trick, similar
to the approaches in [79].

We compared the performance when using raw hyperspectral
data and seven DR methods (including unsupervised, supervised, and semisupervised DR methods) with three popular
classifiers, the parameter settings of which are the same as those
in [74]. The training samples were randomly selected from the
training set, with the sample size corresponding to different
cases: 20, 40, and 80 samples per class, respectively. The results
were averaged over ten runs on different numbers of extracted
features from one to 30, and the averaged overall accuracy (OA)
of the classification was recorded for each method.
The results confirmed that DR can improve classification performance on HSIs. As the size of the training sample
increased, classification accuracy increased. Semisupervised
DR methods (especially those in [73] and [74], designed for
hyperspectral data) outperformed both unsupervised and supervised methods for the one-nearest-neighbor classifier.
DR methods that exploit spatial smoothness produced better
results, even for unsupervised methods; e.g., OTVCA [36]
outperformed the other methods for both random forest
(RF) and SVM classifiers in terms of classification accuracy.

EXPERIMENTAL RESULTS
Table 2 and Figure 8 show the performances of some DR
methods on the classification of the Pavia University HSIs.

TABLE 2. THE DIMENSIONALITY REDUCTION FOR THE CLASSIFICATION OF PAVIA UNIVERSITY DATA, OA%
(OPTIMAL NUMBER OF REDUCED FEATURES).
NUMBER OF LABELED SAMPLES
DR METHODS
Unsupervised

Raw

PCA

LPP [24]

OTVCA [36]

Supervised

Semisupervised

NWFE [38]

SDA [69]

SELF [72]

SELD [73]

SEGL [74]

CLASSIFIER

20

40

80

1NN

63.14

68.36

69.88

SVM

67.29

70.15

71.51

RF

68.72

71.06

73.39

1NN

67.38 (11)

69.46 (12)

70.23 (11)

SVM

70.21 (8)

74.77 (8)

76.81 (9)

RF

73.46 (11)

73.88 (11)

76.13 (11)

1NN

66.97 (18)

69.43 (18)

70.17 (12)

SVM

71.80 (9)

77.14 (12)

77.95 (18)

RF

72.46 (18)

74.20 (19)

75.82 (19)

1NN

71.93 (19)

75.81 (20)

80.39 (23)

SVM

92.74 (19)

96.32 (21)

97.52 (18)

RF

96.24 (23)

97.75 (21)

98.79 (22)

1NN

71.34 (9)

73.34 (9)

74.42 (12)

SVM

72.29 (8)

76.62 (8)

77.18 (9)

RF

75.84 (9)

77.03 (11)

78.74 (8)

1NN

52.67 (7)

62.64 (8)

70.76 (8)

SVM

51.62 (8)

63.64 (9)

70.96 (10)

RF

55.72 (9)

66.97 (9)

71.34 (9)

1NN

61.42 (18)

68.75 (18)

69.56 (16)

SVM

63.93 (19)

75.85 (19)

82.74 (18)

RF

67.98 (18)

75.97 (12)

80.56 (12)

1NN

77.27 (17)

79.03 (10)

81.95 (11)

SVM

75.71 (11)

76.20 (10)

82.03 (11)

RF

75.53 (8)

77.50 (9)

82.26 (9)

1NN

79.40 (9)

81.22 (9)

83.57 (10)

SVM

77.57 (8)

78.16 (8)

82.26 (8)

RF

76.67 (8)

79.14 (8)

83.51 (9)

LPP: locality preserving projections; SEGL: semisupervised graph learning; 1NN: one nearest neighbor.

46

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

DECEMBER 2017
Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2017
