DISCRIMINATIVE PIXEL-PAIRWISE CONSTRAINT-GUIDED EXTREME LEARNING
MACHINE FOR SEMI-SUPERVISED HYPERSPECTRAL IMAGE CLASSIFICATION
Jinhuan Xu
1
, Pengfei Liu
2
, Le Sun
3
, Liang Xiao
1∗
1
School of Computer Science and Engineering,Nanjing University of Science and Technology, Nanjing 210094, China,
2
School of Computer Science, School of Software, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, China,
3
School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
ABSTRACT
Generally, the traditional semi-supervised extreme learning
machine (S
2
-ELM) method cannot fully exploit the limited
label information in hyperspectral image (HSI) classifica-
tion. In this paper, we propose a discriminative S
2
-ELM
method, called pixel-pairwise constrained S
2
-ELM (P
2
S
2
-
ELM) method. Both the manifold regularization to leverage
unlabeled data and the pixel-pairwise constraint between the
labeled pixels are incorporated into a unified minimizing
framework, thus the proposed P
2
S
2
-ELM method is able to
learn a more effective and discriminative projection. Experi-
mental results on several real hyperspectral data sets exhibit
its efficiency and superiority to the counterparts, when only a
small number of labeled samples are available.
Index Terms— Hyperspectral image, semi-supervised
classification, discriminative analysis, pixel-pairwise con-
straint, extreme learning machine (ELM).
1. INTRODUCTION
Hyperspectral images(HSIs) have been widely used in the
fields of military monitoring, environmental monitoring, min-
eral identification etc., due to the abundant spectral and spatial
information [1]. HSI classification is one of the most impor-
tant research topics. Over the past decade, many machine
learning methods have been developed for HSI classification,
such as, support vector machines (SVM) [2], extreme learn-
ing machine (ELM) [3], and multinomial logistic regression
(MLR)[4].
For the supervised classifiers, they require a large quan-
tity of labeled data due to the high dimensional spectral data
vector. However, labeled samples are often difficult, costly, or
time consuming to obtain. To address the problem of limited
labeled samples, semi-supervised learning (SSL) techniques
This work has been supported by the National Natural Science Founda-
tion of China (Grant No. 61571230), the National Major Research Plan of
China (Grant No. 2016YFF0103604), the Jiangsu Provincial Natural Sci-
ence Foundation of China (Grant No. BK20161500), the Jiangsu Provin-
cial 333 Project,Natural Science Foundation of Jiangsu Province under Grant
BK20170905.(corresponding author: Liang Xiao.)
have been adopted for jointly exploring the information of
both labeled and unlabeled samples [5]. The research on SSL
has experienced a quick development in the past few years,
and some popular methods have been proposed, such as gen-
erative mixture models [6], self-learning models [7], trans-
ductive learning models, e.g., transductive support vector ma-
chines (TSVM) [8], and graph-based methods [9,10].
Among SSL methods, graph-based approaches have re-
cently received significant attention due to their efficiency and
computational simplicity [9-11]. In SSL, the data manifold
is represented by a graph constructed from both labeled and
unlabeled data as a graph Laplacian regularization to con-
strain the classification function. In the HSI classification re-
search area, SVM-based SSL approaches [12] have achieved
great popularity. However, the convergence to the correc-
t solution is not always guaranteed [13]. Huang et al. ex-
tended ELMs to combine the manifold regularization into a
framework and proposed a semi-supervised ELM (S
2
-ELM)
method [14]. The S
2
-ELM method is not only inductive (s-
traightforward extension for out-of-sample examples at test
time), but also can inherit the computational efficiency and
the learning capability of traditional ELMs.
Even the aforementioned graph-based manifold learning
method explores the underlying structures among data points,
but it does not take the label discriminative information into
consideration. In general, discriminant analysis can be ex-
pressed in diverse forms, such as fisher discriminant analysis
[15, 16], pairwise constraint [17], and other prior forms [18].
Motivated by the aforementioned thoughts, we adopt the
pairwise constraint to incorporate the discriminative informa-
tion into the S
2
-ELM model, and propose a discriminative
pixel-pairwise constrained S
2
-ELM (P
2
S
2
-ELM) method.
The main contribution of this paper is that the pairwise con-
straint incorporate the discriminant information between the
labeled samples via a graph-based Laplacian matrix, which
makes the learned output weight matrix more discriminative.
More specifically, we integrate the discriminant regulariza-
tion with S
2
-ELM into a unified model and the output weight
matrix can be more efficiently obtained by solving a regular-
ized least square problem.