基于核PCA与关系透视映射的高光谱特征识别方法(KPmapper)
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本文档探讨了一种新颖的基于核主成分分析（Kernel Principal Component Analysis, KPCA）和关系透视映射（Relational Perspective Map, RPM）的高光谱特征识别方法，即KPmapper。KPCA在处理高光谱数据时发挥了关键作用，它通过非线性变换将原始数据转换到一个高维空间中，从而更好地提取与特征相关的主成分，实现了对复杂光谱信息的有效降维。这种方法特别适用于高维非线性数据，能够有效地揭示其中的内在结构。
RPM作为一种可视化工具，通过将高光谱数据映射到二维（2D）地图上，使得原本难以理解的高维数据变得直观。RPM通过将数据分割成若干部分，并将它们投影到二维空间中，有助于发现数据中的规律和模式。这种方法对于特征提取和理解光谱数据之间的关系非常有效，因为它强调了数据之间的关系性和空间组织，有助于识别不同光谱特征之间的关联。
研究者提出KPmapper算法，结合了KPCA的降维能力和RPM的可视化特性，旨在提高高光谱数据的特征识别性能。实验结果显示，该算法在保持数据关键信息的同时，显著降低了数据维度，这对于实际应用，如土壤类型分类、植被健康监测等领域具有重要意义。由于其高效性和准确性，KPmapper方法在处理大规模高光谱数据时展现出了强大潜力，为后续的遥感数据分析和机器学习提供了强有力的支持。
这篇文章的主要贡献在于提供了一个创新的解决方案，将核主成分分析与关系透视映射相结合，以实现高光谱数据的高效降维和特征识别，这不仅提升了数据处理的精度，还简化了复杂的分析过程，为光谱学和遥感科学领域的研究者们提供了一种实用的工具。
August 10, 2010 / Vol. 8, No. 8 / CHINESE OPTICS LETTERS 811
Hyperspectral feature recognition based on kernel PCA and
relational perspective map
Hongjun Su (ùùù) and Yehua Sheng (uuu)
∗
Key Laboratory of Virtual Geographic Environment (Ministry of Education),
Nanjing Normal University, Nanjing 210046, China
∗
E-mail: shengyehua@njnu.edu.cn
Received February 26, 2010
A novel joint kernel principal component analysis (PCA) and relational perspective map (RPM) method
called KPmapper is proposed for hyperspectral dimensionality reduction and spectral feature recognition.
Kernel PCA is used to analyze hyperspectral data so that the major information corresponding to features
can be better extracted. RPM is used to visualize hyperspectral data through two-dimensional (2D) maps,
and it is an efficient approach to discover regularities and extract information by partitioning the data into
pieces and mapping them onto a 2D space. The experimental results prove that the KPmapper algorithm
can effectively obtain the intrinsic features in nonlinear high dimensional data. It is useful and impressing
for dimensionality reduction and spectral feature recognition.
OCIS co des: 100.5010, 280.4788, 300.6170.
doi: 10.3788/COL20100808.0811.
Hyperspectral data can provide fine and detailed spec-
tral information by contiguous spectral range and nar-
row spectrum interval. As a result, some important
and typical spectral features that cannot be expressed
in broadband remote sensed data will be revealed and
extracted obviously, which is significant to target identi-
fication, endmember extraction, anomaly diagnosis, fine
classification, and sophisticated applications of remote
sensing
[1−3]
. But for the given spectra acquired from field
measurement with spectrometer or pixels on hyperspec-
tral remote sensing image by aerial or spaceborne sensors,
how to extract those significant features that can char-
acterize the objects is still the most important topic for
hyperspectral applications. Two critical issues arise from
the above situations. One is “Hughes phenomenon”
[4]
caused by high dimensionality; the other is spectral fea-
ture recognition.
Dimensionality reduction (DR) is the approach to elim-
inate the impact of “Hughes phenomenon”. Gener-
ally speaking, there are two kinds of DR approaches:
one is band selection that selects some interesting
bands or those bands with more information and
weak inter-correlations; the other is feature extrac-
tion, which compresses all bands by certain mathematic
transformation
[5]
. In the past few years, many DR
methods have been presented in remote sensing with
linear techniques such as principal component analysis
(PCA)
[6]
, linear discriminant analysis (LDA)
[7]
, indepen-
dent component analysis (ICA)
[8]
, and so on. However,
the nonlinear features which can be the major properties
in spectral space for hyperspectral data are ignored.
On the other hand, different methods to extract char-
acteristic spectral features have been researched in the
recent years
[9,10]
. Manifold learning, as a new approach,
has been applied to high dimensional data
[11,12]
, and it
can model the nonlinear features (manifold) of high di-
mensional data, while the nonlinear properties are well
preserved. Such manifold learning algorithms as kernel
PCA (KPCA)
[13]
, multi-dimensional scaling (MDS)
[14]
,
isometric mapping (ISOMAP)
[11]
, diffusion maps
[15]
, lo-
cal linear embedding
[12,16]
, Laplacian eigenmap
[17]
, and
local tangent space alignment
[18]
have devoted to pattern
recognition and machine learning while ignoring their ap-
plications in hyperspectral remote sensing. In fact, those
manifold learning algorithms are able to efficiently reveal
geometrical structures and regularities which indwell in
high dimensional space from hyperspectral data
[19]
. In
this letter, a novel joint KPCA and relational perspec-
tive map (RPM) method called KPmapper for DR and
spectral feature recognition is proposed. Experiments are
designed to validate the performance of the proposed al-
gorithm.
PCA is one of the classic linear algorithms in pattern
recognition
[6]
. Its nonlinear version, KPCA, is used to
deal with hyperspectral data in this letter. The details
of KPCA algorithm can be found in Ref. [13]. Sup-
pose that there is a dataset of centered random vector
X ∈ R
n
with N observations x
i
, i ∈ [1, · · · , N]. Firstly,
we mapped the data onto another dot product space Q
d
by φ : R
n
→ Q
d
, X → φ(X). The covariance matrix
φ(X) can be defined as C
φ(X )
=
1
N
N
P
i=1
φ(x
i
)φ(x
i
)
T
. Let
v ∈ Q
d
(v 6= 0) be an eigenvector of C
φ(X)
that corre-
sponds to a positive eigenvalue λ of C
φ(X)
. Similar to
PCA, we can get
λv = C
φ(X )
v, (1)
where v =
N
P
i=1
α
i
φ(x
i
) is lying in the span of
{φ(x
1
), φ(x
2
), · · · , φ(x
N
)}. In addition, by multiplying
Eq. (1) with φ(x
k
) from the left and substituting the
value of v into it, we can get λφ(x)· v
k
= φ(x)·C
φ(x)
·v
k
,
where v
k
=
N
P
i=1
α
k
i
φ(x
i
), k ∈ [1, N ]. In order to construct
the kernel function, we defined an N × N matrix K as
K
i,j
= φ(x
i
) · φ(x
j
) = k(x
i
, x
j
). Consider an eigenvalue
1671-7694/2010/080811-04
c
° 2010 Chinese Optics Letters
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