稀疏子空间聚类提升高光谱遥感图像空间谱分群精度

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本文主要探讨了"稀疏子空间聚类在高光谱遥感图像光谱空间聚类中的应用"这一研究主题。高光谱遥感图像因其丰富的光谱信息和复杂的地理空间特性，传统的聚类方法往往面临挑战。为了克服这些问题，作者提出了一种创新的算法——Spectral-Spatial Sparsifying Subspace Clustering (S4C)模型。 S4C算法的核心思想是将高光谱遥感图像中的每个地物类别视为一个潜在的低维子空间，利用稀疏子空间聚类（SSC）技术进行处理。SSC旨在发现数据中的结构和模式，通过寻找数据样本在低维子空间中的稀疏表示来实现。在高光谱遥感图像中，这种方法特别强调了两个关键特性：高光谱的强相关性和丰富的空间信息。通过结合这两个特性，S4C模型能够更精确地估计光谱系数矩阵，从而提高了聚类的准确性和稳定性。具体来说，S4C算法首先对高光谱数据进行预处理，可能包括降维、特征选择或噪声去除等步骤，以减少冗余信息并突出关键特征。接着，算法会构建一个包含光谱和空间信息的联合模型，利用稀疏约束优化来捕捉数据之间的内在关系。在优化过程中，算法不仅关注样本间的相似性，还考虑了它们在光谱和空间维度上的紧密度，以形成更有效的聚类分组。通过这种方法，S4C算法能够在保持高光谱信息的同时，有效地利用空间关联性，从而显著改善了高光谱遥感图像的聚类效果。相比于传统的方法，S4C在复杂数据集上显示出更高的聚类精度和鲁棒性，对于地球观测、环境监测、遥感影像分类等领域具有重要的实际应用价值。总结来说，这篇研究论文介绍了一种新颖的S4C算法，它在高光谱遥感图像处理中引入了稀疏子空间聚类，结合光谱和空间特性，提升了聚类性能。这不仅为遥感数据分析提供了新的工具，也为后续的研究和实践打开了新的可能性。

Spectral-Spatial Clustering of Hyperspectral Remote Sensing Image with Sparse Subspace

Clustering Model

Han Zhai

, Hongyan Zhang*

, Liangpei Zhang

, Pingxiang Li

and Xiong Xu

1: The State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, and Collaborative Innovation

Center for Geospatial Technology, Wuhan University, P.R. China

2: College of Surveying and Geo-Informatics, Tongji University, Shanghai, P.R. China

*Corresponding author: zhanghongyan@whu.edu.cn

ABSTRACT

Clustering for hyperspectral imagery (HSI) is a very

challenging task due to its inherent spectral and spatial

complexity. In this paper, we propose a novel

spectral-spatial sparse subspace clustering (S

C) algorithm

for hyperspectral imagery. Firstly, by treating each kind of

ground class as a subspace, we introduce sparse subspace

clustering (SSC) algorithm to HSIs. Then considering the

spectral and spatial property of HSI, the high spectral

correlation and rich spatial information of the HSIs are

taken into consideration in the sparse subspace clustering

model to obtain a more accurate coefficient matrix, which is

used to build the adjacent matrix. Lastly, spectral clustering

is applied to the adjacent matrix to obtain the final image

clustering result. Several experiments were conducted to

illustrate the performance of the proposed algorithm.

Index Terms—hyperspectral image, sparse

representation, subspace cluster, spectral clustering

1. INTRODUCTION

Hyperspectral image clustering can be defined as the

process of segmenting pixels into corresponding sets, which

satisfies that differences between sets are much greater than

differences within sets. As known to us all, HSIs are typical

high-dimensional data with large spectral variability and

complex structure [1], which makes HSI clustering a very

challenging problem.

To date, many clustering methods for HSIs have been

proposed, such as the centroid clustering methods [2], the

density-based methods [3], the biological methods [4], the

spectral methods [5] and so on. However, most of them

suffer from heavy misclassification because of the uniform

feature point distribution caused by the large spectral

variability of HSI. In recent years, sparse subspace

clustering (SSC) algorithm was proposed to group data

points into different subspaces by finding the sparsest

representation for each data point with only selecting the

data points from its own subspace to represent itself, and has

been widely applied in various computer vision fields [6].

For HSIs, although pixels of the same class may have

different spectrums because of the varying illumination,

topography and imaging condition, they would lie in the

same subspace. Based on this fact, it is natural to introduce

the SSC algorithm to the HSI clustering task. However,

directly applying the SSC algorithm to the HSI usually fails

to take advantage of the high spectral correlation and rich

spatial information of the HSI, which is far from fully

exploiting the potential of the SSC algorithm for HSI

clustering.

In view of this, we proposed a novel spectral-spatial

sparse subspace clustering algorithm (S

C) for hyperspectral

imagery. The contributions of this paper are summarized as

follows. Firstly, to the best of our knowledge, by

considering that the pixels of the same class lie in one

independent subspace, we are the first to segment HSI pixels

into different clusters with the SSC algorithm. Secondly,

considering the working mechanism of sparse representation,

a spectral weighted sparse subspace clustering model

(SWSSC) is built to ensure that each pixel can be

represented by the corresponding signals with the highest

correlation. Thirdly, with the spectral similarity of a local

neighborhood of the HSI, the rich spatial information is also

incorporated to the SSC model to improve the performance.

The experimental results demonstrate that the proposed S

algorithm significantly improve the clustering performance

both in visual and quantitative evaluations.

2. HSI CLUSTERING VIA SPARSE SUBSPACE

CLUSTERING MODEL

In the SSC model, let

 



be an arrangement of

affine subspace of

of dimensions

 



, where

is the

dimension of the ambient space. Considering a given

collection of N noise-free data points

 



that lie in the

union of the

subspaces [6]. Denote the matrix containing

all the data points as

   

, , , ,

yyY Y Y Γ

(1)

where



Y

is a rank-

matrix of the

Nd

points

that lie in

and

NN

Γ

is an unknown permutation

matrix.

For HSI, every hyperspectral pixel can be denoted as a

-dimensional vector, where

refers to the number of band.

By this way, the HSI can be denoted by a 2-D matrix

 

, , , ,

p MN



Y Y Y Y Y

, where

represents the

width of the HSI data, and

stands for the height of the

data. By using the data matrix itself as a dictionary, the

sparse representing model can be built as

 

, ,

diag 0 1 1   Y YC N C C

(2)

where

MN MN

C

is the self-representation coefficient

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