非负低秩表示在高光谱图像半监督聚类中的应用

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"通过非负低秩表示对高光谱图像进行半监督子空间聚类" 高光谱图像（Hyperspectral Images, HSI）是遥感技术中的一种重要数据形式，它提供了丰富的光谱信息，使得我们可以对地物进行精细分类和识别。然而，由于HSI的内在复杂性，例如高维性和噪声干扰，对其进行有效的聚类是一项极具挑战性的任务。本文针对这一问题，提出了一种基于非负低秩表示（Non-negative Low-Rank Representation, NNLRR）的半监督子空间聚类方法。传统的低秩表示（Low-Rank Representation, LRR）模型常用于处理高光谱图像的聚类问题，它假设图像中的大部分像素在低维子空间中可以表示为其他像素的线性组合。但LRR模型未考虑数据的非负特性，这可能导致表示结果的不准确。因此，本研究引入了非负约束，使数据表示更符合实际物理意义，同时利用高斯场和调和函数来改进LRR模型。具体来说，首先，NNLRR算法结合高斯场和调和函数，这两者分别代表了数据的局部相似性和全局结构，以增强低秩表示的表达能力。接着，通过监督信息指导邻接矩阵的构建，将已知类别信息融入聚类过程，提高聚类的准确性。然后，找到一个非负的低秩矩阵，这个矩阵可以表示每个样本由其他样本的线性组合来描述，从而得到邻接矩阵。最后，通过这个邻接矩阵同时完成邻接矩阵构建和子空间聚类，实现了聚类过程的整体优化。实验结果表明，该算法在经典数据集上的表现优秀，适用于高光谱图像的聚类问题，验证了非负低秩表示与半监督学习相结合的有效性。此方法对于环境监测、军事侦察、地理信息系统等领域具有重要的应用价值。关键词：高光谱图像，非负低秩表示，高斯场，调和函数，子空间聚类，半监督学习

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Abstract-----Hyperspectral images (HSIs) own inherent

complexity, so, clustering for HSIs is a very challenging

task. In this paper, we utilized a semi-supervised

subspace clustering method based on non-negative

low-rank representation (NNLRR) algorithm for HSI

clustering. Firstly, NNLRR used Gaussian fields and

harmonic functions into the low-rank representation

(LRR) model. Secondly, NNLRR guided the affinity

matrix construction by the supervision information. Next,

finding a non-negative low-rank matrix, the matrix

represents each sample by some other linear combination

points, and the affinity matrix is obtained by the matrix.

Then, accomplishing the affinity matrix construction and

subspace clustering simultaneously. Thanks for the

unification of the two steps, we can guarantee the overall

optimum. Experimental results on classical data set show

that, the algorithm is effective for hyperspectral image

clustering.

Index Terms: hyperspectral image, non-negative

low-rank representation, Gaussian fields and harmonic

functions

I. I

NTRODUCTION

HSIs have a wide application in our real lives [1-3],

such as urban planning, surveillance, agriculture, and so on.

However, as everyone knows, it is a little difficulty to

process the HSIs data, because of its high dimensionality,

which is prone to cause the curse of the dimensionality [4

,5].

Recently, for HSIs, various clustering methods with

different work mechanisms have been proposed. For example,

the k-means [6

] algorithm, which is a classically

unsupervised learning method, is applied for HSIs clustering.

However, the k-means is represented by centroid-based

clustering, which can be hampered by their large

computational complexity. In addition, the Fuzzy c-means

(FCM) [7

] is also widely used for HSIs. FCM is improved by

traditional clustering algorithm, but it is sensitive to the

1 Corresponding author

†

The first author.

J. Yang is with the College of Electrical Engineering and Automation,

Anhui University, Hefei, Anhui 230601, China.

Q. Yan is with the College of Computer Science and Technolog, and

College of Electrical Engineering and Automation, Anhui University, Hefei,

Anhui 230601, China(e-mail: 21429717@qq.com).

D. Zhang is with the College of Electrical Engineering and Automation,

Anhui University, Hefei, Anhui 230601, China.

T. Li is with the College of Electrical Engineering and Automation,

Anhui University, Hefei, Anhui 230601, China.

Y. Wang is with the College of Computer Science and Technolog, Anhui

University, Hefei, Anhui 230601, China.

initial cluster center, and it is necessary to determine the

cluster number in advance, and easy to get into the local

optimal solution. Except for these, Sparse subspace

clustering (SSC) [8

] maps the essential features of

high-dimensional data to the lower dimensional subspace.

And then, the SSC algorithm clusters data points that lie in a

union of low-dimensional subspaces. But unfortunately,

these clustering methods have an obvious disadvantage.

They have no prior information because of only unlabeled

samples used. However, the labeled samples can obtain

discriminant self-expressive coefficients. In exploiting the

subspace structure, it makes a great contribution. In this

paper, we utilize the non-negative low-rank representation

(NNLRR) [9

] algorithm, which is proposed by Fang et al. to

cluster normal data, to cluster HSIs. The method integrate the

LRR and the Gaussian fields and harmonic functions (GFHF)

[10

] into a single optimization problem, and it guided the

affinity matrix construction by the supervision information,

then accomplish the affinity matrix construction and

subspace clustering simultaneously, thus, the overall

optimum can be guaranteed.

We organize the remainder of this paper as follows. In

Section Ċ, we give some introdution of Gaussian Fields and

Harmonic Functions and LRR. Section ċ expresses the

related work of the algorithm. Some experiments and

analyses are shown in Section Č. In Section č, we draw a

conclusion about the algorithm and outline the future work.

II. R

ELATED WORKS

In this section, we introduce the low-rank representation

(LRR) [11

] algorithm firstly. Then, we introduce the

well-known semi-supervised learning method, called

Gaussian Fields and Harmonic Functions.

A. Low-Rank Representation

In a given dictionary, the LRR’s idea is to seek the

lowest rank representation among the many possible linear

combinations of the bases. We assume that the observed data

matrix  אԸ

ܯൈܰ

is approximately drawn from a union of c

low-dimensional subspaces contaminated by error E. So, this

formulates the model shown in (1):

EAZYtsEZ

 



ǂǂǂǂ

ǂǂ

..mi n

(1)

Where ൌ

ሾ



ǡ

ǡ ǥǡ



ሿ

is the base matrix. In a

general way, the dictionary allways choose the data matrix Y

(i.e. ൌ). And

represents the sum of the singular

values of a matrix, called nuclear norm matrix. The error

matrix is E.

Ͳ

is the number of nonzero entries, called

the sparsity measure. As we know, we can’t optimize the

Semi

-Supervised Subspace Clustering via Non-Negative Low-

Rank

Representation for Hyperspectral Images

Jipan Yang

†

, Dexiang Zhang, Teng Li, Yan Wang, Qing Yan

108

Proceedings of The 2018 IEEE International

Conference on Real-time Computing and Robotics

August 1-5, 2018, Kandima, Maldives

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