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Received：09 April 2019，
Revised：2019-6-17，
Accepted：24 June 2019，
Published：16 January 2020
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目的
2
高光谱图像的高维特性和非线性结构给聚类任务带来了"维数灾难"和线性不可分问题，以往的工作将特征提取过程与聚类过程互相剥离，难以同时优化。为了解决上述问题，提出了一种新的嵌入式深度神经网络模糊C均值聚类方法（EDFCC）。
方法
2
EDFCC算法为了提取更加有效的深层特征，联合优化高光谱图像的特征提取和聚类过程，将模糊C均值聚类算法嵌入至深度自编码器网络中，可以保持两任务联合优化的优势，同时利用深度自编码器网络降维以及逼近任意非线性函数的能力，逐步将原始数据映射到潜在特征空间，提取数据的深层特征。所提方法采用模糊C均值聚类算法约束特征提取过程，学习适用于聚类的高光谱数据深层特征，动态调整聚类指示矩阵。
结果
2
实验结果表明，EDFCC算法在Indian Pines和Pavia University两个高光谱数据集上的聚类精度分别达到了42.95%和60.59%，与当前流行的低秩子空间聚类算法（LRSC）相比分别提高了3%和4%，相比于基于自编码器的数据聚类算法（AEKM）分别提高了2%和3%。
结论
2
EDFCC算法能够从高光谱图像的高维光谱信息中提取更加有效的深层特征，提升聚类精度，并且由于EDFCC算法不需要额外的训练过程，大大提升了聚类效率。
Objective
2
Hyperspectral remote sensing
which is also called imaging spectral remote sensing
is a combined imaging and spectroscopy of multi-dimensional information retrieval technology. It carries abundant spectral information and is widely used in earth observation. A hyperspectral image is a kind of nonlinear structured data with a high dimension
and it poses a great challenge to the clustering task. If direct processing of the spectral information of hyperspectral images requires a large amount of computation
then appropriate dimensionality reduction methods for the nonlinear structure of hyperspectral data must be adopted. Although many clustering methods have been proposed
these traditional methods involve shallow linear models
the efficiency of the similarity measure is low
and the clustering effect is often poor for high-dimensional or hyperspectral data with a nonlinear structure. Traditional clustering algorithms encounter difficulties when clustering high-dimensional data. The concept of subspace clustering has been proposed to solve the problem of high-dimensional data clustering. Subspace clustering can solve the clustering problem of high-dimensional data. However
existing subspace clustering algorithms typically employ shallow models to estimate the underlying subspaces of unlabeled data points and cluster them into corresponding clusters. They have several limitations. First
the clustering effect of these subspace clustering methods depends on the quality of the affinity matrix. Second
due to the linear assumption of the data
these methods cannot deal with data with a nonlinear structure. Several nuclear methods have been proposed to overcome these shortcomings. These methods map the data to a predefined kernel space where they perform subspace clustering. A disadvantage of these nuclear space clustering methods is that their performance depends heavily on the kernel functions used. Existing data transformation methods include linear transformation
such as principal component analysis (PCA)
and nonlinear transformation
such as the kernel method. However
data with a highly complex potential structure is still a huge challenge to the effectiveness of existing clustering methods
and most clustering algorithms
such as shallow models
can only extract shallow features. Owing to the limited representation capacity of the employed shallow models
the algorithms may fail in handling realistic data with high-dimensional nonlinear structures. Moreover
most learning approaches treat feature extraction and clustering separately
train the feature extraction model well
and only use the clustering algorithm once in the feature representation of data to obtain clustering results.
Method
2
To solve these problems
the use of spectral information is maximized
and a new subspace clustering algorithm
that is
embedded deep neural network fuzzy c-means clustering (EDFCC)
is proposed in this study. The EDFCC algorithm can effectively extract the spectral information of hyperspectral images and be used for hyperspectral image clustering. The fuzzy c-means clustering algorithm is embedded into the deep autoencoder network
and the joint learning deep autoencoder network and fuzzy c-means clustering algorithm are used. Optimizing the two tasks jointly can substantially improve the performance of both. First
the feature extraction process of data is assumed to be an unknown transformation
which may be a nonlinear function. To preserve the local structure
the representation of each data point is learned by minimizing the reconstruction error
that is
the feature extraction process is completed by learning the deep autoencoder network. Data should be clustered in an effective manner to learn the representation of the potential features of data suitable for clustering. The fuzzy c-means clustering algorithm is used to constrain the feature extraction process and make the generated features suitable for clustering. The motivation for designing the EDFCC algorithm is to maintain the advantage of the joint optimization of the two tasks while using the capability of the deep autoencoder network to approximate any nonlinear function
gradually map the input data points to the potential nonlinear space
and adjust the clustering indicator matrix dynamically with the model training.
Result
2
Two hyperspectral data sets
namely
Indian Pines and Pavia University
are used to test the validity of the EDFCC algorithm. The quantitative evaluation metrics include accuracy and normalized mutual information. The Indian Pines dataset contains data acquired by the airborne visible infrared imaging spectrometer with a spectral range of 0.41~2.45 m
spatial resolution of 25 m
spectral resolution of 10 nm
and a total of 145×145 sample points. A total of 220 original bands are available
but the water vapor absorption band and bands with a low signal-to-noise ratio are excluded. The remaining 200 bands are used as research objects. The Indian Pines dataset has 16 different feature categories. Indian Pines shows that the overall clustering accuracy of the EDFCC algorithm is 42.95%
which is 3% higher than that of the best LRSC algorithm. The Pavia University dataset was obtained by the airborne reflector optical spectral imager in Germany. Its spectral range is 0.43~0.86 m
and its spatial resolution is 1.3 m. The dataset contains 610×340 sample points. A total of 115 original bands exist
but the noise bands are removed. The 103 remaining bands are used as research objects. The Pavia University dataset has nine types of ground objects. The dataset shows that the overall clustering accuracy of the EDFCC algorithm is 60.59%
which is 4% higher than that of the best LRSC algorithm. When compared with the AEKM algorithm for deep clustering
the AEKM algorithm is improved by 2% and 3%.
Conclusion
2
The EDFCC algorithm is proposed in this study. The algorithm is first applied in hyperspectral image clustering as a joint learning framework. The indicator matrix can be dynamically adjusted because of joint learning
and no additional training process is required
which greatly improves the training efficiency. Experimentalresults show that the EDFCC algorithm can extract many effective deep features from the high-dimensional spectral information of hyperspectral images and improve clustering accuracy.
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