WO2022001159A1 - 无监督高光谱图像隐低秩投影学习特征提取方法 - Google Patents

无监督高光谱图像隐低秩投影学习特征提取方法 Download PDF

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WO2022001159A1
WO2022001159A1 PCT/CN2021/079597 CN2021079597W WO2022001159A1 WO 2022001159 A1 WO2022001159 A1 WO 2022001159A1 CN 2021079597 W CN2021079597 W CN 2021079597W WO 2022001159 A1 WO2022001159 A1 WO 2022001159A1
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low
matrix
feature extraction
rank
samples
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潘磊
黄细凤
廖泓舟
李春豹
陈伟晴
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西南电子技术研究所（中国电子科技集团公司第十研究所）
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
    • G06V10/77—Processing image or video features in feature spaces; using data integration or data reduction, e.g. principal component analysis [PCA] or independent component analysis [ICA] or self-organising maps [SOM]; Blind source separation
    • G06V10/776—Validation; Performance evaluation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2411—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on the proximity to a decision surface, e.g. support vector machines
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/22—Matching criteria, e.g. proximity measures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
    • G06V10/764—Arrangements for image or video recognition or understanding using pattern recognition or machine learning using classification, e.g. of video objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
    • G06V10/77—Processing image or video features in feature spaces; using data integration or data reduction, e.g. principal component analysis [PCA] or independent component analysis [ICA] or self-organising maps [SOM]; Blind source separation
    • G06V10/7715—Feature extraction, e.g. by transforming the feature space, e.g. multi-dimensional scaling [MDS]; Mappings, e.g. subspace methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/70—Arrangements for image or video recognition or understanding using pattern recognition or machine learning
    • G06V10/77—Processing image or video features in feature spaces; using data integration or data reduction, e.g. principal component analysis [PCA] or independent component analysis [ICA] or self-organising maps [SOM]; Blind source separation
    • G06V10/774—Generating sets of training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V20/00—Scenes; Scene-specific elements
    • G06V20/10—Terrestrial scenes

Definitions

  • the invention relates to remote sensing image processing technology in many fields such as aviation, aerospace, agricultural management, disaster forecasting, environmental monitoring, resource exploration, land planning and utilization, disaster dynamic monitoring, crop yield estimation, weather forecasting, etc., and specifically relates to unsupervised hyperspectral image concealment. Low-rank projection learning feature extraction method.
  • Hyperspectral images are characterized by the integration of atlas, and are a new remote sensing technology developed at home and abroad recently. Compared with multispectral images, hyperspectral images have more spectral bands, higher spectral resolution, and narrower band widths, which can distinguish and identify ground objects with higher reliability. However, these advantages of hyperspectral images come at the cost of their higher data dimension and larger data volume, and the correlation between the bands of hyperspectral images is high, resulting in information redundancy. Image processing such as target recognition and classification does not necessarily require all the bands, so it is necessary to reduce the data dimension of hyperspectral images. Feature extraction of remote sensing images is a key technology for automatic recognition of remote sensing images.
  • Remote sensing is a comprehensive method that is far away from the target, without direct contact with the target object, obtains its characteristic information through a sensor mounted on a certain platform, and then extracts, determines, processes and applies the obtained information.
  • Technology It is the only means so far that can provide dynamic observation data on a global scale.
  • Hyperspectral images are obtained via imaging spectrometers.
  • Hyperspectral remote sensing is a three-dimensional remote sensing technology formed by adding one-dimensional spectral remote sensing on the basis of traditional two-dimensional space remote sensing. Spatial information and spectral information, whose spatial characteristics describe the spatial characteristics of the corresponding ground objects, and whose spectral characteristics describe the spectral information of each pixel of the corresponding ground objects.
  • Hyperspectral images are inevitably polluted by various noises, such as Gaussian noise, impulse noise, stripes, etc., during the acquisition and transmission process, which seriously restricts the further application of hyperspectral images.
  • various noises such as Gaussian noise, impulse noise, stripes, etc.
  • Hyperspectral remote sensing technology refers to the use of airborne or spaceborne hyperspectral imaging spectrometers to obtain dozens of hundreds of continuous spectral bands containing feature information of ground objects to form hyperspectral images, and to analyze and process the obtained hyperspectral images to achieve A technique for detailed cognition of features.
  • a hyperspectral image consists of one spectral dimension and two spatial dimensions. Each pixel in the image represents an object in a certain area of the ground.
  • each pixel corresponds to a continuous spectral curve.
  • the richness of information is the advantage of hyperspectral images, but poor processing may also become its disadvantage.
  • the huge amount of data with dozens or hundreds of spectral bands will bring a lot of inconvenience to the later processing, especially in the aspect of calculation and storage in the data processing process.
  • due to spectral similarity many of the hundreds of consecutive narrow spectral bands are similar, so there is data redundancy to a certain extent. Redundant data will not bring us any help.
  • hyperspectral data will become "informative and knowledge-poor".
  • Hyperspectral images have rich spectral information, and also have good spatial structure characteristics, that is, the so-called “atlas integration" feature. Therefore, hyperspectral images are widely used in many fields such as agricultural management, environmental monitoring, and military reconnaissance. However, hyperspectral images also have problems such as high spectral dimension, large information redundancy, and few labeled training samples, which seriously restrict the further promotion of hyperspectral image processing technology. Research shows that feature extraction technology is an effective means to solve the problem of high data dimension and large information redundancy, and feature extraction technology is also a research hotspot in the direction of hyperspectral image processing technology. In the process of classification and recognition of remote sensing images, various image feature extraction techniques play an important role.
  • Remote sensing image feature extraction mainly includes three parts: spectral feature extraction, texture feature extraction and shape feature extraction.
  • Spectral information reflects the magnitude of electromagnetic wave energy reflected by ground objects, and is the basic basis for visual interpretation of images. In the current remote sensing image processing research, spectral features are mostly used.
  • Feature extraction technology converts high-dimensional data into low-dimensional features through mapping or transformation, which reduces the data dimension while retaining valuable information in the data, which is convenient for subsequent classification or other processing. So far, researchers have proposed a large number of feature extraction methods, and continue to combine new theories and new technologies to expand the scope of feature extraction methods. Generally, feature extraction methods can be classified into unsupervised, semi-supervised and supervised algorithms according to the presence or absence of labeled training samples. Principal component analysis is one of the most classic unsupervised feature extraction methods, which finds a linear projection matrix by maximizing variance, preserving the most important feature information in the data. After that, researchers have successively proposed methods such as minimum noise separation transformation and independent principal component analysis.
  • sparse graph embedding model constructed in an unsupervised manner defines the adjacent pixels of a pixel by the sparse reconstruction coefficient of a pixel, and then obtains a sparse graph, and then uses a locality preserving projection technique to obtain a low-dimensional projection matrix.
  • sparse graph embedding combined with sample label information, some researchers proposed a sparse graph discriminant analysis model, which was extended to a block sparse graph discriminant analysis model by means of intra-class composition.
  • low-rank representation is mainly used for subspace segmentation, that is, given a set of data, this set of data comes from certain subspaces, and low-rank representation can achieve the data from these subspaces. Clustering, you can find which data comes from which subspace.
  • subspace segmentation such as those based on probabilistic models.
  • Kumar et al. proposed to reduce the feature dimension of hyperspectral images by fusing adjacent hyperspectral bands. The method first segments hyperspectral imagery into multiple band subsets according to specific criteria. Finally, the dimensionality-reduced hyperspectral data is obtained by calculating the fused bands of each band subset by weighted summation.
  • This method can effectively preserve the physical properties of the data while reducing the dimensionality of the hyperspectral data.
  • band segmentation usually involves complex clustering and optimization procedures, thus increasing the computational complexity of dimensionality reduction methods.
  • hyperspectral data is inevitably affected by factors such as lighting conditions, atmospheric conditions, and sensor accuracy during the imaging process, there are different degrees of noise in the data. These noises seriously affect the performance of feature extraction.
  • the new problem is that there are too few labeled data, and data labeling requires a lot of manpower and material resources. . In this case, the unsupervised feature extraction method has a broader application prospect.
  • At least some embodiments of the present invention provide an unsupervised hyperspectral feature extraction method capable of realizing fast and high robustness, so as to at least partially solve the problems in the related art for hyperspectral data with high spectral dimensions, large information redundancy, and labels. Problems such as the small number of samples.
  • an unsupervised hyperspectral image latent low-rank projection learning feature extraction method including the following steps:
  • the input hyperspectral image data without sample label information is divided into training set and test set proportionally; a robust weight function is designed to calculate the spectral similarity between the training set samples, and the spectral constraint matrix is constructed according to the training set , while constructing graph regularization constraints according to the local preservation projection rules; then approximately decompose the row representation coefficients of the latent low-rank representation model into the product of two matrices of the same scale, and use one of the matrices as the projection matrix, combined with spectral constraints
  • the matrix and graph regularization constraints are used to construct an implicit low-rank projection learning model; the alternative iterative multiplier method is used to optimize the solution of the implicit low-rank projection learning model, a low-dimensional projection matrix is obtained, and the low-dimensional representation features of the test set are extracted; the output of the support vector machine classifier is used.
  • the low-dimensional features of the training set are used as training samples of support vector machines, and the low-dimensional features of the test set are classified to evaluate the
  • a spectral constraint matrix is constructed according to the training set, and a graph regularization constraint is constructed according to the local preservation projection rule; a latent low-rank representation model is introduced, and interference such as noise can be effectively overcome through the representation learning of row space and column space
  • the row representation coefficients in the model are decomposed into the product of two matrices of the same scale, and one of the matrices is used as the projection matrix.
  • the new model can achieve low-dimensional features of any dimension. extract.
  • the embodiment of the present invention designs and sets a robust weight function, a spectral constraint and a graph regularization constraint, and the spectral constraint mines the local structure of the data from the original data space.
  • the graph regularization constraint mines the local structure of the data from the low-dimensional feature space; the combination of the two with the implicit low-rank representation model can better mine the eigenstructure of hyperspectral data and improve the separability of low-dimensional features.
  • the row representation coefficients of the implicit low-rank representation model are approximately decomposed into the product of two matrices of the same scale, and one of the matrices is used as the projection matrix, and is constructed by combining the spectral constraint matrix and the graph regularization constraint Hidden low-rank projection learning model, an integrated model of representation learning and projection learning is designed, and low-dimensional projection can be obtained by optimizing the solution of the model, which effectively avoids the complex process of the graph embedding model, and the interaction between representation learning and projection learning can be Significantly improves the discriminativeness of low-dimensional projections.
  • the embodiment of the present invention adopts the alternate iterative multiplier method to optimize and solve the hidden low-rank projection learning model, obtains the low-dimensional projection matrix, extracts the low-dimensional representation features of the test set, uses the support vector machine classifier to output the categories of all the test set samples, and divides the training set
  • the low-dimensional features of the SVM are used as training samples of the support vector machine, and the low-dimensional features of the test set are classified, and the performance of feature extraction is evaluated by the quality of the classification results.
  • Simulation experiments on public hyperspectral datasets show that the feature extraction performance of the proposed method is significantly better than other unsupervised feature extraction methods, and the extracted low-dimensional features can obtain higher classification accuracy of hyperspectral images.
  • the embodiments of the present invention are suitable for feature extraction of hyperspectral images.
  • the core of the embodiment of the present invention is an integrated model of latent low-rank representation learning and projection learning combining spectral constraints and graph regularization constraints, so as to realize accurate mining of data eigenstructures, thereby improving the discriminability of low-dimensional features. As long as it is related to image feature extraction or dimensionality reduction, the embodiments of the present invention are all effective.
  • FIG. 1 is a flowchart of feature extraction of hyperspectral images by unsupervised latent low-rank projection learning according to one embodiment of the present invention.
  • FIG. 2 is a flow chart of solving based on the implicit low-rank projection learning model of FIG. 1 according to an embodiment of the present invention.
  • the input hyperspectral image data without sample label information is divided into a training set and a test set in proportion; a robust weight function is designed to calculate the spectral similarity between the training set samples , construct the spectral constraint matrix according to the training set, and construct the graph regularization constraint according to the local preservation projection rule; then approximately decompose the row representation coefficient of the implicit low-rank representation model into the product of two matrices of the same scale, and use one of the The matrix is used as the projection matrix, and the implicit low-rank projection learning model is constructed by combining the spectral constraint matrix and the graph regularization constraint; the alternate iterative multiplier method is used to optimize the solution of the implicit low-rank projection learning model, the low-dimensional projection matrix is obtained, and the low-dimensional representation of the test set is extracted.
  • Step 1 in an optional embodiment, divide the input hyperspectral image data into a training set and a test set.
  • Step 2 constructing a spectrally constrained configuration matrix. According to the training set, construct the spectral constraint matrix C and design the robust weight function of the ijth element C ij in the spectral constraint matrix C
  • x i represents the ith training sample
  • x j represents the jth training sample
  • dist( xi , x j ) represents the Euclidean distance between the training sample xi and the training sample x j
  • Step 3 graph regularization constraint construction. Construct the graph regularization constraint expression according to the local preserving projection rule
  • min represents the minimum value of the function
  • P represents the projection matrix
  • i and j represent the element labels
  • ⁇ represents the sum of the elements
  • x i represents the i-th training sample
  • x j represents the j-th training sample
  • T represents the matrix transpose
  • W ij represents the ij-th element of the graph weight matrix W
  • D is the diagonal matrix
  • the diagonal elements are the sum of each row or column of the graph weight matrix
  • L represents the Laplacian matrix
  • Tr( ) represents the trace of the matrix.
  • the graph weight matrix W is calculated by the following formula:
  • x i represents the ith training sample
  • x j represents the jth training sample
  • ⁇ represents belonging
  • N k (x j ) represents the k nearest neighbor samples of the jth training sample x j.
  • Step 4 the step 4 further includes the following steps:
  • min represents the minimum value of the function
  • X represents the training sample set
  • Z represents the coefficient in the column space
  • L represents the coefficient in the row space
  • E represents the noise
  • * represents the matrix kernel norm
  • 2,1 represents the matrix 21 norm
  • ⁇ represents the regularization parameter
  • st represents the constraint.
  • P and Q represent the decomposition matrix
  • ⁇ represents the regularization parameter
  • F is the sign of the F-norm
  • 1 represents the matrix 1-norm
  • T represents the matrix transpose
  • I represents the identity matrix.
  • ⁇ represents the dot product of matrix elements
  • ⁇ represents the regularization parameter
  • the alternate direction multiplier method is used to solve the implicit low-rank projection learning model, and auxiliary variables A and B are introduced to obtain the following model to be optimized:
  • l ( ⁇ ) represents the Lagrangian function
  • ⁇ > represents the matrix inner product
  • Y 1 , Y 2 , and Y 3 represent the Lagrangian multipliers
  • ⁇ represents the penalty factor
  • the rule of the alternating direction multiplier method is to update only one variable at a time and keep the other variables unchanged.
  • the variable values of the t+1th iteration are as follows:
  • t represents the t-th iteration
  • 1 represents an all-one matrix
  • S 2 XLX T , Indicates that the threshold is Soft threshold operation.
  • the alternate direction multiplier method to optimize and solve the hidden low-rank projection learning model, and judge whether the convergence condition is reached: if no, continue to perform the alternate direction multiplier method optimization solution and iterative operation; if yes, reach the maximum number of iterations or before and after the variable If the error of the results of the two iterations is less than a certain threshold, the projection matrix P obtained in the last iteration is the optimal low-dimensional projection matrix, and the iteration is terminated.
  • Step 5 Calculate the low-dimensional features of the training set and the test set. Use the projection matrix P obtained in step 4 to perform feature extraction operations on training set X and test set Y respectively: low-dimensional features of training set X Low-dimensional features of test set Y
  • Step 6 use the support vector machine classifier to output the categories of all test set samples.
  • the low-dimensional features of the training set X As the training samples of the support vector machine, the low-dimensional features of the test set Y Perform classification to evaluate the performance of the feature extraction algorithm with the class classification accuracy of the final test set samples.

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Abstract

本发明公开的无监督高光谱图像隐低秩投影学习特征提取方法，旨在提供一种能够实现快速、高鲁棒性的无监督高光谱特征提取方法。本发明通过下述技术方案予以实现：首先将输入的高光谱图像数据按比例划分成训练集和测试集；设计鲁棒性权重函数，计算训练集样本两两之间的光谱相似度，根据训练集构建谱约束矩阵和图正则化约束；然后将隐低秩表示模型的行表示系数近似分解，结合谱约束矩阵和图正则化约束构建隐低秩投影学习模型，采用交替迭代乘子法优化求解隐低秩投影学习模型，获取低维投影矩阵，输出所有测试集样本的类别，将训练集的低维特征作为支持向量机的训练样本，对测试集的低维特征进行分类，以分类结果的质量评估特征提取的性能。

Description

无监督高光谱图像隐低秩投影学习特征提取方法 技术领域
本发明涉及航空、航天、农业管理、灾害预报、环境监测、资源勘探、土地规划与利用、灾害动态监测、农作物估产、气象预报等很多领域的遥感图像处理技术，具体涉及无监督高光谱图像隐低秩投影学习特征提取方法。
背景技术
高光谱图像具有图谱合一的特点，是近期国内外发展起来的新的遥感技术。与多光谱图像相比，高光谱图像光谱波段数目多、光谱分辨率高、波段宽度窄，能够以较高的可信度区分和辨识地物目标。但是，高光谱图像的这些优点是以其较高的数据维数和较大的数据量为代价的，且高光谱图像波段间相关性较高，造成了信息的冗余。目标识别和分类等图像处理并不一定需要全部的波段来进行，因此对高光谱图像进行数据降维是十分必要的。遥感图像的特征提取是进行遥感图像自动识别的关键技术。遥感是一种远离目标，在不与目标对象直接接触的情况下，通过某种平台上装载的传感器获取其特征信息，然后对所获取的信息进行提取、判定、加工处理及应用分析的综合性技术。它是目前为止能够提供全球范围的动态观测数据的唯一手段。高光谱图像经由成像光谱仪获得。高光谱遥感是在传统二维空间遥感的基础上增加了一维光谱遥感后形成的一种三维遥感技术，高光谱图像数据呈现出三维立方体的形式，立方体式数据很好的融合了地物的空间信息和光谱信息，其空间特性描述了对应地物的空间特征，其光谱特性描述了相应地物每个像元的光谱信息。高光谱图像在采集与传输过程中不可避免地会受到各种噪声，例如高斯噪声、脉冲噪声、条纹等的污染，严重制约了高光谱图像的进一步应用。同时，高光谱图像维数的急剧增长，导致了“维数灾难”。高光谱遥感技术是指利用机载或星载的高光谱成像光谱仪获取包含地物特征信息的几十数百个连续的光谱波段堆叠组成高光谱图像，对获得的高光谱图像进行分析处理从而实现对地物详细认知的一种技术。高光谱图像由一个光谱维和两个空间维构成，图像中每一个像素点代表地面某区域的物体，空间分辨率不同，所表示的区域也不同，每个像素点对应着一条连续的光谱曲线。信息丰富是高光谱图像的优点但是处理不好也有可能成为其缺点。数十上百个光谱波段的超大数据量会给后期的处理带来很多的不便，在数据处理过程中的计算和存储方面尤 为凸显。就目前的硬件条件而言，要想直接处理如此大量的数据是比较难做到的，当然要是想做到也是可以的只不过成本会高很多。同时由于光谱相似性，在连续上百个窄光谱波段中有很多波段都是相似的，这样在一定程度上就存在数据的冗余现象，冗余的数据并不会给我们带来什么帮助反而会占用本就不多的存储空间，以及降低数据处理的效率。采集到的大量细节数据不无例外的会包括噪声，这样会使得原本纯净的数据受到污染而且还会对地物分类识别的精度造成不好的影响。如果不能很好地克服高光谱数据的缺点那么高光谱数据就会变得“信息丰富而知识匮乏”。
高光谱图像具有丰富的光谱信息，同时也具有良好的空间结构特征，即所谓的“图谱合一”特性，因此，高光谱图像在农业管理、环境监测、军事侦察等诸多领域得到广泛应用。然而，高光谱图像同时存在光谱维度高，信息冗余大、有标签训练样本少等问题，这些严重制约了高光谱图像处理技术的进一步推广。研究表明，特征提取技术是解决数据维度高、信息冗余大的有效手段，而且特征提取技术也是高光谱图像处理技术方向的研究热点。在遥感图像的分类识别过程中，图像的各种特征提取技术在其中扮演了重要角色。遥感图像特征提取主要包括三个部分:光谱特征提取、纹理特征提取以及形状特征提取。光谱信息反映了地物反射电磁波能量的大小，是图像目视判读的基本依据。在目前的遥感图像处理研究中，多利用光谱特征。
特征提取技术通过映射或变换将高维数据变成低维特征，在降低数据维度的同时保留了数据中有价值的信息，便于后续的分类或其它处理。迄今为止，研究学者已提出了大量特征提取方法，并不断结合新的理论、新的技术来拓展特征提取方法的范围。通常，根据有无带标签的训练样本，特征提取方法可以分为无监督、半监督和有监督三种算法。主成分分析是一种最经典的无监督特征提取方法，其通过最大化方差找到一个线性投影矩阵，保留数据中最重要的特征信息。之后，研究学者又相继提出了最小噪声分离变换、独立主成分分析等方法。隐式低秩表示(LatLRR)作为经典的无监督特征提取算法已应用于模式识别领域。然而该算法得到的特征维数无法降低,且由于算法分别学习2个低秩矩阵,因此无法保证整体最优；另外,算法忽略了样本在学习过程中存在的残差。无监督鉴别投影(Unsupervised Discriminant Projection，UDP)准则函数可以通过非局部散度与局部散度之比的最大化来描述的。用UDP算法投影后，尽管在最大程度上实现了相互邻近的样本的集中和相互远离的样本之间的分离，但由于特征分量之间信息的高度冗余，所以，所获得的真正有效的鉴别信息并不多。无法消除模式样本各特征分量之间的相关性，从而使得错误率在某些时候随着鉴别矢量个数的增加收敛速度变得十分缓慢。然而，这些无监督的方法在没有使用样本标签信息的情况下，特征 提取的性能并不能满足实际需求。为此，有学者提出了线性判别分析方法，由数据的均值和方差入手，设计了类内散度矩阵和类间散度矩阵，并使类内散度最小，类间散度最大来增强同类数据的聚集性和不同类数据的可分性。但上述特征提取方法均是以统计学理论为基础，优点是模型简单、易于理解、便于求解，缺点是忽略了数据的空间结构，缺乏对数据的有力表征。这一类方法属于传统特征提取方法的范畴。
随着稀疏表示在人脸识别上的成功应用，以稀疏表示为基础的特征提取方法不断涌现。例如，以无监督方式构建的稀疏图嵌入模型，通过一个像素的稀疏重构系数来定义像素的邻接像素，进而得到稀疏图，然后利用局部保持投影技术得到低维投影矩阵。在稀疏图嵌入的基础上，结合样本标签信息，有学者提出了稀疏图判别分析模型，并以类内构图的方式扩展为块稀疏图判别分析模型。随后，又衍生出了加权稀疏图判别分析、拉普拉斯正则化协作图、稀疏图学习等方法。然而，稀疏图仅能挖掘高光谱数据的局部结构信息，有学者认为全局结构信息更为重要，因此，以低秩表示为基础，提出了低秩图嵌入模型。该算法能够最大限度的保持原始数据在各个空间中的整体几何结构，可以有效地对受损的人脸图像进行恢复。然而现有的低秩表示算法对训练样本中含噪的图像去噪恢复的稳定性不好，导致识别率较低。低秩表示模型是一个无约束的算法，具有一定的局限性，对于稀疏矩阵的稀疏性有特别的要求，去噪效果不稳定。在满足某些条件下，低秩算法的一个特性就是来自同一个子空间数据之间的联系可以通过低秩表示系数来得到准确的揭示，并用此特性进行数据子空间的分割。但是，该算法在原始数据的整体几何结构得到保持的同时，数据的局部几何结构不能得到保持，对于局部噪声很敏感，去噪恢复的效果不好。随后，结合稀疏图和低秩图，学者提出了稀疏低秩图判别分析模型，同时挖掘高光谱数据的局部结构和全局结构，特征提取性能的改善十分明显。
目前低秩表达(LatLLR)主要用在子空间分割上，也就是给定一组数据，这组数据是从某几个子空间上来的，通过低秩表达可以达到对来自这几个子空间的数据进行聚类，可以找到哪些数据时来自具体的哪个子空间。首先子空间分割有很多种方法比如基于概率模型的。考虑到相邻高光谱波段的强相关性，Kumar等人提出通过融合相邻高光谱波段的方法降低高光谱影像的特征维数。该方法首先根据特定的准则将高光谱影像分割成多个波段子集。最后通过加权求和计算每个波段子集的融合波段获得降维后的高光谱数据。该方法在降维高光谱数据的同时，能够有效的保留数据的物理特性。然而，波段分割通常涉及复杂的聚类和优化过程，因此增加了降维方法的计算复杂度。由于高光谱数据在成像过程中不可避免地受到光照条件、大气条件、传感器精度等因素的影响，因而数据中存在不同程度的噪声。这些噪声 严重影响了特征提取的性能。从另一个方面来说，随着我国高分专项地不断推进，已获取了大量有价值的高光谱遥感数据，然而新的问题是有标签的数据太少，而且数据标注需要花费大量的人力物力。这种情况下，无监督特征提取方法有着更为广阔的应用前景。
发明内容
本发明至少部分实施例提供了一种能够实现快速、高鲁棒性的无监督高光谱特征提取方法，以至少部分地解决相关技术中针对高光谱数据光谱维度高、信息冗余大、有标签样本少等问题。
在本发明其中一实施例中，提供了一种无监督高光谱图像隐低秩投影学习特征提取方法，包括如下步骤：
首先将输入的无样本标签信息的高光谱图像数据按比例划分成训练集和测试集；设计鲁棒性权重函数，计算训练集样本两两之间的光谱相似度，根据训练集构建谱约束矩阵，同时根据局部保持投影规则构建图正则化约束；然后将隐低秩表示模型的行表示系数近似分解，分解成相同尺度的两个矩阵的乘积，并以其中一个矩阵作为投影矩阵，结合谱约束矩阵和图正则化约束构建隐低秩投影学习模型；采用交替迭代乘子法优化求解隐低秩投影学习模型，获取低维投影矩阵，提取测试集低维表示特征；采用支持向量机分类器输出所有测试集样本的类别，将训练集的低维特征作为支持向量机的训练样本，对测试集的低维特征进行分类，以分类结果的质量评估特征提取的性能。
本发明实施例相比于现有技术的技术效果在于：
(1)本发明实施例根据训练集构建谱约束矩阵，同时根据局部保持投影规则构建图正则化约束；引入隐低秩表示模型，通过行空间和列空间的表示学习，能够有效克服噪声等干扰因素的不利影响；同时，将模型中的行表示系数分解成相同尺度的两个矩阵的乘积，并以其中一个矩阵作为投影矩阵，与原模型相比，新模型可以实现任意维度低维特征的提取。
(2)本发明实施例为弥补隐低秩表示仅能挖掘数据全局结构的不足，设计设了鲁棒性权重函数，谱约束和图正则化约束，谱约束从原始数据空间挖掘数据的局部结构，图正则化约束从低维特征空间挖掘数据的局部结构；二者与隐低秩表示模型的结合能够更好地挖掘高光谱数据本征结构，提升低维特征的可分性。
(3)本发明实施例将隐低秩表示模型的行表示系数近似分解，分解成相同尺度的两个矩阵的乘积，以其中一个矩阵作为投影矩阵，并结合谱约束矩阵和图正则化约束构建隐低秩投影学习模型，设计了表示学习与投影学习一体化模型，通过模型的优化求解即可得到低维投影，有效避免了图嵌入模型的复杂过程，而且表示学习与投影学习相互作用，能够明显改 善低维投影的判别性。
本发明实施例采用交替迭代乘子法优化求解隐低秩投影学习模型，获取低维投影矩阵，提取测试集低维表示特征，采用支持向量机分类器输出所有测试集样本的类别，将训练集的低维特征作为支持向量机的训练样本，对测试集的低维特征进行分类，以分类结果的质量评估特征提取的性能。在公开高光谱数据集上的仿真实验表明所提出方法的特征提取性能明显优于其它的无监督特征提取方法，提取的低维特征能够获得更高的高光谱图像分类精度。
本发明实施例适用于高光谱图像特征提取。本发明实施例的核心是结合谱约束和图正则化约束的隐低秩表示学习与投影学习一体化模型，实现数据本征结构的准确挖掘，进而提升低维特征的判别性。只要是有关图像特征提取或降维，本发明实施例都是有效的。
附图说明
图1是根据本发明其中一实施例的无监督的隐低秩投影学习高光谱图像特征提取流程图。
图2是根据本发明其中一实施例的基于图1隐低秩投影学习模型的求解流程图。
为使本发明的目的、技术方案和优点更加清楚明白，下面结合附图和具体实施方式对本发明做更进一步的具体说明，但本发明的应用范围不限于此：以下结合具体实施例，并参照附图，对本发明进一步详细说明。
具体实施方式
参阅图1。根据本发明其中一实施例，首先将输入的无样本标签信息的高光谱图像数据按比例划分成训练集和测试集；设计鲁棒性权重函数，计算训练集样本两两之间的光谱相似度，根据训练集构建谱约束矩阵，同时根据局部保持投影规则构建图正则化约束；然后将隐低秩表示模型的行表示系数近似分解，分解成相同尺度的两个矩阵的乘积，并以其中一个矩阵作为投影矩阵，并结合谱约束矩阵和图正则化约束构建隐低秩投影学习模型；采用交替迭代乘子法优化求解隐低秩投影学习模型，获取低维投影矩阵，提取测试集低维表示特征，采用支持向量机分类器输出所有测试集样本的类别，将训练集的低维特征作为支持向量机的训练样本，以分类结果的质量评估特征提取的性能。
具体包括以下步骤：
步骤1，在可选实施例中，将输入的高光谱图像数据划分成训练集和测试集。根据设定的比例，将输入具有(N+M)个样本的高光谱数据，划分成包含N个样本的训练集和包含M个样本的测试集X＝[x 1,x 2,…,x N]∈R d×N和包含M个样本的测试集Y＝[y 1,y 2,…,y M]∈R d×M， 其中，∈表示属于，R表示实数空间，d表示样本的光谱维度，输入高光谱数据的样本总数为(N+M)个。
步骤2，谱约束构矩阵构建。根据训练集，构建谱约束矩阵C和设计谱约束矩阵C中的第ij个元素C ij的鲁棒性权重函数
Figure PCTCN2021079597-appb-000001
式中，x i表示第i个训练样本，x j表示第j个训练样本，dist(x i,x j)表示训练样本x i和训练样本x j之间的欧氏距离，
Figure PCTCN2021079597-appb-000002
表示任意元素，
Figure PCTCN2021079597-appb-000003
表示对任意标号为i的样本x i与样本x j之间距离的最大值。
步骤3，图正则化约束构建。根据局部保持投影规则，构建图正则化约束表达式
Figure PCTCN2021079597-appb-000004
式中，min表示函数最小值，P表示投影矩阵，i和j表示元素标号，∑表示元素之和，
Figure PCTCN2021079597-appb-000005
表示2范数的平方，x i表示第i个训练样本，x j表示第j个训练样本，T表示矩阵转置，W ij表示图权重矩阵W的第ij个元素，D是对角阵，对角元素是图权重矩阵的每一行或每一列之和，L表示拉普拉斯矩阵，Tr(·)表示矩阵的迹。
图权重矩阵W由下式计算得到：
Figure PCTCN2021079597-appb-000006
式中，x i表示第i个训练样本，x j表示第j个训练样本，∈表示属于，N k(x j)表示第第j个训练样本x j的k个最近邻样本。
步骤4，所述步骤4进一步包括以下步骤：
隐低秩表示模型可以表示为：
Figure PCTCN2021079597-appb-000007
s.t.X＝XZ+LX+E
式中，min表示函数最小值，X表示训练样本集，Z表示列空间表示系数，L表示行空间表示系数，E表示噪声，||·|| *表示矩阵核范数，||·|| 2,1表示矩阵21范数，λ表示正则化参数，s.t.表示约束。
本实施例将行空间表示系数进行分解，以相同维度的两个矩阵的乘积表示，并经过相应变换，可以得到
Figure PCTCN2021079597-appb-000008
s.t.X＝XZ+QP TX+E,Q TQ＝I
式中，P和Q表示分解矩阵，β表示正则化参数，
Figure PCTCN2021079597-appb-000009
表示矩阵的F范数的平方，F是F范数的标志，||·|| 1表示矩阵1范数，T表示矩阵转置，I表示单位矩阵。进一步结合步骤2的谱约束矩阵和步骤3的图正则化约束，构建隐低秩投影学习模型，其表达式如下：
Figure PCTCN2021079597-appb-000010
s.t.X＝XZ+QP TX+E,Q TQ＝I
式中，⊙表示矩阵元素点乘，γ表示正则化参数。
如图2所示，求解隐低秩投影学习模型：
采用交替方向乘子法求解隐低秩投影学习模型，引入辅助变量A和变量B，得到如下待优化模型：
Figure PCTCN2021079597-appb-000011
s.t.X＝XZ+QP TX+E,Z＝A,P＝B,Q TQ＝I
上述优化模型的拉格朗日函数为：
Figure PCTCN2021079597-appb-000012
式中，l (·)表示拉格朗日函数，<·>表示矩阵内积，Y 1、Y 2、Y 3表示拉格朗日乘子，μ表示惩罚因子。
初始化拉格朗日函数中的矩阵：Z＝A＝0，P＝B＝0，E＝0，Y 1＝0，Y 2＝0，Y 3＝0。交替方向乘子法的规则是每次仅更新一个变量而保持其它变量不变，第t+1次迭代的变量值如下：
Figure PCTCN2021079597-appb-000013
Figure PCTCN2021079597-appb-000014
Figure PCTCN2021079597-appb-000015
Figure PCTCN2021079597-appb-000016
Figure PCTCN2021079597-appb-000017
式中，t表示第t次迭代，1表示全1矩阵，
Figure PCTCN2021079597-appb-000018
S 2＝XLX T，
Figure PCTCN2021079597-appb-000019
表示阈值为
Figure PCTCN2021079597-appb-000020
软阈值运算。
Q t+1可通过如下方法得到最优解：
Figure PCTCN2021079597-appb-000021
式中，
Figure PCTCN2021079597-appb-000022
表示矩阵的奇异值分解，Q t+1＝UV T。
采用交替方向乘子法优化求解隐低秩投影学习模型，判断是否达到收敛条件：如果为否，则继续执行交替方向乘子法优化求解和迭代运算；如果为是，达到最大迭代次数或变量前后两次迭代结果的误差小于某一设定阈值，获得最后一次迭代的投影矩阵P即为最优低维投影矩阵，则终止迭代。
步骤5，计算训练集和测试集的低维特征。利用步骤4求得的投影矩阵P对训练集X和测试集Y分别执行特征提取运算：训练集X的低维特征
Figure PCTCN2021079597-appb-000023
测试集Y的低维特征
Figure PCTCN2021079597-appb-000024
步骤6，采用支持向量机分类器输出所有测试集样本的类别。将训练集X的低维特征
Figure PCTCN2021079597-appb-000025
作为支持向量机的训练样本，对测试集Y的低维特征
Figure PCTCN2021079597-appb-000026
进行分类，以最终测试集样本的类别分类准确率评估特征提取算法的性能。
以上所述的具体实施例，对本发明的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施例而已，并不用于限制本发明，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种无监督高光谱图像隐低秩投影学习特征提取方法，包括：
    将输入的无样本标签信息的高光谱图像数据按比例划分成训练集和测试集；设计鲁棒性权重函数，计算训练集样本两两之间的光谱相似度，根据训练集构建谱约束矩阵，同时根据局部保持投影规则构建图正则化约束；将隐低秩表示模型的行表示系数近似分解，分解成相同尺度的两个矩阵的乘积，并以其中一个矩阵作为投影矩阵，结合谱约束矩阵和图正则化约束构建隐低秩投影学习模型；采用交替迭代乘子法优化求解隐低秩投影学习模型，获取低维投影矩阵，提取测试集低维表示特征；采用支持向量机分类器输出所有测试集样本的类别，将训练集的低维特征作为支持向量机的训练样本，对测试集的低维特征进行分类，以分类结果的质量评估特征提取的性能。
  2. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：根据设定的比例，将输入具有(N+M)个样本的高光谱数据，划分成包含N个样本的训练集、M个样本的测试集X＝[x 1,x 2,…,x N]∈R d×N和M个样本的测试集Y＝[y 1,y 2,…,y M]∈R d×M，其中，R表示实数空间，d表示样本的光谱维度。
  3. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：根据训练集，构建谱约束矩阵C和设计谱约束矩阵C中的第ij个元素C ij的鲁棒性权重函数：
    Figure PCTCN2021079597-appb-100001
    式中，x i表示第i个训练样本，x j表示第j个训练样本，dist(x i,x j)表示训练样本x i和训练样本x j之间的欧氏距离，
    Figure PCTCN2021079597-appb-100002
    表示任意元素，
    Figure PCTCN2021079597-appb-100003
    表示对任意标号为i的样本x i与样本x j之间距离的最大值。
  4. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：根据局部保持投影规则，
    构建图正则化约束表达式
    Figure PCTCN2021079597-appb-100004
    式中，min表示函数最小值，P表示投影矩阵，i和j表示元素标号，∑表示元素之和，
    Figure PCTCN2021079597-appb-100005
    表示2范数的平方，x i表示第i个训练样本，x j表示第j个训练样本，T表示矩阵转置，W ij表示图权重矩阵W的第ij个元素，D是对角阵，对角元素是图权重矩阵的每一行或每一列之和，Tr(·)表示矩阵的迹，L表示拉普拉斯矩阵。
  5. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：隐低秩表示模型表示为：
    Figure PCTCN2021079597-appb-100006
    s.t.X＝XZ+LX+E
    式中，min表示函数最小值，Z表示列空间表示系数，L表示行空间表示系数，E表示噪声，λ表示正则化参数，s.t.表示约束，X表示训练样本集，||·|| *表示矩阵核范数，||·|| 2,1表示矩阵21范数。
  6. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：将行空间表示系数进行分解，以相同维度的两个矩阵的乘积表示，并经过相应变换得到
    Figure PCTCN2021079597-appb-100007
    s.t.X＝XZ+QP TX+E,Q TQ＝I
    式中，P和Q表示分解矩阵，β表示正则化参数，F是F范数的标志，
    Figure PCTCN2021079597-appb-100008
    表示矩阵的F范数的平方，||·|| 1表示矩阵1范数，T表示矩阵转置，I表示单位矩阵。
  7. 如权利要求6所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：采用交替方向乘子法求解隐低秩投影学习模型，引入辅助变量A和变量B，得到如下待优化模型：
    Figure PCTCN2021079597-appb-100009
    s.t.X＝XZ+QP TX+E,Z＝A,P＝B,Q TQ＝I
    上述优化模型的拉格朗日函数为：
    Figure PCTCN2021079597-appb-100010
    式中，l (·)表示拉格朗日函数，<·>表示矩阵内积，Y 1、Y 2、Y 3表示拉格朗日乘子，μ表示惩罚因子。
  8. 如权利要求7所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：初始化拉格朗日函数中的矩阵：Z＝A＝0，P＝B＝0，E＝0，Y 1＝0，Y 2＝0，Y 3＝0，并且第t+1次迭代的变量值
    Figure PCTCN2021079597-appb-100011
    Figure PCTCN2021079597-appb-100012
    Figure PCTCN2021079597-appb-100013
    Figure PCTCN2021079597-appb-100014
    s.t.Q TQ＝I
    Figure PCTCN2021079597-appb-100015
    Figure PCTCN2021079597-appb-100016
    S 2＝XLX T，
    Figure PCTCN2021079597-appb-100017
    式中，t表示第t次迭代，1表示全1矩阵，λ表示正则化参数，
    Figure PCTCN2021079597-appb-100018
    表示阈值为
    Figure PCTCN2021079597-appb-100019
    软阈值运算。
  9. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中，采用交替方向乘子法优化求解隐低秩投影学习模型，判断是否达到收敛条件：如果为否，则继续执行交替方向乘子法优化求解和迭代运算；如果为是，达到最大迭代次数或变量前后两次迭代结果的误差小于某一设定阈值，获得最后一次迭代的投影矩阵P即为最优低维投影矩阵，则终止迭代。
  10. 如权利要求1所述的无监督高光谱图像隐低秩投影学习特征提取方法，其中：将训练集X的低维特征
    Figure PCTCN2021079597-appb-100020
    作为支持向量机的训练样本，对测试集Y的低维特征
    Figure PCTCN2021079597-appb-100021
    进行分类，以最终测试集样本的类别分类准确率评估特征提取算法的性能。
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