目的 高光谱图像具有高维度的光谱结构，而且邻近波段之间往往存在大量冗余信息，导致在随机样本选择策略和图像分类过程中出现选择波段算法复杂度较高和不适合小样本的现象。针对该问题，在集成学习算法的基础上，考虑不同波段在高光谱图像分类过程中的作用不同，提出一种融合累积变异比和超限学习机的高光谱图像分类算法。方法 定义波段的累积变异比函数来确定各波段在分类算法的贡献程度。基于累积变异比函数剔除低效波段，并结合空谱特征进行平均分组加权随机选择策略进行数据降维。为了进一步提高算法的泛化能力，对降维后提取的空谱特征进行多次样本重采样，训练得到多个超限学习机弱分类器，再将多个弱分类器的结果通过投票表决法得到最后的分类结果。结果 实验使用Indian Pines、Pavia University scene和Salinas这3种典型的高光谱图像作为实验标准数据集，采用支持向量机（support vector machine，SVM），超限学习机（extreme learning machine，ELM），基于二进制多层Gabor超限学习机（ELM with Gabor，GELM），核函数超限学习机（ELM with kernel，KELM），GELM-CK（GELM with composite kernel），KELM-CK（KELM with composite kernel）和SS-EELM（spatial-spectral and ensemble ELM）为标准检测算法验证本文算法的有效性，在样本比例较小的实验中，本文算法的总体分类精度在3种数据集中分别为98.0%、98.9%和97.9%，比其他算法平均分别高出9.6%和4.7%和4.1%。本文算法耗时在3种数据集中分别为15.2 s、60.4 s和169.4 s。在同类目标空谱特性差异较大的情况下，相比于分类精度较高的KELM-CK和SS-EELM算法减少了算法耗时，提高了总体分类精度；在同类目标空谱特性相近的情况下，相比于其他算法，样本数量的增加对本文算法的耗时影响较小。结论 本文算法通过波段的累积变异比函数优化了平均分组波段选择策略，针对各类地物目标分布较广泛并且同类目标空谱特性差异较大的高光谱数据集，能够有效提取特征光谱维度的差异性，确定参数较少，总体分类效果较好。

Objective Hyperspectral remote sensing has become a promising research field and is applied to various aspects. Hyperspectral image classification has become a key part of hyperspectral image processing. However, high-dimensional data structures bring new challenges for hyperspectral image classification. In particular, problems may occur in the feature extraction and classification process of a hyperspectral image dataset, e.g., the Hughes phenomenon, because of the unbalance between the high-dimensionality of the data and the limited number of training samples. To improve the accuracy of hyperspectral image classification, we propose a hyperspectral image classification algorithm based on ensemble extreme learning machine (ELM) with cumulative variation quotient, referred to as EELM with cumulative variation quotient (CVQ-EELM). Method In this study, the coefficient of variation is usually used as the index to show the data dispersion. Compared with the standard deviation, its main advantage is that it is not affected by the measurement scale. In particular, the coefficient of variation takes into account the influence of the average value of the data. The coefficient of variation is improved and applied to the dimensionality reduction of the HIS dataset. First, the cumulative variation functions of the intraclass and the interclass and the cumulative variation quotient are proposed. In actual operation, some pixels may contain multiple ground objects, while the gray values of the intraclass are quite different. Therefore, the cumulative variation function of the interclass and the cumulative variation function of the intraclass should be comprehensively considered to define the cumulative variation quotient function of bands. On the premise of the same band, the quotient of the norm of the interclass’ cumulative variation function and the sum of the norm of the intraclass’ cumulative variation function is called the cumulative variation quotient of the band. If the cumulative variation quotient of the band is far from 1, it means that the classification effect is better by using this band. If the cumulative variation quotient of band is close to 1, it means that the classification effect is poor by using this band. The inefficient bands are eliminated on the basis of the cumulative variation quotient function. Second, to provide the input information of hyperspectral bands for ELM and considering the strong correlation relationship between neighboring bands, average grouping is performed for the remaining effective bands after eliminating the inefficient bands. A certain number of bands are then selected by the weighted-random-selecting-based approach to reduce the dimension of the hyperspectral image dataset. Specifically, the hyperspectral bands are grouped on average and then the weights of each group are calculated based on the cumulative variation quotient. The bands of each group are selected randomly according to their weights. Finally, the spatial spectral features extracted after dimensionality reduction are sampled repeatedly to train several weak ELM classifiers. The results of several weak classifiers are majority voted to build a strong classifier. Result Three well-known HIS datasets (Indian Pines, Pavia University scene, and Salinas) are used to verify the effectiveness of the proposed method. SVM (support vector machine), ELM, GELM (ELM with Gabor), KELM (ELM with kernel), GELM-CK (GELM with composite kernel), KELM-CK (KELM with composite kernel), and SS-EELM (spatial-spectral and ensemble ELM) serve as the benchmark algorithms to measure the performance of the proposed CVQ-EELM. SVM, ELM, GELM, and KELM methods use only spectral features. Although SVM and KELM introduce the kernel function and increase the computational cost, SVM and KELM have better classification performance than ELM and GELM. GELM-CK, KELM-CK, SS-EELM, and CVQ-EELM methods incorporate the spatial information into the spectral information. The four spatial-spectral-feature-based methods show better classification performance than the four spectral-feature-based methods. Further analysis shows that the classification capacities of KELM-CK, SS-EELM, and CVQ-EELM are better than that of GELM-CK. However, KELM-CK, SS-EELM, and CVQ-EELM are amenable to more time cost than GELM-CK. For example, in three typical HIS datasets, KELM-CK method consumes classification times up to 15.8 s, 143 s, and 54.6 s, respectively. Although SS-EELM avoids referencing kernel functions, SS-EELM based on the ensemble extreme learning machines also has a large operation time, equal to 32.4 s, 85.5 s, and 171 s. The proposed CVQ-EELM only needs 15.2 s, 60.4 s, and 169.4 s to do so. The time-consuming characteristic of the SS-EELM and CVQ-EELM algorithms is related to the number of weak classifiers. Specifically, the greater the number of weak classifiers, the more time-consuming the algorithm will take. Compared with KELM-CK, the time-consuming growth rates of SS-EELM and CVQ-EELM are smaller with an increasing number of samples. When the spatial-spectral features of the same category are quite different, the proposed CVQ-EELM outperforms KELM-CK and SS-EELM. For example, in two typical HIS datasets (Indian Pines and Pavia University scene), overall accuracy (OA) of the proposed CVQ-EELM is 98.0% and 98.9%, respectively; OA of KELM-CK is 97.8% and 98.8%, respectively; and OA of SS-EELM is 97.2% and 98.6%, respectively. The computational cost of CVQ-EELM is also still lower than that of SS-EELM in two typical HIS datasets. According to the above experimental comparison, the computational cost of CVQ-EELM is similar to that of KELM-CK in the Indian Pines dataset. However, the classification accuracy of CVQ-EELM is higher than that of KELM-CK. Especially in the Pavia University dataset, the computational cost of CVQ-EELM is still low, approximately 2.5 times faster than KELM-CK. Moreover, the classification accuracy of CVQ-EELM is higher than KELM-CK. Therefore, the proposed CVQ-EELM has the best classification performance among all the classification algorithms. Conclusion The conclusion shows that the proposed algorithm optimizes the band selection strategy of average grouping through the cumulative variation quotient function. For hyperspectral data sets with a wide distribution of various objects and a large difference in spatial-spectral features of similar objects, the characteristics of spectral differences can be extracted effectively. The proposed CVQ-EELM has the advantages of few adjustable parameters and fast training speed. It also outperforms various state-of-the-art hyperspectral image classification counterparts in terms of classification accuracy.