基于快速层次交替最小二乘非负张量Tucker分解的干涉高光谱图像光谱信息压缩方法

提出一种基于快速层次交替最小二乘非负张量Tucker分解的高光谱图像光谱信息压缩算法。首先,将干涉高光谱图像光程差方向的三维信息采用三维光程差方向提升小波变换(3D OPT-LDWT)进行分解,将三维小波子带系数看作三阶非负张量,采用快速层次交替最小二乘非负张量Tucker分解(FHALS-NTD)算法对进行分解,得到核心张量和模式矩阵。对每个模式矩阵进行量化,对核心张量采用比特平面重要系数编码算法进行编码,得出最终的压缩码流。结果表明,此压缩算法可以稳定可靠地工作。与传统压缩算法比较,平均信噪比提高了1.23 dB。有效的提高了干涉高光谱图像压缩性能。     

多源光谱特征组合的COD光学检测方法研究

水样的化学需氧量大小直接决定水质的污染程度,传统的检测方法都是源于氧化还原反应,对水样会造成二次污染。为此,提出一种基于多源光谱特征组合的水质化学需氧量光学检测方法,以不同地点实际水样为被测对象,分别采集其紫外和近红外光谱曲线,进行预处理后,通过非负矩阵分解算法进行光谱数据的特征提取、数据特征归一化,然后将组合特征输入训练集样本,通过粒子群最小二乘支持向量机算法对验证集水样的化学需氧量进行定量预测。讨论了非负矩阵分解算法中基光谱数目对预测模型的影响。实验结果显示,紫外光谱的最佳基光谱数目为5,近红外光谱的最佳基光谱数目为2;预测模型的验证集平方相关系数为0.999 8,预测均方根误差为3.26 mg·L-1;分别与不同特征提取方法(主成分分析, 独立成分分析)、不同光谱法(紫外光谱法, 近红外光谱法)以及不同的组合方式(数据直接组合, 先组合数据再提取特征)加以比较,表明非负矩阵分解算法更适合光谱数据的特征提取,粒子群最小二乘支持向量机算法作为实际水样的定量模型校正方法可以得到良好的预测精度。     

Performance evaluation of nonnegative matrix factorization algorithms to estimate task-related neuronal activities from fMRI data

Nonnegative matrix factorization (NMF) is a blind source separation (BSS) algorithm which is based on the distinct constraint of nonnegativity of the estimated parameters as well as on the measured data. In this study, according to the potential feasibility of NMF for fMRI data, the four most popular NMF algorithms, corresponding to the following two types of (1) least-squares based update [i.e., alternating least-squares NMF (ALSNMF) and projected gradient descent NMF] and (2) multiplicative update (i.e., NMF based on Euclidean distance and NMF based on divergence cost function), were investigated by using them to estimate task-related neuronal activities. These algorithms were applied firstly to individual data from a single subject and, subsequently, to group data sets from multiple subjects. On the single-subject level, although all four algorithms detected task-related activation from simulated data, the performance of multiplicative update NMFs was significantly deteriorated when evaluated using visuomotor task fMRI data, for which they failed in estimating any task-related neuronal activities. In group-level analysis on both simulated data and real fMRI data, ALSNMF outperformed the other three algorithms. The presented findings may suggest that ALSNMF appears to be the most promising option among the tested NMF algorithms to extract task-related neuronal activities from fMRI data.     

稀疏正交联合约束多通道非负矩阵分解声信号分离算法

针对复杂环境下多通道声信号分离问题,提出稀疏正交联合约束多通道非负矩阵分解声信号分离方法。首先设计基于多通道扩展坂仓斋藤(Itakura-Saito,IS)散度的稀疏正交联合约束项构造代价函数,给出信号稀疏和信号正交约束辅助函数,实现代价函数最小化求解。然后通过迭代更新规则设计,得到稀疏正交优化的多通道非负矩阵分解基矩阵和系数矩阵,讨论了稀疏正交约束对基矩阵和系数矩阵稀疏性与连续性影响。最后基于多通道信号空间特性,进行了非负矩阵分解基聚类以获得多通道非负矩阵分解声信号的分离结果。双通道音频数据与四通道声学目标分离实验数据测试表明,对音频数据,所提算法在性能指标信号失真比(SDR)上提高了0.84 dB,对于直升机声源数据,所提算法在SDR上提高了4.53 dB。     

Semi-supervised clustering algorithm for community structure detection in complex networks

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.     

一种稀疏约束的图正则化非负矩阵光谱解混方法

由于受到高光谱遥感图像传感器平台的限制,图像的空间分辨率受到一定影响,这导致高光谱遥感图像的像元通常是多种地物的混合, 也叫做混合像元。混合像元的存在制约了高光谱遥感图像的准确分析和应用领域。采用高光谱解混技术可将混合像元分解为纯净的物质光谱（Endmember, 端元）和每种物质光谱所对应的混合比例（Abundance, 丰度）,为获取更多更精细的光谱提供了可能。这对高精度的地物分类识别、目标检测和定量遥感分析等研究领域具有重要的意义。因此,解混技术成为高光谱遥感图像领域的一个研究热点。基于线性光谱混合模型(linear spectral mixing model, LMM),提出了一种端元丰度联合稀疏约束的图正则化非负矩阵分解（endmember and abundance sparse constrained graph regularized nonnegative matrix factorization, EAGLNMF）算法。该算法通过研究基于非负矩阵分解(nonnegative matrix factorization, NMF)的方法,结合图正则化理论来考虑高光谱数据内部的几何结构,将端元光谱稀疏约束和丰度稀疏约束应用于其中,从而能够对高光谱数据的内部流形结构进行更为有效的表达。首先,构造了EAGLNMF算法的损失函数,采用VCA-FCLS方法进行初始化,然后,设定相关参数,包括图正则化权重矩阵参数、端元光谱稀疏约束因子和丰度矩阵稀疏约束因子,最后,通过推导得到了端元矩阵与丰度矩阵的迭代公式,并且设置了迭代停止条件。该方法不受图像中是否有纯像元的限制。实际上,在现行高光谱遥感传感器平台情况下,高光谱遥感图像中几乎不存在纯像元,因此,EAGLNMF方法为高光谱遥感图像的实际应用提供了一种思路。采用合成的高光谱数据,构造了4个实验来分析该方法的可行性和有效性,实验将该算法与VCA-FCLS,标准NMF及GLNMF等经典的解混算法进行比较,通过光谱角距离(spectral angle distance, SAD)和丰度角距离(abundance angle distance, AAD)这两个度量标准来进行比较。实验1是总体分析实验。在固定的信噪比和固定端元数目的情况下,用以上三种经典方法与EAGLNMF同时进行解混。实验2是SNR影响分析实验。在固定端元数目和不同信噪比的情况下,用这四种方法进行解混。实验3端元数目分析实验。在固定信噪比和不同端元数目的情况下,用四种方法进行解混,并且将结果进行对比。实验结果发现提出的EAGLNMF方法在提取端元精度和估计丰度精度上都更为准确。同时,实验4是稀疏因子分析实验。对端元稀疏约束和丰度稀疏约束之间的影响因子进行分析,实验结果表明引入的端元稀疏约束对于解混结果也具有较好的影响,并且端元稀疏约束和丰度稀疏约束之间的影响因子也对解混结果具有一定影响。最后,将该算法应用于AVIRIS所采集的真实高光谱图像数据,将其解混结果与美国地质勘探局光谱库中光谱进行匹配对比,其提取的平均端元精度相比于其他三种方法要稍好。     

特征提取算法在福美双表面增强拉曼光谱定量分析中的应用

表面增强拉曼散射(SERS)技术具有快速、指纹效应与极低的检测限等优点,被越来越多地应用到有害污染物、有毒物质、危险物质的检测与分析中。在SERS光谱的测量过程中,易受基底、仪器、宇宙射线与测量环境等因素影响,出现波动现象,对后续的分析与检测造成较大的干扰。基于农药福美双SERS光谱数据,尝试利用多种特征提取算法,如主成分分析(PCA)、离散余弦变换(DCT)、非负因式分解(NMF) ,对光谱的主分量进行提取,以减弱光谱数据波动对其后续的定量分析结果的影响。然后将提取后的分量分别结合线性回归算法——偏最小二乘法回归(PLSR),非线性回归算法——支持向量机回归(SVR)建立定量模型。最后,利用5-折交叉验证方法对比不同特征提取算法在不同类型的回归算法下的效果。通过实验验证可知,SVR对福美双溶液的分析精度要明显高于PLSR,这主要是由于SERS光谱强度与被分析物浓度之间为非线性关系。同时针对两种类型回归算法,特征提取算法都能明显地提升了分析结果,主要是由于其提取了源数据的主体信息,去除干扰信息。其中在线性回归中使用PCA效果最佳,在非线性拟合中使用NMF结果最佳,分析误差最好时可降低近3倍。最优回归模型(NMF+SVR)的交叉验证均方误差(RMSECV)为0.0455 μmol·L-1(10-6 mol·L-1),达到国家对福美双的检测标准,为农药快速检测提供一种新的方法。     

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks, solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.     

云计算环境下不可靠数据恢复方法研究

由于云计算环境下不可靠数据中包含有利用价值的信息,但直接使用可能会给计算机带来负担,所以需要对云计算环境下不可靠数据进行恢复。当前大多数方法对不可靠数据进行复写时,利用地址映射层分配新的写入地址,因此不可靠的数据在一段时间内仍存在于云存储中,在这样的系统上实现对其的保护,不需额外保存数据的更新信息。通过FLASH的带外区记录时间戳,在FTL的映射项中增加时间戳信息,在不跟踪映射表每次更新的情况下,达到数据快速恢复的目的。但这种方法对云存储系统性能产生不利影响。为此,提出一种基于张量Tucker阈值的云计算环境下不可靠数据恢复方法,首先利用云计算环境下节点自身的随机秘钥生成器产生随机会话密钥,并对不可靠数据HMAC报文鉴别码进行计算,从而实现保护和重构。在此基础上,将不可靠数据的阈值分解过程与奇异阈值方法相结合,从而得到Tncker阈值算子,实现动态的数据恢复,恢复过程中利用Tucker阈值算子与增广拉格朗日乘子方法相结合的方式选择n-秩相似张量,提出基于增广拉格朗日乘子方法的不可靠数据Tucker阈值恢复方法,完成云计算环境下不可靠数据恢复。实验证明,所提方法能够有效提高不可靠数据恢复的准确性,降低数据恢复的能耗和时间,具有较强的可行性,为该课题的应用研究提供理论依据。     

Hyperspectral image fusion based on sparse constraint NMF

The spatial resolution of hyperspectral image is often low due to the limitation of the imaging spectrometer. Fusing the original hyperspectral image with high-spatial-resolution panchromatic image is an effective approach to enhance the resolution of hyperspectral image. However, it is hard to preserve the spectral information at the same time of enhancing the resolution by the traditional fusion methods. In this paper, we proposed a fusion method based on the spectral unmixing model called sparse constraint nonnegative matrix factorization (SCNMF). This method has a superior balance of the spectral preservation and the spatial enhancement over some traditional fusion methods. In addition, the added sparse prior and NMF based unmixing model make the fusion more stable and physically reasonable. This method first decomposes the hyperspectral image into an endmember-matrix and an abundance-matrix, then sharpens the abundance-matrix with the panchromatic image, finally obtains the fused image by solving the spectral constraint optimization problem. The experiments on both synthetic and real data show the effectiveness of the proposed method.     

基于NMF-PLS对含水量影响下土壤重金属含量反演模型研究

土壤中过高的重金属含量危害巨大,不仅造成了严重的环境污染,而且通过食物链进入人体对人体健康造成严重威胁,所以对重金属检测十分重要。X射线荧光光谱法具有检测时间短、无损检测、检测成本低等特点被广泛使用,然而检测的光谱数据因受到土壤含水量因素的严重干扰,导致直接对土壤重金属含量估算精度较低。以河北省保定市满城区土样为研究对象,对采集的土样进行除杂、过筛、烘干后加入一定量重金属溶液制备不同含水量不同重金属的样本进行检测。对实验中异常数据计算了马氏距离和进行NJW聚类予以剔除,分析了土壤含水量对土壤重金属光谱的影响,结果表明不同含水量间光谱重复性差,随着土壤含水量的增加光谱强度呈非线性降低。采用Savitzky-Golay卷积平滑去噪法和线性本底法对光谱进行预处理,以解决因环境、仪器本身带来的噪声和基线漂移等问题。然后针对于土壤含水量这一主要干扰,采用非负矩阵分解算法进行处理,并使用峰值信噪比这一评价模型确定端元数目,结果表明当端元数目增至10时峰值信噪比趋于稳定波动很小,非负矩阵分解处理后相同重金属含量不同含水量间光谱重复性好、相似性好,并计算了光谱间的相关系数进一步证明了光谱间的相似性。去除含水量对于光谱干扰后建立了偏最小二乘法预测模型,为了验证预测模型的精度,建立了未去除含水量的偏最小二乘法预测模型和使用外部参数正交化法去除含水量建立的偏最小二乘法预测模型,并使用评价参数决定系数(R2)、交叉验证均方根误差(RMSECV)、平均绝对误差(MAE)和相对分析误差(RPD)进行评价。验证结果表明,相比较未去除含水量建立的模型,使用非负矩阵分解去除含水量建立的偏最小二乘法模型R2和RPD分别提高了0.019 7和1.029 2,RMSECV和MAE分别降低了2.386 3和1.439 6;相对于外部参数正交化法建立的偏最小二乘法模型,R2和RPD分别提高了0.009 9和0.108 1,RMSECV和MAE分别降低了0.244 7和0.356 6,说明了经过非负矩阵分解去噪后建立的模型有效提高了预测的精度和鲁棒性。非负矩阵分解可以有效消除土壤含水量对光谱的影响,在此基础上建立的偏最小二乘法模型实现了土壤重金属含量的反演,为重金属定量检测提供了一定的技术支持。     

代谢组学数据分析方法及在糖尿病研究中的应用

对NMR波谱数据的统计分析是基于NMR代谢组学研究的关键问题之一. 鉴于NMR波谱信号可以近似为样品中各种成分谱信号的线性叠加,本文将非负矩阵分解(NMF)方法引入基于NMR代谢组学的数据处理中,并与代谢组学中常用的统计方法--主成分分析(PCA)进行比较. 通过NMF和PCA两种方法对健康志愿者与2型糖尿患者血液和尿液的NMR谱图的统计分析,对所获取的特征代谢物进行比较和验证,并探讨了PCA方法可能存在的不足之处及其原因;阐明了NMF方法是基于NMR的代谢组学研究中较理想的数据分析方法. 最后,讨论了基于NMR代谢组学在糖尿病研究中的前景.     

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (相似文献   

Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT)

Various sparse transform models have been explored for compressed sensing-based dynamic cardiac MRI reconstruction from vastly under-sampled k-space data. Recently emerged low rank tensor model using Tucker decomposition could be viewed as a special form of sparse model, where the core tensor, which is obtained using high-order singular value decomposition, is sparse in the sense that only a few elements have dominantly large magnitude. However, local details tend to be over-smoothed when the entire image is conventionally modeled as a global tensor. Moreover, low rankness is sensitive to motion as spatiotemporal correlation is corrupted by spatial misalignment between temporal frames. To overcome these limitations, this paper presents a novel motion aligned locally low rank tensor (MALLRT) model for dynamic MRI reconstruction. In MALLRT, low rank constraint is enforced on image patch-based local tensors, which correspond to overlapping blocks extracted from the reconstructed high-dimensional image after group-wise inter-frame motion registration. For solving the proposed model, this paper presents an efficient optimization algorithm by using variable splitting and alternating direction method of multipliers (ADMM). MALLRT demonstrated promising performance as validated on one cardiac perfusion MRI dataset and two cardiac cine MRI datasets using retrospective under-sampling with various acceleration factors, as well as one prospectively under-sampled cardiac perfusion MRI dataset. Compared to four state-of-the-art methods, MALLRT achieved substantially better image reconstruction quality in terms of both signal to error ratio (SER) and structural similarity index (SSIM) metrics, and visual perception in preserving spatial details and capturing temporal variations.     

Non‐negative matrix factorization for the near real‐time interpretation of absorption effects in elemental distribution images acquired by X‐ray fluorescence imaging

Elemental distribution images acquired by imaging X‐ray fluorescence analysis can contain high degrees of redundancy and weakly discernible correlations. In this article near real‐time non‐negative matrix factorization (NMF) is described for the analysis of a number of data sets acquired from samples of a bi‐modal α+β Ti‐6Al‐6V‐2Sn alloy. NMF was used for the first time to reveal absorption artefacts in the elemental distribution images of the samples, where two phases of the alloy, namely α and β, were in superposition. The findings and interpretation of the NMF results were confirmed by Monte Carlo simulation of the layered alloy system. Furthermore, it is shown how the simultaneous factorization of several stacks of elemental distribution images provides uniform basis vectors and consequently simplifies the interpretation of the representation.     

Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.     

Regularised finite element model updating using measured incomplete modal data

This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.     

Speeding up Training of Linear Predictors for Multi-Antenna Frequency-Selective Channels via Meta-Learning

An efficient data-driven prediction strategy for multi-antenna frequency-selective channels must operate based on a small number of pilot symbols. This paper proposes novel channel-prediction algorithms that address this goal by integrating transfer and meta-learning with a reduced-rank parametrization of the channel. The proposed methods optimize linear predictors by utilizing data from previous frames, which are generally characterized by distinct propagation characteristics, in order to enable fast training on the time slots of the current frame. The proposed predictors rely on a novel long short-term decomposition (LSTD) of the linear prediction model that leverages the disaggregation of the channel into long-term space-time signatures and fading amplitudes. We first develop predictors for single-antenna frequency-flat channels based on transfer/meta-learned quadratic regularization. Then, we introduce transfer and meta-learning algorithms for LSTD-based prediction models that build on equilibrium propagation (EP) and alternating least squares (ALS). Numerical results under the 3GPP 5G standard channel model demonstrate the impact of transfer and meta-learning on reducing the number of pilots for channel prediction, as well as the merits of the proposed LSTD parametrization.     

反演与拟合相结合处理核磁共振弛豫数据的方法

讨论非负最小二乘（NNLS）法和非线性拟合在分析处理核磁共振（NMR）弛豫数据中的应用.同时将二者结合，提出用NNLS的反演结果来设定非线性拟合初值的方法，并用计算机模拟和实验证明了该方法在分析处理NMR弛豫数据中的有效性. 关键词： 非负最小二乘法 非线性拟合 核磁共振 弛豫时间     

三维荧光光谱结合组合算法在环境污染监测中的应用:油种鉴别与定量分析

针对油类污染物成分复杂,光谱重叠难以识别的问题,提出采用三维荧光光谱结合组合算法对油类污染物进行了定性和定量分析。荧光光谱中存在的瑞利散射对三维荧光光谱检测有较大影响,提出了缺损数据修复-主成分分析（MDR-PCA）方法对矿物油三维荧光光谱的瑞利散射进行处理,原理是单个荧光光谱激发发射矩阵符合双线性,可用主成分分析（PCA）法来解析。MDR-PCA法首先将荧光数据中的散射干扰数据全部扣除,之后利用主成分分析（PCA）迭代过程对扣除数据进行重构修复后补全数据。该方法在消除散射干扰的同时充分利用了荧光物质光谱矩阵中的有效信息。利用不同浓度的矿物油的激发-发射荧光光谱构建了三维数据。样品数据来源于柴油、汽油和煤油三种溶质的四氯化碳溶液。常用于三维荧光光谱数据分析的三线性分解算法有平行因子分析（PARAFAC）、交替三线性分解（ATLD）和自加权交替三线性分解算法（SWATLD）等。PARAFAC基于严格意义上的最小二乘原则,具有抗噪声强、模型稳定、微小预期误差等优点,可以实现三维数据阵列的最佳拟合,但该算法收敛速度较慢,对组分数敏感。ATLD算法通过提取对角主元和切尾奇异值求解广义逆,极大提高了收敛速度并降低了对组分数的敏感度,从而实现三线性分解。然而,取对角元时易使ATLD方法对噪声敏感。SWATLD算法既继承了对组分数不敏感、收敛速度快等优点,又降低了噪声水平的影响。但是在抗共线程度方面,SWATLD算法在抵抗共线性程度方面的能力较ATLD略有降低。基于此,论文根据三线性分解算法迭代过程中损失函数的变化,对迭代过程进行划分,提出了三线性迭代方法的组合算法（algorithm combination methodology, ACM）—将ATLD, SWATLD与PARAFAC组合在一起,充分发挥各算法的优点,实现二阶校正算法的优势互补。采用ACM算法对两组分及三组分矿物油样品的三维荧光光谱数据进行解析,并对三种矿物油的回收率进行了计算。柴油的回收率为97.08%,汽油的回收率为97.34%,煤油的回收率为97.25%。解析光谱和回收率表明,ACM算法能够实现油类污染物的种类识别及浓度测量。