CN107194410B - 一种基于多线性ica的光谱张量降维的分类方法 - Google Patents
一种基于多线性ica的光谱张量降维的分类方法 Download PDFInfo
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Abstract
本发明公开了一种基于多线性ICA的光谱张量降维的分类方法,该方法将影响地物光谱特征的因素作为类内因素,并将类内因素、类与像素光谱分别作为一种模式构建成一个3阶张量,对其进行基于低秩张量分解的降维;对3阶张量D进行多线性ICA(独立成分分析)分解得到类空间矩阵Cclass、类内因素空间矩阵Cwithin‑class;采用有监督分类器对无类别的测试高光谱图像d进行分类。本发明在模型建立后即可对高光谱图像进行分类,无需调整,而其他张量建模方法则需要反复设置、调整参数才能达到最佳分类效果;本发明将一类的所有像素光谱映射到同一系数向量上,从而将各种因素的影响减至最小,不但提高了分类精度,而且结果稳定;对未知像素光谱分类时,可推断出其受哪一个因素影响。
Description
技术领域
本发明属于遥感图像处理技术领域,具体涉及一种基于多线性ICA的光谱张量降维的分类方法。
背景技术
高光谱图像提供了细致丰富的地物光谱特性描述,大大提高了对地物的分类能力,已广泛应用于地质勘探与地球资源调查、城市遥感与规划管理、环境与灾害监测、精细农业、测绘及考古等方面。
然而,高光谱图像由大量波段数据组成,这些波段构成高维特征空间,对其处理需要巨大的计算量,引发“数据灾难”。针对这个问题,最为有效的方式就是降维。主分量分析(Principal Component Analysis,PCA)由于简单有效是目前应用最广泛的降维方法。但是PCA需要将高光谱图像向量化,并且只是在高光谱图像的光谱维上进行处理,忽略了高光谱图像的空间信息。
为了充分利用高光谱图像的空间信息,学者们提出了许多将高光谱图像建模为张量的方法。高光谱图像可是一组二维图像,因此可以用多维数据表示,包括两个空间维和一个光谱维。Letexier等人将高光谱图像建模为三阶张量其中I1和I2为像素位置,I3为波段数。使用张量分解模型对高光谱图像进行空间和光谱联合分析。其中使用Tucker3分解模型生成张量数据的低秩近似,称为LRTA-(k1,k2,k3)方法。
基于张量的低秩近似,Nadine Renard等提出了先在高光谱数据的空间维上进行低秩近似,以降低空间维上的噪声;然后在光谱维上使用PCA进行降维的LRTAdr-(k1,k2,p)方法。该方法改善了分类精度。但是该方法仅仅将高光谱立方体简单建模为三阶张量,没有考虑到影响高光谱分类精度的真正原因:地物的光谱特征受到如光照、混合、大气散射、大气辐射等多种因素影响。
发明内容
针对现有技术中存在的缺陷,本发明提出了一种基于多线性ICA的光谱张量降维的分类方法,包括以下步骤:
步骤1,随机选取高光谱图像中的像素光谱作为训练集,所选取的像素光谱有L个波段、C类样本,分别在C类样本中的每类样本中随机选取W个像素光谱作为类内因素,其中C大于等于1的自然数,W为大于等于1的自然数;
步骤3,判断待测试像素光谱d所属类、所属因素:
步骤31,计算基张量
(式1)中,为3阶张量;Cclass为类空间矩阵;Cwithin-class为类内因素空间矩阵;Upixels为像素光谱矩阵;对3阶张量进行多线性ICA分解得到类空间矩阵Cclass、类内因素空间矩阵Cwithin-class;
其中,
步骤33,计算响应张量;
其中,
步骤35,对R(pixels)进行奇异值分解得到左矩阵U和右矩阵V;
步骤36,取U的第一列记为cd,取V的第一列记为wd;
步骤37,如果ck满足则测试像素光谱d属于C类中的类别k,k≤C;
其中,ck=Cclass(k,:)T。
步骤38,如果wm满足则测试像素光谱d属于W个因素中的因素m,m≤W;
其中,wm=Cwithin-class(m,:)T。
与现有技术相比,本发明具有以下技术效果:
(1)本发明第一次将影响高光谱图像的因素建模为张量,解决了对影响高光谱图像的因素建模的问题;
(2)本发明在模型建立后即可对高光谱图像进行分类,无需调整,而其他张量建模方法则需要反复设置、调整参数才能达到最佳分类效果;
(3)本发明将一类的所有像素光谱映射到同一系数向量上,从而将各种因素的影响减至最小,不但提高了分类精度,而且结果稳定。
(4)对未知像素光谱分类时,可推断出其受哪一个因素影响。
附图说明
图1为光谱张量综合降维分解图;
图2(a)为Indian Pine数据集波段60、27及17的伪彩色合成图;
图2(b)为Indian Pine数据集真实标记图;
图3为Indian Pine数据集中各类的光谱曲线;
图4为形成3阶光谱张量;
具体实施方式
下面通过实施例和附图对本发明做进一步说明。
实施例1
本实施例提供了一种基于多线性的光谱张量降维方法,该方法将随机选取的像素光谱作为类内因素,并将类内因素、类与像素光谱的波段分别作为一种模式构建成一个3阶张量,对其进行基于多线性ICA的降维;
步骤1,本实施例选用的是Indian Pine的高光谱图像中的像素光谱,原始图像尺寸为145×145。如图2所示,该高光谱图像包括10类样本,分别为:Corn-notill、Corn-min、Grass/Pasture、Grass/Tree、Hay-windrowed、Soybeans-notill、soybeans-min、soybeans-clean、Woods、Bldg-Grass Tree;本实施例中,从上述10类样本中的每类样本中选择50个像素光谱作为类内因素;
由于地物的光谱特征易受到如光照、混合、大气散射、大气辐射等多种因素影响,所以本实施例将地物的光谱特征作为类内因素来建模,提高高光谱图像的分类精度。
使用多线性ICA分解生成张量数据的低秩近似,改善了高光谱图像的分类精度。
实施例2
本实施例将实施例1选取的高光谱图像的像素光谱作为训练集,输入任意一幅Indian Pine中未分类的像素光谱作为测试像素光谱d。
其中,d为(0.3172,0.4142,0.4506,0.4279,0.4782,0.5048,0.5213,0.5106,0.5053,0.4750,0.4816,0.4769,0.4610,0.4805,0.4828,0.4861,0.4767,0.4624,0.4549,0.4463,0.4462,0.4446,0.4445,0.4336,0.4381,0.4319,0.4207,0.4305,0.4311,0.3991,0.4168,0.3942,0.4061,0.4365,0.4318,0.4252,0.4869,0.5284,0.5055,0.3591,0.5175,0.5217,0.5058,0.4969,0.4721,0.4291,0.4555,0.4886,0.4868,0.4806,0.4783,0.4811,0.4709,0.3903,0.3795,0.3715,0.3359,0.2130,0.2269,0.2480,0.3145,0.3626,0.4060,0.4296,0.4211,0.4225,0.4157,0.4133,0.4082,0.4048,0.3935,0.3843,0.3784,0.3642,0.3271,0.2707,0.1707,0.1564,0.1838,0.1719,0.2229,0.2764,0.2919,0.2873,0.2977,0.2913,0.3034,0.3051,0.3124,0.3101,0.3033,0.2713,0.2740,0.2947,0.2706,0.2834,0.2856,0.2683,0.2400,0.2229,0.1822,0.1542,0.1097,0.1029,0.1020,0.1026,0.1009,0.1011,0.1047,0.1069,0.1100,0.1122,0.1259,0.1365,0.1261,0.1374,0.1630,0.1851,0.2028,0.2130,0.2170,0.2205,0.2214,0.2204,0.2100,0.2106,0.2146,0.2089,0.2078,0.2134,0.2127,0.2074,0.2057,0.2045,0.2003, 0.1999,0.1959,0.1924,0.1883,0.1843,0.1781,0.1716,0.1698,0.1645,0.1540,0.1410,0.1294,0.1131,0.1044,0.1029,0.1006,0.1017,0.1000,0.0995,0.0997,0.1003,0.1016,0.1001,0.1003,0.1002,0.1005,0.1004,0.1008,0.1032,0.1045,0.1100,0.1212,0.1295,0.1244,0.1100,0.1103,0.1216,0.1346,0.1330,0.1259,0.1251,0.1313,0.1372,0.1393,0.1402,0.1396,0.1381,0.1396,0.1381,0.1353,0.1346,0.1341,0.1332,0.1324,0.1310,0.1318,0.1330,0.1310,0.1292,0.1280,0.1275,0.1266,0.1264,0.1233,0.1241,0.1232,0.1215,0.1215,0.1187,0.1168,0.1171,0.1150,0.1134,0.1123,0.1135,0.1094,0.1090,0.1112,0.1090,0.1062,0.1069,0.1057,0.1020,0.1020,0.1005);
本实施例在实施例1的基础上判断待测试像素光谱d所属类,所属因素,包括以下步骤:
(式1)中,为10×50×220张量;Cclass为10×10的类空间矩阵;Cwithin-class为50×50类内因素空间矩阵;对3阶张量进行多线性ICA分解得到类空间矩阵Cclass、类内因素空间矩阵Cwithin-class;
其中,
步骤3,计算响应张量;
(式3)中,为响应张量,为基张量的逆张量,d为待测试像素光谱。
步骤5,对R(pixels)进行奇异值分解得到左矩阵U和右矩阵V;
步骤6,取U的第一列记为cd,取V的第一列记为wd;
其中,ck=Cclass(k,:)T。
其中,wm=Cwithin-class(m,:)T。
本发明提出了一种新的高光谱图像的降维方法,这种方法的优点如下:1)第一次将影响高光谱图像的因素建模为张量。2)模型建立后即可使用,无需调整,而其他张量建模方法则需要反复设置、调整参数才能达到最佳分类效果。3)本发明方法的最大优点是将一类的所有像素光谱映射到同一系数向量上,从而将各种因素的影响减至最小,不但提高了分类精度,而且结果稳定。4)对未知像素光谱分类时,可推断出其受哪一个因素影响。
Claims (1)
1.一种基于多线性ICA的光谱张量降维的分类方法,其特征在于,包括以下步骤:
步骤1,随机选取高光谱图像中的像素光谱作为训练集,所选取的像素光谱有L个波段、C类样本,分别在C类样本中的每类样本中随机选取W个像素光谱作为类内因素,其中C为大于等于1的自然数,W为大于等于1的自然数;
步骤3,判断待测试像素光谱d所属类、所属因素:
(式1)中,为3阶张量;Cclass为类空间矩阵;Cwithin-class为类内因素空间矩阵;Upixels为像素光谱矩阵;对3阶张量进行多线性ICA分解得到类空间矩阵Cclass、类内因素空间矩阵Cwithin-class;
其中,
步骤36,取U的第一列记为cd,取V的第一列记为wd;
步骤37,如果ck满足argkmin||cd-ck||,则测试像素光谱d属于C类中的类别k,k≤C;
其中,ck=Cclass(k,:)T;
其中,wm=Cwithin-class(m,:)T。
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