主要内容
特征提取工作流程
这个例子展示了从图像数据中提取特征的完整工作流。
获取数据
此示例使用Mnist Image Data [1]，由手写数字的图像组成。图像以灰度为28×28像素。每个图像具有0到9的相关标签，这是图像所代表的数字。
首先获取图像和标签数据
http://yann.lecun.com/exdb/mnist/
解压文件。为了在这个长示例中获得更好的性能，可以将测试数据用作训练数据，将训练数据用作测试数据。
imageFileName ='t10k-images.idx3-ubyte'；Labelfilename =“t10k-labels.idx1-ubyte”；
处理这些文件以在工作区中加载它们。此处理函数的代码出现在本示例的末尾。
[Xtrain, LabelTrain] = processMNISTdata (imageFileName labelFileName);
读取Mnist图像数据...数据集中的图像数：10000 ...每个图像为28个像素......图像数据被读取为尺寸的矩阵：10000到784 ...阅读图像的结束数据。读取Mnist标签数据...数据集中的标签数：10000 ...标签数据被读取为尺寸的矩阵：10000×1 ...读取标签数据结束。
查看一些图像。
RNG（'默认'）%的再现性numrows =大小(Xtrain, 1);ims =兰迪(numrows 4 1);:一个= Xtrain (ims);为了I = 1:4 pp{I} =重塑(imgs(I，:)，28,28);结尾ppf = [pp {1}，pp {2}; pp {3}，pp {4}];imshow（ppf）;
选择新功能维度
选择要提取的功能数量有几个考虑因素：
更多功能使用更多内存和计算时间。
较少的特征会产生较差的分类器。
对于此示例，请选择100个功能。
q = 100;
提取特征
有两个特征提取函数，Sparsefilt.和r。从这开始Sparsefilt.函数。将迭代次数设置为10，以便提取不会花费太长时间。
通常，您可以通过运行Sparsefilt.算法为几次迭代到几百次迭代。运行算法过多的迭代会导致分类精度下降，这是一种过拟合问题。
使用Sparsefilt.使用10个迭代时获取稀疏过滤模型。
Mdl = sparsefilt (Xtrain q'iterationlimit'10);
警告:解算器LBFGS不能收敛到一个解。
Sparsefilt.警告内部LBFGS优化器没有收敛。优化器没有收敛，因为您将迭代限制设置为10.然而，您可以使用结果培训分类器。
创建分类器
将原始数据转换为新功能表示。
Xtrain NewX =变换(Mdl);
根据转换后的数据和中正确的分类标签训练线性分类器LabelTrain.。学习模型的准确性对此敏感fitcecoc正则化参数lambda.。尝试找到最优雅的价值lambda.通过使用OptimizeHyperparameters名称-值对。请注意，这种优化需要时间。如果您有并行计算工具箱™许可证，请使用并行计算以更快地执行。如果您没有并行许可证，请删除UseParallel在运行此脚本之前调用。
t = templateLinear (“规划求解”那“lbfgs”）;选项= struct（'使用指平行',真正的);cmdl = fitcecoc（newx，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);
复制目标函数，工人...完成复制目标函数的工人。|================================================================================================| | Iter | |活跃Eval客观客观| | | BestSoFar | BestSoFar |λ| | |工人结果| | |运行时| | (estim(观察) .) | | |================================================================================================| | 1 | 6 |最好的0.5777 | 8.5334 | 0.5777 | 0.5777 | 0.20606 | | 2 | 5 | Accept | 0.8865 | 8.9062 | 0.2041 | 0.27206 | 8.8234 | | 3 | 5 | Best | 0.2041 | 9.7024 | 0.2041 | 0.27206 | 0.026804 | | 4 | 6 | Best | 0.1077 | 14.629 | 0.1077 | 0.10773 | 1.7309e-09 | | 5 | 6 | Best | 0.0962 | 15.767 | 0.0962 | 0.096203 | 0.0002442 | | 6 | 6 | Accept | 0.1999 | 6.4363 | 0.0962 | 0.09622 | 0.024862 | | 7 | 6 | Accept | 0.2074 | 6.4171 | 0.0962 | 0.096222 | 0.029034 | | 8 | 6 | Accept | 0.1065 | 12.974 | 0.0962 | 0.096222 | 2.037e-08 | | 9 | 6 | Accept | 0.0977 | 22.976 | 0.0962 | 0.096216 | 8.0495e-06 | | 10 | 6 | Accept | 0.1237 | 8.5033 | 0.0962 | 0.096199 | 0.0029745 | | 11 | 6 | Accept | 0.1076 | 10.653 | 0.0962 | 0.096208 | 0.00080903 | | 12 | 6 | Accept | 0.1034 | 16.761 | 0.0962 | 0.0962 | 3.2145e-07 | | 13 | 6 | Best | 0.0933 | 16.715 | 0.0933 | 0.093293 | 6.3327e-05 | | 14 | 6 | Accept | 0.109 | 12.946 | 0.0933 | 0.09328 | 5.7887e-09 | | 15 | 6 | Accept | 0.0994 | 18.805 | 0.0933 | 0.093312 | 1.8981e-06 | | 16 | 6 | Accept | 0.106 | 15.088 | 0.0933 | 0.093306 | 7.4684e-08 | | 17 | 6 | Accept | 0.0952 | 20.372 | 0.0933 | 0.093285 | 2.2831e-05 | | 18 | 6 | Accept | 0.0933 | 14.528 | 0.0933 | 0.093459 | 0.00013097 | | 19 | 6 | Accept | 0.1082 | 12.764 | 0.0933 | 0.093458 | 1.0001e-09 | | 20 | 6 | Best | 0.0915 | 16.157 | 0.0915 | 0.092391 | 8.3234e-05 | |================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Lambda | | | workers | result | | runtime | (observed) | (estim.) | | |================================================================================================| | 21 | 6 | Accept | 0.8865 | 6.6373 | 0.0915 | 0.092387 | 1.6749 | | 22 | 6 | Accept | 0.0929 | 17.306 | 0.0915 | 0.092457 | 0.00010668 | | 23 | 6 | Accept | 0.0937 | 19.046 | 0.0915 | 0.092535 | 5.0962e-05 | | 24 | 6 | Accept | 0.0916 | 17.932 | 0.0915 | 0.092306 | 9.023e-05 | | 25 | 6 | Accept | 0.0935 | 17.53 | 0.0915 | 0.092431 | 0.00011726 | | 26 | 6 | Accept | 0.1474 | 8.3795 | 0.0915 | 0.092397 | 0.006997 | | 27 | 6 | Accept | 0.0939 | 19.188 | 0.0915 | 0.092427 | 5.2557e-05 | | 28 | 6 | Accept | 0.1147 | 10.686 | 0.0915 | 0.092432 | 0.0015036 | | 29 | 6 | Accept | 0.1049 | 16.609 | 0.0915 | 0.092434 | 1.4871e-07 | | 30 | 6 | Accept | 0.1069 | 13.929 | 0.0915 | 0.092435 | 1.0899e-08 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 83.1976 seconds. Total objective function evaluation time: 416.8767 Best observed feasible point: Lambda __________ 8.3234e-05 Observed objective function value = 0.0915 Estimated objective function value = 0.09245 Function evaluation time = 16.1569 Best estimated feasible point (according to models): Lambda _________ 9.023e-05 Estimated objective function value = 0.092435 Estimated function evaluation time = 17.0972
评估分类器
当应用到测试数据时检查分类器的错误。首先，加载测试数据。
imageFileName ='train-images.idx3-ubyte'；Labelfilename =“train-labels.idx1-ubyte”；[Xtest, LabelTest] = processMNISTdata (imageFileName labelFileName);
读取MNIST图像数据…数据集中的图像数量:60000…每个图像是28 × 28像素…图像数据被读取为一个维数为60000 × 784的矩阵。读取图像数据结束。读取MNIST标签数据…数据集中的标签数量:60000…标签数据被读取为一个矩阵:60000 × 1…标签数据读取结束。
计算将分类器应用于测试数据时的分类损失。
Xtest TestX =变换(Mdl);损失=损失(Cmdl TestX LabelTest)
损失= 0.1009.
这种转换是否产生了比在原始数据上训练的更好的分类器?基于原始训练数据创建分类器并评估其损失。
omdl = fitcecoc（xtrain，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);LOSTO =损失（OMDL，XTEST，LABELTEST）
复制目标函数，工人...完成复制目标函数的工人。|================================================================================================| | Iter | |活跃Eval客观客观| | | BestSoFar | BestSoFar |λ| | |工人结果| | |运行时| | (estim(观察) .) | | |================================================================================================| | 1 | 5 |最好的0.0779 | 46.965 | 0.0779 | 0.0779 | 5.7933e-08 | | 2 | 5 | Accept | 0.0779 | 47.003 | 0.0779 | 0.0779 | 3.8643e-09 | | 3 | 5 | Accept | 0.0779 | 47.068 | 0.0779 | 0.0779 | 1.3269e-06 | | 4 | 6 | Accept | 0.078 | 60.714 | 0.0779 | 0.077925 | 3.0332e-05 | | 5 | 6 | Accept | 0.0787 | 133.21 | 0.0779 | 0.0779 | 0.011605 | | 6 | 6 | Best | 0.0775 | 135.97 | 0.0775 | 0.077983 | 0.00020291 | | 7 | 6 | Accept | 0.0779 | 44.642 | 0.0775 | 0.077971 | 5.735e-08 | | 8 | 6 | Accept | 0.0785 | 123.19 | 0.0775 | 0.0775 | 0.024589 | | 9 | 6 | Accept | 0.0779 | 43.574 | 0.0775 | 0.0775 | 1.0042e-09 | | 10 | 6 | Accept | 0.0779 | 43.038 | 0.0775 | 0.0775 | 4.7227e-06 | | 11 | 6 | Best | 0.0774 | 137.51 | 0.0774 | 0.077451 | 0.00021639 | | 12 | 6 | Accept | 0.0779 | 44.07 | 0.0774 | 0.077452 | 6.7132e-09 | | 13 | 6 | Accept | 0.0779 | 44.822 | 0.0774 | 0.077453 | 2.873e-07 | | 14 | 6 | Best | 0.0744 | 233.12 | 0.0744 | 0.074402 | 6.805 | | 15 | 6 | Accept | 0.0778 | 140.49 | 0.0744 | 0.074406 | 0.66889 | | 16 | 6 | Accept | 0.0774 | 149.32 | 0.0744 | 0.074405 | 0.0002769 | | 17 | 6 | Accept | 0.0774 | 155 | 0.0744 | 0.074404 | 0.00046083 | | 18 | 6 | Accept | 0.0765 | 152.63 | 0.0744 | 0.074687 | 0.00027101 | | 19 | 6 | Accept | 0.0768 | 156.32 | 0.0744 | 0.077558 | 0.00026573 | | 20 | 6 | Best | 0.0725 | 255.51 | 0.0725 | 0.073249 | 9.9961 | |================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Lambda | | | workers | result | | runtime | (observed) | (estim.) | | |================================================================================================| | 21 | 6 | Best | 0.0723 | 221.5 | 0.0723 | 0.073161 | 4.212 | | 22 | 6 | Accept | 0.0732 | 259.51 | 0.0723 | 0.073166 | 9.9916 | | 23 | 6 | Best | 0.072 | 261.94 | 0.072 | 0.072848 | 9.9883 | | 24 | 6 | Accept | 0.0778 | 122.56 | 0.072 | 0.072854 | 0.13413 | | 25 | 6 | Accept | 0.0733 | 258.54 | 0.072 | 0.072946 | 9.9904 | | 26 | 6 | Accept | 0.0746 | 244.53 | 0.072 | 0.073144 | 7.0911 | | 27 | 6 | Accept | 0.0779 | 44.573 | 0.072 | 0.073134 | 2.1183e-08 | | 28 | 6 | Accept | 0.078 | 45.478 | 0.072 | 0.073126 | 1.1663e-05 | | 29 | 6 | Accept | 0.0779 | 43.954 | 0.072 | 0.073118 | 1.336e-07 | | 30 | 6 | Accept | 0.0779 | 44.574 | 0.072 | 0.073112 | 1.7282e-09 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 690.8688 seconds. Total objective function evaluation time: 3741.3176 Best observed feasible point: Lambda ______ 9.9883 Observed objective function value = 0.072 Estimated objective function value = 0.073112 Function evaluation time = 261.9357 Best estimated feasible point (according to models): Lambda ______ 9.9961 Estimated objective function value = 0.073112 Estimated function evaluation time = 257.9556 Losso = 0.0865
基于稀疏滤波的分类器基于原始数据的分类器具有稍微较高的损耗。但是，分类器仅使用100个功能而不是原始数据中的784个功能，并且要更快地创建。尝试通过增加进行更好的稀疏过滤分类器问：从100到200，仍然远低于784。
q = 200;mdl2 = sparsefilt（xtrain，q，'iterationlimit'10);NewX =变换(Mdl2 Xtrain);TestX =变换(Mdl2 Xtest);cmdl = fitcecoc（newx，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);LOST2 =损失（CMDL，TESTX，LABELTEST）
警告：解算器LBFGS无法收敛到解决方案。正在将目标函数复制到工人。。。已完成将目标函数复制到工作人员。|=====================================================================================================================================================================================================================================================================================================================================================================================================================================================================第二天，中国热火（1244）对中国热火（1244）对中国热火（1244）对中国热火（1244）对中国热火（244）对中国热火（1244）Lamb达（1244））的测量结果：中国热火（1244）对中国热火（1244）对中国热火（1244）对中国热火（1244）对中国热火（1244）最好）对中国热火（244）的BeBeBe斯of（244）Lamb达（244）Lamb达（244）方方方方方方方）的测量测量，工人们（1244）工人，工人们（1244）工人们，结果，结果工人们，结果，结果，结果工人们（1244）工人们，结果，结果，结果，结果，运行时（124124刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺刺1244）的运行时，运行时，运行时（运行时）的运行时（运行1 | 5 |最佳| 0.8865 | 7.3578 | 0.8865 | 0.8865 | 1.93 | 2 | 5 |接受| 0.8865 | 7.3408 | 0.8865 |0.0693 0.067 7 0.067 7 7 0.0665 0 0.0665 0 0.8865 0 0 0.8865 0 0 0 0 0 0 0 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4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4|26 | 6 |接受| 0.0598 | 28.536 | 0.0593 | 0.059465 | 5.0819e-05 | 27 | 6 |接受| 0.0701 | 9.0545 | 0.0593 | 0.059466 |1.897 7 7.7 7 7.117 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0.059 9 9 0 0 0.5 9 9 9 9 9 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0| 31 | 3 |接受| 0.0725 | 16.069 | 0.0593 | 0.059422 | 0.00069403 | 32 |接受| 0.1928 | 8.3732 | 0.0593 | 0.059422 |0.040402 | | | uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu。MaxObjectiveEvaluation达到了30。总功能评估：32总运行时间：97.7946秒。目标函数总评价时间：545.3255最佳观测可行点：Lambdauuuuuuu7.8179e-05观测目标函数值=0.0593估计目标函数值=0.059422函数评价时间=26.2624最佳估计可行点（根据模型）：Lambdauuuuuuuu-05估计目标函数值=0.059422估计功能评估时间=26.508损失2=0.0682
这次分类损失比原始数据分类器的分类损失小。
试着黎加
试试其他的特征提取函数，r。提取200个功能，创建分类器，并在测试数据上检查其丢失。使用更多的迭代r功能,因为r迭代次数越多，性能是否会更好Sparsefilt.用途。
通常在特征提取之前，将输入数据“预白化”作为数据预处理步骤。预白步骤包括两个变换，去相关和标准化，使预测器具有零均值和恒等协方差。r万博1manbetx仅支持标准化转换。您使用标准化名称-值对参数使预测器的平均值和单位方差为零。或者，您可以通过应用zscore在呼叫前转换Sparsefilt.或r。
mdl3 = rica（xtrain，q，'iterationlimit', 400,“标准化”,真正的);NewX =变换(Mdl3 Xtrain);TestX =变换(Mdl3 Xtest);cmdl = fitcecoc（newx，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);Loss3 =损失(Cmdl TestX LabelTest)
警告:解算器LBFGS不能收敛到一个解。复制目标函数，工人...完成复制目标函数的工人。|================================================================================================| | Iter | |活跃Eval客观客观| | | BestSoFar | BestSoFar |λ| | |工人结果| | |运行时| | (estim(观察) .) | | |================================================================================================| | 1 | 6 |最好的0.1179 | 12.012 | 0.1179 | 0.1179 | 8.4727 | | 2 | 6 | Best | 0.082 | 13.384 | 0.082 | 0.083897 | 4.3291e-09 | | 3 | 6 | Best | 0.0809 | 18.917 | 0.0809 | 0.080902 | 1.738e-05 | | 4 | 6 | Accept | 0.0821 | 19.172 | 0.0809 | 0.08091 | 3.8101e-06 | | 5 | 6 | Accept | 0.0921 | 14.445 | 0.0809 | 0.086349 | 2.3753 | | 6 | 6 | Accept | 0.0809 | 13.393 | 0.0809 | 0.083836 | 1.3757e-08 | | 7 | 6 | Best | 0.076 | 28.075 | 0.076 | 0.081808 | 0.00027773 | | 8 | 6 | Best | 0.0758 | 29.686 | 0.0758 | 0.078829 | 0.00068195 | | 9 | 6 | Accept | 0.0829 | 13.373 | 0.0758 | 0.078733 | 1.7543e-07 | | 10 | 6 | Accept | 0.0826 | 14.031 | 0.0758 | 0.078512 | 1.0045e-09 | | 11 | 6 | Accept | 0.0817 | 13.662 | 0.0758 | 0.078077 | 2.4568e-08 | | 12 | 6 | Accept | 0.0799 | 19.311 | 0.0758 | 0.077658 | 1.4061e-05 | | 13 | 6 | Best | 0.065 | 25.148 | 0.065 | 0.064974 | 0.060326 | | 14 | 6 | Accept | 0.0787 | 23.434 | 0.065 | 0.064947 | 0.00012407 | | 15 | 6 | Accept | 0.072 | 19.167 | 0.065 | 0.064997 | 0.43899 | | 16 | 6 | Accept | 0.073 | 28.39 | 0.065 | 0.065053 | 0.0023721 | | 17 | 6 | Accept | 0.0787 | 29.887 | 0.065 | 0.064928 | 0.00042914 | | 18 | 6 | Accept | 0.0662 | 26.374 | 0.065 | 0.064295 | 0.0077638 | | 19 | 6 | Accept | 0.0652 | 24.937 | 0.065 | 0.064502 | 0.087389 | | 20 | 6 | Accept | 0.0655 | 25.416 | 0.065 | 0.064762 | 0.072931 | |================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Lambda | | | workers | result | | runtime | (observed) | (estim.) | | |================================================================================================| | 21 | 6 | Best | 0.0645 | 25.529 | 0.0645 | 0.064691 | 0.059245 | | 22 | 6 | Accept | 0.065 | 23.832 | 0.0645 | 0.06474 | 0.025521 | | 23 | 6 | Accept | 0.0819 | 20.343 | 0.0645 | 0.064732 | 7.2593e-07 | | 24 | 6 | Accept | 0.0664 | 23.732 | 0.0645 | 0.064718 | 0.1534 | | 25 | 6 | Accept | 0.0651 | 24.796 | 0.0645 | 0.064693 | 0.038371 | | 26 | 6 | Accept | 0.0651 | 25.449 | 0.0645 | 0.064613 | 0.014318 | | 27 | 6 | Accept | 0.0652 | 25.092 | 0.0645 | 0.064713 | 0.037107 | | 28 | 6 | Accept | 0.0645 | 24.404 | 0.0645 | 0.0647 | 0.042959 | | 29 | 6 | Accept | 0.0649 | 24.704 | 0.0645 | 0.064729 | 0.042776 | | 30 | 6 | Accept | 0.0652 | 24.341 | 0.0645 | 0.064786 | 0.035788 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 124.9755 seconds. Total objective function evaluation time: 654.4364 Best observed feasible point: Lambda ________ 0.059245 Observed objective function value = 0.0645 Estimated objective function value = 0.064932 Function evaluation time = 25.5294 Best estimated feasible point (according to models): Lambda ________ 0.042776 Estimated objective function value = 0.064786 Estimated function evaluation time = 24.7849 Loss3 = 0.0749
这r与稀疏过滤分类器相比，基于稀疏过滤分类器的测试损失略高。
尝试更多的功能
特征提取功能几乎没有调谐参数。一个可能影响结果的一个参数是所请求的功能的数量。请参阅分类器基于1000个功能时如何工作，而不是先前尝试的200个功能，或原始数据中的784个功能。使用比在原始数据中出现的更多功能被称为“超越”学习。相反，使用更少的功能被称为“uchifallete”学习。超越学习可以导致分类准确性提高，而欠顺列学习可以节省内存和时间。
q = 1000;mdl4 = sparsefilt（xtrain，q，'iterationlimit'10);newx =变换（MDL4，XTrain）;testx =变换（mdl4，xtest）;cmdl = fitcecoc（newx，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);Loss4 =损失(Cmdl TestX LabelTest)
警告:解算器LBFGS不能收敛到一个解。复制目标函数，工人...完成复制目标函数的工人。|================================================================================================| | Iter | |活跃Eval客观客观| | | BestSoFar | BestSoFar |λ| | |工人结果| | |运行时| | (estim(观察) .) | | |================================================================================================| | 1 | 6 |最好的0.5293 | 39.885 | 0.5293 | 0.5293 | 0.20333 | | 2 | 6 | Accept | 0.8022 | 43.475 | 0.5293 | 0.66575 | 0.77337 | | 3 | 6 | Best | 0.0406 | 52.594 | 0.0406 | 0.11113 | 9.1082e-09 | | 4 | 6 | Best | 0.0403 | 54.73 | 0.0403 | 0.060037 | 2.3947e-09 | | 5 | 6 | Accept | 0.0695 | 124.96 | 0.0403 | 0.040319 | 0.001361 | | 6 | 6 | Accept | 0.0406 | 53.691 | 0.0403 | 0.040207 | 1.0005e-09 | | 7 | 6 | Best | 0.0388 | 178.69 | 0.0388 | 0.038811 | 1.4358e-06 | | 8 | 6 | Accept | 0.0615 | 138.53 | 0.0388 | 0.038817 | 0.00088731 | | 9 | 6 | Best | 0.0385 | 61.81 | 0.0385 | 0.038557 | 7.4709e-08 | | 10 | 6 | Accept | 0.0399 | 54.198 | 0.0385 | 0.038555 | 2.1909e-08 | | 11 | 6 | Accept | 0.0402 | 234.55 | 0.0385 | 0.038639 | 0.000101 | | 12 | 6 | Accept | 0.0431 | 198.09 | 0.0385 | 0.038636 | 0.00018896 | | 13 | 6 | Accept | 0.0393 | 75.811 | 0.0385 | 0.039016 | 1.1597e-07 | | 14 | 6 | Accept | 0.0387 | 61.281 | 0.0385 | 0.038908 | 7.0518e-08 | | 15 | 6 | Accept | 0.0393 | 125.73 | 0.0385 | 0.038931 | 2.8429e-07 | | 16 | 6 | Accept | 0.0397 | 89.804 | 0.0385 | 0.039106 | 1.4603e-07 | | 17 | 6 | Accept | 0.0391 | 126.88 | 0.0385 | 0.039081 | 3.0065e-07 | | 18 | 6 | Accept | 0.0398 | 56.157 | 0.0385 | 0.039123 | 4.1563e-08 | | 19 | 6 | Accept | 0.0406 | 55.25 | 0.0385 | 0.039122 | 1.0014e-09 | | 20 | 6 | Accept | 0.0385 | 272.92 | 0.0385 | 0.039127 | 9.568e-06 | |================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Lambda | | | workers | result | | runtime | (observed) | (estim.) | | |================================================================================================| | 21 | 6 | Accept | 0.0412 | 55.191 | 0.0385 | 0.039124 | 3.3737e-09 | | 22 | 6 | Accept | 0.0394 | 229.72 | 0.0385 | 0.039117 | 3.2757e-06 | | 23 | 6 | Best | 0.0379 | 295.55 | 0.0379 | 0.039116 | 2.8439e-05 | | 24 | 6 | Accept | 0.0394 | 168.74 | 0.0379 | 0.039111 | 9.778e-07 | | 25 | 6 | Accept | 0.039 | 281.91 | 0.0379 | 0.039112 | 8.0694e-06 | | 26 | 6 | Accept | 0.8865 | 54.865 | 0.0379 | 0.038932 | 9.9885 | | 27 | 6 | Accept | 0.0381 | 300.7 | 0.0379 | 0.037996 | 2.6027e-05 | | 28 | 6 | Accept | 0.0406 | 54.611 | 0.0379 | 0.037996 | 1.6057e-09 | | 29 | 6 | Accept | 0.1272 | 76.648 | 0.0379 | 0.037997 | 0.012507 | | 30 | 6 | Accept | 0.0403 | 57.931 | 0.0379 | 0.037997 | 4.9907e-08 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 724.6036 seconds. Total objective function evaluation time: 3674.8899 Best observed feasible point: Lambda __________ 2.8439e-05 Observed objective function value = 0.0379 Estimated objective function value = 0.03801 Function evaluation time = 295.5515 Best estimated feasible point (according to models): Lambda __________ 2.6027e-05 Estimated objective function value = 0.037997 Estimated function evaluation time = 297.6756 Loss4 = 0.0440
基于提取1000个特征的过完备稀疏滤波分类器的测试损失最小。
Mdl5 =黎加(Xtrain q'iterationlimit', 400,“标准化”,真正的);newx =变换（mdl5，xtrain）;testx =变换（mdl5，xtest）;cmdl = fitcecoc（newx，labeltrain，'学习者't．．.'OptimizeHyperParameters'，{'lambda'}，．．.“HyperparameterOptimizationOptions”、选择);丢失5 =损失（cmdl，testx，labeltest）
警告:解算器LBFGS不能收敛到一个解。复制目标函数，工人...完成复制目标函数的工人。|================================================================================================| | Iter | |活跃Eval客观客观| | | BestSoFar | BestSoFar |λ| | |工人结果| | |运行时| | (estim(观察) .) | | |================================================================================================| | 1 | 6 |最好的0.0764 |46.206 |0.0764 |0.0764 |8.4258E-09 || 2 | 6 | Accept | 0.077 | 141.95 | 0.0764 | 0.0767 | 6.9536e-06 | | 3 | 6 | Accept | 0.0771 | 146.87 | 0.0764 | 0.076414 | 7.3378e-06 | | 4 | 6 | Best | 0.0709 | 182.51 | 0.0709 | 0.0709 | 0.48851 | | 5 | 6 | Accept | 0.0764 | 46.923 | 0.0709 | 0.070903 | 5.0695e-09 | | 6 | 6 | Best | 0.068 | 294.89 | 0.068 | 0.068004 | 0.0029652 | | 7 | 6 | Accept | 0.125 | 99.095 | 0.068 | 0.068001 | 9.9814 | | 8 | 6 | Accept | 0.0693 | 321.66 | 0.068 | 0.067999 | 0.0015167 | | 9 | 6 | Accept | 0.0882 | 138.03 | 0.068 | 0.068 | 1.8203 | | 10 | 6 | Accept | 0.0753 | 285.07 | 0.068 | 0.067991 | 0.00042423 | | 11 | 6 | Accept | 0.0764 | 47.704 | 0.068 | 0.067984 | 1.6326e-07 | | 12 | 6 | Accept | 0.0763 | 46.514 | 0.068 | 0.06798 | 1.0048e-09 | | 13 | 6 | Best | 0.0643 | 252.2 | 0.0643 | 0.0643 | 0.095965 | | 14 | 6 | Accept | 0.0766 | 168.37 | 0.0643 | 0.0643 | 9.1336e-07 | | 15 | 6 | Accept | 0.0753 | 153.29 | 0.0643 | 0.064301 | 4.8641e-05 | | 16 | 6 | Accept | 0.0662 | 256.65 | 0.0643 | 0.064298 | 0.0093576 | | 17 | 6 | Best | 0.0632 | 224.2 | 0.0632 | 0.063226 | 0.031314 | | 18 | 6 | Accept | 0.0673 | 219.59 | 0.0632 | 0.063201 | 0.20528 | | 19 | 6 | Accept | 0.0637 | 244.17 | 0.0632 | 0.063208 | 0.075001 | | 20 | 6 | Accept | 0.064 | 234.85 | 0.0632 | 0.06321 | 0.081232 | |================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Lambda | | | workers | result | | runtime | (observed) | (estim.) | | |================================================================================================| | 21 | 6 | Accept | 0.0646 | 242.2 | 0.0632 | 0.063315 | 0.078081 | | 22 | 6 | Accept | 0.0633 | 217.97 | 0.0632 | 0.063233 | 0.039495 | | 23 | 6 | Accept | 0.0643 | 224.22 | 0.0632 | 0.063496 | 0.052107 | | 24 | 6 | Accept | 0.0761 | 45.102 | 0.0632 | 0.063509 | 4.3946e-08 | | 25 | 6 | Accept | 0.0645 | 221.24 | 0.0632 | 0.063778 | 0.044455 | | 26 | 6 | Accept | 0.0763 | 44.572 | 0.0632 | 0.063778 | 1.9139e-09 | | 27 | 6 | Accept | 0.0639 | 216.9 | 0.0632 | 0.063791 | 0.041759 | | 28 | 6 | Accept | 0.0766 | 45.609 | 0.0632 | 0.06379 | 2.0642e-08 | | 29 | 6 | Accept | 0.0765 | 121.35 | 0.0632 | 0.063789 | 3.5882e-07 | | 30 | 6 | Accept | 0.0636 | 215.47 | 0.0632 | 0.063755 | 0.038062 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 952.7987 seconds. Total objective function evaluation time: 5145.3787 Best observed feasible point: Lambda ________ 0.031314 Observed objective function value = 0.0632 Estimated objective function value = 0.063828 Function evaluation time = 224.2018 Best estimated feasible point (according to models): Lambda ________ 0.044455 Estimated objective function value = 0.063755 Estimated function evaluation time = 219.4845 Loss5 = 0.0748
基于具有1000个提取功能的RICA的分类器基于200提取的特征对RICA分类器具有类似的测试丢失。
通过使用优化HyperParametersBayesopt.
特征提取功能具有以下调整参数：
迭代限制
函数,要么
r或Sparsefilt.范围
lambda.学习功能的数量
问：
这fitcecoc正则化参数也会影响学习分类器的准确性。在HyperParameters列表中包含该参数。
要有效地搜索可用参数，请尝试Bayesopt.。使用以下目标函数，包括从工作区传递的参数。
函数target = filterica(x,Xtrain,Xtest,LabelTrain,LabelTest,winit) initW = winit(1:size(Xtrain,2)，1:x.q);如果char（x.solver）=='r'Mdl =黎加(Xtrain x.q,'lambda'，x.lambda，'iterationlimit'，x.iterlim，．．.“InitialTransformWeights”initW,“标准化”,真正的);其他的mdl = sparsefilt（xtrain，x.q，'lambda'，x.lambda，'iterationlimit'，x.iterlim，．．.“InitialTransformWeights”, initW);结尾Xtrain NewX =变换(Mdl);Xtest TestX =变换(Mdl);t = templateLinear ('lambda'，x.lambdareg，“规划求解”那“lbfgs”）;cmdl = fitcecoc（newx，labeltrain，'学习者'，t）;目标=损失（cmdl，testx，labeltest）;
为了消除变化源，确定一个初始变换权矩阵。
W = randn (1 e4, 1 e3);
为目标函数创建HyperParameters。
iterlim =优化不变（“iterlim”，[5,500]，“类型”那'整数'）;λ= optimizableVariable (“λ”[0, 10]);解算器= optimizableVariable (“解算器”，{'r'那'}，“类型”那“分类”）;qvar = optimizableVariable ('Q'(1000),“类型”那'整数'）;lambdareg =优化的可变（“lambdareg”(1 e-6, 1),“转换”那'日志'）;vars = [iterlim，lambda，求解器，qvar，lambdareg];
运行优化时不要出现内部优化未运行完成时出现的警告。运行60次迭代，而不是默认的30次，以使优化有更好的机会找到一个好的值。
警告(“关闭”那的统计数据:classreg:学习:fsutils:解决:LBFGSUnableToConverge”）;结果= bayesopt(@ x) filterica(x,Xtrain,Xtest,LabelTrain,LabelTest,W)，var，．．.'使用指平行'是的，“MaxObjectiveEvaluations”、60);警告('在'那的统计数据:classreg:学习:fsutils:解决:LBFGSUnableToConverge”）;
复制目标函数，工人...完成复制目标函数的工人。| ============================================================================================================================================================ ||磨练|活动|eval |目标|目标|Bestsofar |Bestsofar | iterlim | lambda | solver | q | lambdareg | | | workers | result | | runtime | (observed) | (estim.) | | | | | | |============================================================================================================================================================| | 1 | 6 | Best | 0.16408 | 33.743 | 0.16408 | 0.16408 | 140 | 9.4661 | s | 98 | 0.0007106 | | 2 | 6 | Best | 0.079213 | 51.975 | 0.079213 | 0.09064 | 10 | 9.466 | r | 685 | 0.010462 | | 3 | 6 | Best | 0.074897 | 82.031 | 0.074897 | 0.074983 | 32 | 3.7554 | r | 689 | 0.13737 | | 4 | 6 | Accept | 0.07546 | 93.221 | 0.074897 | 0.075073 | 178 | 3.9741 | r | 196 | 0.1829 | | 5 | 6 | Accept | 0.13924 | 30.444 | 0.074897 | 0.074933 | 282 | 0.36123 | r | 33 | 0.99029 | | 6 | 6 | Accept | 0.083964 | 133 | 0.074897 | 0.074933 | 58 | 9.7653 | r | 685 | 0.0014623 | | 7 | 6 | Accept | 0.08128 | 33.609 | 0.074897 | 0.074957 | 8 | 5.6351 | r | 519 | 0.0065822 | | 8 | 6 | Accept | 0.090751 | 203.96 | 0.074897 | 0.074913 | 131 | 0.73308 | r | 577 | 2.1172e-05 | | 9 | 6 | Accept | 0.090001 | 172.38 | 0.074897 | 0.074904 | 146 | 8.1899 | r | 454 | 1.4417e-05 | | 10 | 6 | Accept | 0.080191 | 316.8 | 0.074897 | 0.074897 | 164 | 0.48783 | r | 727 | 0.004936 | | 11 | 6 | Best | 0.060472 | 40.777 | 0.060472 | 0.060731 | 5 | 2.3201 | s | 530 | 1.1957e-06 | | 12 | 6 | Accept | 0.079027 | 45.841 | 0.060472 | 0.060632 | 8 | 0.55541 | r | 696 | 0.030914 | | 13 | 6 | Accept | 0.074823 | 237.43 | 0.060472 | 0.06067 | 109 | 4.5352 | r | 781 | 0.12274 | | 14 | 6 | Accept | 0.84009 | 85.121 | 0.060472 | 0.060468 | 306 | 0.59533 | s | 148 | 0.89675 | | 15 | 6 | Accept | 0.15637 | 200.13 | 0.060472 | 0.060451 | 90 | 3.0192 | s | 999 | 0.0043768 | | 16 | 6 | Accept | 0.69006 | 14.273 | 0.060472 | 0.06047 | 6 | 9.4568 | s | 407 | 0.13833 | | 17 | 6 | Accept | 0.093035 | 205.83 | 0.060472 | 0.060469 | 263 | 2.3083 | r | 308 | 1.0016e-06 | | 18 | 6 | Accept | 0.18753 | 6.0238 | 0.060472 | 0.060527 | 36 | 9.806 | s | 24 | 8.3653e-06 | | 19 | 6 | Accept | 0.119 | 749.98 | 0.060472 | 0.060751 | 482 | 0.51927 | s | 818 | 1.5416e-06 | | 20 | 6 | Accept | 0.076414 | 751.21 | 0.060472 | 0.060754 | 387 | 9.9936 | r | 784 | 0.26786 | |============================================================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | iterlim | lambda | solver | q | lambdareg | | | workers | result | | runtime | (observed) | (estim.) | | | | | | |============================================================================================================================================================| | 21 | 6 | Accept | 0.099332 | 7.2298 | 0.060472 | 0.060828 | 20 | 0.78894 | s | 49 | 1.0335e-06 | | 22 | 6 | Accept | 0.090139 | 7.9815 | 0.060472 | 0.060858 | 11 | 3.2973 | r | 88 | 2.7437e-06 | | 23 | 6 | Accept | 0.076696 | 323.64 | 0.060472 | 0.060872 | 120 | 1.9199 | r | 999 | 0.2537 | | 24 | 6 | Accept | 0.098003 | 50.544 | 0.060472 | 0.060876 | 492 | 1.7197 | r | 27 | 0.00020896 | | 25 | 6 | Accept | 0.10383 | 56.568 | 0.060472 | 0.06101 | 11 | 5.256 | s | 971 | 0.00054471 | | 26 | 6 | Accept | 0.14405 | 30.426 | 0.060472 | 0.060797 | 477 | 5.5475 | r | 12 | 0.022342 | | 27 | 6 | Accept | 0.09046 | 53.398 | 0.060472 | 0.060815 | 13 | 2.1216 | r | 986 | 1.1811e-06 | | 28 | 6 | Best | 0.051641 | 99.452 | 0.051641 | 0.051368 | 23 | 2.6976 | s | 985 | 1.0558e-06 | | 29 | 6 | Accept | 0.10016 | 6.4162 | 0.051641 | 0.051365 | 6 | 3.7223 | r | 69 | 9.2926e-05 | | 30 | 6 | Accept | 0.10943 | 40.676 | 0.051641 | 0.051391 | 488 | 5.2092 | r | 19 | 2.4162e-05 | | 31 | 6 | Accept | 0.086761 | 7.8419 | 0.051641 | 0.051393 | 24 | 6.5535 | r | 42 | 0.0013244 | | 32 | 6 | Best | 0.0504 | 96.816 | 0.0504 | 0.050526 | 14 | 9.929 | s | 1000 | 2.8809e-06 | | 33 | 6 | Accept | 0.088789 | 81.158 | 0.0504 | 0.050525 | 14 | 1.0441 | r | 927 | 0.00021061 | | 34 | 6 | Accept | 0.083083 | 887.17 | 0.0504 | 0.05052 | 351 | 6.8834 | r | 978 | 0.0026404 | | 35 | 6 | Best | 0.050023 | 99.493 | 0.050023 | 0.050372 | 19 | 9.9813 | s | 899 | 1.0257e-06 | | 36 | 6 | Accept | 0.053338 | 113.36 | 0.050023 | 0.050499 | 7 | 4.7855 | s | 984 | 1.8611e-06 | | 37 | 6 | Accept | 0.089024 | 70.047 | 0.050023 | 0.0505 | 15 | 8.8301 | r | 984 | 6.0636e-06 | | 38 | 6 | Accept | 0.052029 | 95.822 | 0.050023 | 0.050551 | 7 | 9.759 | s | 996 | 3.7871e-06 | | 39 | 6 | Accept | 0.085992 | 73.422 | 0.050023 | 0.050528 | 5 | 2.7837 | r | 968 | 0.004483 | | 40 | 6 | Accept | 0.091159 | 5.8348 | 0.050023 | 0.05052 | 15 | 8.7732 | r | 37 | 0.084632 | |============================================================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | iterlim | lambda | solver | q | lambdareg | | | workers | result | | runtime | (observed) | (estim.) | | | | | | |============================================================================================================================================================| | 41 | 6 | Best | 0.046444 | 152.93 | 0.046444 | 0.047062 | 30 | 4.0843 | s | 997 | 7.279e-06 | | 42 | 6 | Accept | 0.052712 | 58.107 | 0.046444 | 0.04698 | 12 | 0.99592 | s | 652 | 1.0258e-06 | | 43 | 6 | Accept | 0.058005 | 91.928 | 0.046444 | 0.047263 | 10 | 5.511 | s | 1000 | 2.4589e-05 | | 44 | 6 | Accept | 0.055413 | 103.25 | 0.046444 | 0.047306 | 7 | 5.6791 | s | 953 | 1.4656e-06 | | 45 | 6 | Accept | 0.052517 | 96.201 | 0.046444 | 0.049604 | 10 | 5.9403 | s | 996 | 1.0525e-05 | | 46 | 6 | Accept | 0.089527 | 76.617 | 0.046444 | 0.046888 | 20 | 1.0744 | r | 965 | 0.96766 | | 47 | 6 | Accept | 0.050062 | 99.709 | 0.046444 | 0.046735 | 12 | 9.9236 | s | 975 | 4.5916e-06 | | 48 | 6 | Accept | 0.21166 | 90.117 | 0.046444 | 0.049716 | 495 | 1.1996 | s | 86 | 0.00022338 | | 49 | 6 | Accept | 0.054535 | 79.1 | 0.046444 | 0.046679 | 6 | 0.22929 | s | 967 | 7.6974e-06 | | 50 | 6 | Accept | 0.12385 | 964.74 | 0.046444 | 0.049963 | 474 | 4.7085 | s | 991 | 8.6984e-05 | | 51 | 6 | Accept | 0.052016 | 76.098 | 0.046444 | 0.049914 | 10 | 1.0798 | s | 922 | 1.133e-06 | | 52 | 6 | Accept | 0.048984 | 95.054 | 0.046444 | 0.049891 | 12 | 4.69 | s | 976 | 1.0189e-06 | | 53 | 6 | Accept | 0.1948 | 889.11 | 0.046444 | 0.047903 | 466 | 7.9582 | s | 986 | 0.0012319 | | 54 | 6 | Accept | 0.10652 | 5.076 | 0.046444 | 0.047961 | 10 | 5.9107 | r | 40 | 0.52677 | | 55 | 6 | Accept | 0.074194 | 319.41 | 0.046444 | 0.04981 | 130 | 2.6437 | s | 997 | 7.8756e-06 | | 56 | 6 | Accept | 0.1014 | 45.184 | 0.046444 | 0.049828 | 480 | 6.1835 | r | 24 | 2.0019e-06 | | 57 | 6 | Accept | 0.33214 | 3.1996 | 0.046444 | 0.049785 | 12 | 7.4538 | s | 13 | 0.016248 | | 58 | 6 | Accept | 0.054348 | 96.616 | 0.046444 | 0.050832 | 12 | 2.8605 | s | 987 | 4.7951e-06 | | 59 | 6 | Accept | 0.71471 | 3.0555 | 0.046444 | 0.050852 | 10 | 9.8909 | s | 24 | 0.21362 | | 60 | 6 | Accept | 0.074353 | 67.118 | 0.046444 | 0.05084 | 8 | 5.5275 | s | 986 | 8.9716e-05 | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 60 reached. Total function evaluations: 60 Total elapsed time: 1921.1117 seconds. Total objective function evaluation time: 9107.7006 Best observed feasible point: iterlim lambda solver q lambdareg _______ ______ ______ ___ _________ 30 4.0843 s 997 7.279e-06 Observed objective function value = 0.046444 Estimated objective function value = 0.053743 Function evaluation time = 152.932 Best estimated feasible point (according to models): iterlim lambda solver q lambdareg _______ ______ ______ ___ _________ 10 1.0798 s 922 1.133e-06 Estimated objective function value = 0.05084 Estimated function evaluation time = 90.9315
产生的分类器没有比使用的分类器有更好(更低)的损失Sparsefilt.对于1000个特性，经过10次迭代的训练。
查看过滤器系数的最佳超参数Bayesopt.发现。生成的图像显示了所提取特征的形状。这些形状可以识别为手写数字的一部分。
Xtbl = results.XAtMinObjective;Q = Xtbl.q;initW = W(1:尺寸(Xtrain, 2), 1:问);如果char (Xtbl.solver) = ='r'Mdl =黎加(Xtrain Q'lambda'Xtbl.lambda,'iterationlimit'Xtbl.iterlim,．．.“InitialTransformWeights”initW,“标准化”,真正的);其他的mdl = sparsefilt（xtrain，q，'lambda'Xtbl.lambda,'iterationlimit'Xtbl.iterlim,．．.“InitialTransformWeights”, initW);结尾但是= Mdl.TransformWeights;但是=重塑(Wts,[问]28日28日);(dx, dy, ~, ~) = (Wts)大小;为了Wvec = Wts(:，:，f);Wvec = Wvec (:);Wvec = (Wvec - min (Wvec)) / (max (Wvec) - min (Wvec));但是(::f) =重塑(Wvec, dx, dy);结尾m = CEIL（SQRT（Q））;n = m;IMG =零（m * dx，n * dy）;f = 1;为了i = 1: m为了j = 1：n如果（f <= q）img（（i-1）* dx + 1：i * dx，（j-1）* dy + 1：j * dy，:) = wts（：：，f）;f = f + 1;结尾结尾结尾imshow (img);
警告:解算器LBFGS不能收敛到一个解。
读取mist数据的代码
将数据读入工作区的函数的代码是：
函数[x，l] = processmnistdata（imagefilename，labelfilename）[fileId，ertmsg] = fopen（imagefilename，'r'那“b”）;如果fileID < 0错误(errmsg);结尾%%先读这个神奇的数字。对于图像数据，这个数字是2051％2049用于标签数据MagicNum = fread（fileid，1，“int32”0,“b”）;如果magicNum == 2051 fprintf('\nRead mist图像数据…\n'）结尾%%%然后读取图像数量、行数、列数numImages =从文件中读(文件标识,1“int32”0,“b”）;流('数据集中的图像数量:%6d…\n', numImages);numRows =从文件中读(文件标识,1“int32”0,“b”）;numCols =从文件中读(文件标识,1“int32”0,“b”）;流(“每个图像是%2d × %2d像素……\n”，numrows，numcols）;%%%读取镜像数据X =从文件中读(inf文件标识,'无符号的字符'）;%%%将数据重塑为数组XX =重塑(X, numCols numRows numImages);X = permute(X，[2 1 3]);%%然后，％将每个图像数据达到1（numrows * numcols）向量，%将所有图像数据存储到一个numImages by (numRows*numCols)数组中。X =重塑(X, numRows * numCols numImages) ';fprintf（['图像数据被读取为一个维度矩阵:%6d by %4d…\n'那．．.'阅读图像数据结束。\ n'),大小(X, 1),大小(X, 2));%%%关闭文件fclose（fileid）;%%％同样，读取标签数据。[fileid，ertmsg] = fopen（Labelfilename，'r'那“b”）;如果fileID < 0错误(errmsg);结尾MagicNum = fread（fileid，1，“int32”0,“b”）;如果magicNum == 2049 fprintf('\nRead nist label data…\n'）结尾numItems =从文件中读(文件标识,1“int32”0,“b”）;流('数据集中的标签数量:%6d…\n', numItems);L =从文件中读(inf文件标识,'无符号的字符'）;fprintf（['标签数据被读取到一个维度为:%6d by %2d…\n'那．．.'读取标签数据结束。\n'),大小(L, 1),大小(L, 2));fclose（fileid）;
参考
Yann LeCun (Courant Institute, NYU)和Corinna Cortes(谷歌Labs, New York)拥有MNIST数据集的版权，该数据集是NIST原始数据集的衍生作品。MNIST数据集是在知识共享署名-共享相似3.0许可条款下提供的，https://creativecommons.org/licenses/by-sa/3.0/
也可以看看
重建|r|Sparsefilt.|SparseFiltering
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