在電腦文件夾E:\other\matlab 2007a\work\SVM\libsvm-mat-3.0-1 ，這個是已經編譯好的，到64位機上要重新編譯(不要利用別人傳的，因為可能改過SVM程序，例如Libing wang他改過其中程序，最原始版本：E:\other\matlab 2007a\work\SVM\libsvm-mat-3.0-1.zip,從http://www.csie.ntu.edu.tw/~cjlin/libsvm/matlab/libsvm-mat-3.0-1.zip下載)。svmtrain在matlab自帶的工具箱中也有這個函數， libing 講libsvm-mat-3.0-1放到C:\Program Files\MATLAB\R2010a\toolbox\目錄，再adddpath和savepath即可。如果產生以下問題：每次都要 adddpath和savepath ，在matlab重新啟動后要重新
adddpath和savepath。解決方案：可以在要運行的程序前面添加如下語句即可：
addpath('C:\Program Files\MATLAB\R2010a\toolbox\libsvm-mat-3.0-1');
README文件寫得很好，其中的Examples完全理解(包括Precomputed Kernels.Constructing a linear kernel matrix and then using the precomputed kernel gives exactly the same testing error as using the LIBSVM built-in linear kernel.核就是相似度，自己想定義什么相似度都可以)
(1) model = svmtrain(training_label_vector, training_instance_matrix [, 'libsvm_options']);
libsvm_options的設置：
Examples of options: -s 0 -c 10 -t 1 -g 1 -r 1 -d 3
Classify a binary data with polynomial kernel (u'v+1)^3 and C = 10
options:
-s svm_type : set type of SVM (default 0)
0 -- C-SVC
1 -- nu-SVC
2 -- one-class SVM
3 -- epsilon-SVR
4 -- nu-SVR
C-SVC全稱是什么？
C-SVC(C-support vector classification),nu-SVC(nu-support vector classification),one-class SVM(distribution estimation),epsilon-SVR(epsilon-support vector regression),nu-SVR(nu-support vector regression)
-t kernel_type : set type of kernel function (default 2)
0 -- linear: u'*v
1 -- polynomial: (gamma*u'*v + coef0)^degree
2 -- radial basis function: exp(-gamma*|u-v|^2)
3 -- sigmoid: tanh(gamma*u'*v + coef0)
-d degree : set degree in kernel function (default 3)
-g gamma : set gamma in kernel function (default 1/num_features)
-r coef0 : set coef0 in kernel function (default 0)
-c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)
-n nu : set the parameter nu of nu-SVC, one-class SVM, and nu-SVR (default 0.5)
-p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)
-m cachesize : set cache memory size in MB (default 100)
-e epsilon : set tolerance of termination criterion (default 0.001)
-h shrinking: whether to use the shrinking heuristics, 0 or 1 (default 1)
-b probability_estimates: whether to train a SVC or SVR model for probability estimates, 0 or 1 (default 0)
-wi weight: set the parameter C of class i to weight*C, for C-SVC (default 1)
The k in the -g option means the number of attributes in the input data.
(2)如何采用線性核？
matlab> % Linear Kernel
matlab> model_linear = svmtrain(train_label, train_data, '-t 0');
嚴格講，線性核也要像高斯核一樣調整c這個參數，Libing wang講一般C=1效果比較好，可能調整效果差異不大，當然要看具體的數據集。c大，從SVM目標函數可以看出，c越大，相當于懲罰松弛變量，希望松弛變量接近0，即都趨向于對訓練集全分對的情況，這樣對訓練集測試時準確率很高，但推廣能力未必好，即在測試集上未必好。c小點，相當于邊界的有些點容許分錯，將他們當成噪聲點，這樣外推能力比較好。
(3)如何采用高斯核？
matlab> load heart_scale.mat
matlab> model = svmtrain(heart_scale_label, heart_scale_inst, '-c 1 -g 0.07');
高斯的SVM比線性SVM效果要差，為什么？
20150420 libing討論，可能的解釋：樣本少，不適合高斯核。范圍有限，也許更廣泛的參數范圍會有更好的效果
(4)如何實現交叉驗證？
README文件有如下一句話：If the '-v' option is specified, cross validation is
conducted and the returned model is just a scalar: cross-validation
accuracy for classification and mean-squared error for regression.
(5) 如何調整高斯核的兩個參數？
思路1：在訓練集上調整兩個參數使在訓練集上測試錯誤率最低，就選這樣的參數來測試測試集
思路1的問題：Libing Wang講這樣很容易過學習，因為在訓練集上很容易達到100%準確率，但在測試集上未必好，即過學習。用思路2有交叉驗證，推廣性能比較好(交叉驗證將訓練集隨機打亂，推廣性能很好)
思路2：% E:\other\matlab 2007a\work\DCT\DCT_original\network.m
思路2的問題：針對不同的數據集，這兩個參數分別在什么范圍內調整,有沒有什么經驗？
方式1：就是network.m中gamma的取值
方式2：http://www.shnenglu.com/guijie/archive/2010/12/02/135243.html.
其他答案：除了在訓練集上做交叉驗證，還有另外一種思路：類似A Regularized Approach to Feature Selection for Face Detection (ACCV 2007)的4.2節:訓練集、驗證集和測試集，Libing講該文4.2節調參數除了分成訓練集、驗證集和測試集，沒有其他什么的。Libing講在訓練集上交叉驗證也相當于訓練集挑了一部分做驗證，原理一樣。
(6)如何采用預定義核？
To use precomputed kernel, you must include sample serial number asthe first column of the training and testing data (assume your kernel matrix is K, # of instances is n):
matlab> K1 = [(1:n)', K]; % include sample serial number as first column
matlab> model = svmtrain(label_vector, K1, '-t 4');
matlab> [predict_label, accuracy, dec_values] = svmpredict(label_vector, K1, model); % test the training data
We give the following detailed example by splitting heart_scale into 150 training and 120 testing data. Constructing a linear kernel matrix and then using the precomputed kernel gives exactly the same testing error as using the LIBSVM built-in linear kernel.
matlab> load heart_scale.mat
matlab>
matlab> % Split Data
matlab> train_data = heart_scale_inst(1:150,:);
matlab> train_label = heart_scale_label(1:150,:);
matlab> test_data = heart_scale_inst(151:270,:);
matlab> test_label = heart_scale_label(151:270,:);
matlab>
matlab> % Linear Kernel
matlab> model_linear = svmtrain(train_label, train_data, '-t 0');
matlab> [predict_label_L, accuracy_L, dec_values_L] = svmpredict(test_label, test_data, model_linear);
matlab>
matlab> % Precomputed Kernel
matlab> model_precomputed = svmtrain(train_label, [(1:150)', train_data*train_data'], '-t 4');
matlab> [predict_label_P, accuracy_P, dec_values_P] = svmpredict(test_label, [(1:120)', test_data*train_data'], model_precomputed);
matlab>
matlab> accuracy_L % Display the accuracy using linear kernel
matlab> accuracy_P % Display the accuracy using precomputed kernel
(7)如何實現概率估計？
For probability estimates, you need '-b 1' for training and testing:
matlab> load heart_scale.mat
matlab> model = svmtrain(heart_scale_label, heart_scale_inst, '-c 1 -g 0.07 -b 1');
matlab> load heart_scale.mat
matlab> [predict_label, accuracy, prob_estimates] = svmpredict(heart_scale_label, heart_scale_inst, model, '-b 1');
非概率估計
matlab> load heart_scale.mat
matlab> model = svmtrain(heart_scale_label, heart_scale_inst, '-c 1 -g 0.07');
matlab> [predict_label, accuracy, dec_values] = svmpredict(heart_scale_label, heart_scale_inst, model); % test the training data
(8) svmpredict的用法(摘自libsvm-mat-2.9-1的README)
[predicted_label, accuracy, decision_values/prob_estimates] = svmpredict(testing_label_vector, testing_instance_matrix, model [, 'libsvm_options']);
輸入：testing_label_vector， If labels of test data are unknown, simply use any random values. (type must be double)。模型一旦確定，預測的標記就確定了，如果不利用第二個輸出accuracy，則testing_label_vector隨便設置，當然如果要利用accuracy，就要將testing_label_vector設置成測試標記了。(Action recognition\ASLAN database中的代碼CLSlibsvmC，第九行用到svmpredict，testing_label_vector設置成ones(size(Samples,2),1)，是無所謂的)。
svmpredict輸出的含義：
predictd_label, is a vector of predicted labels(故CLSlibsvmC的12到14行沒用);
胥志偉I-Rising(285308540) 2015/5/31 21:56:30
各位老師，同學。請問有人研究過svm 中predict的decision value嗎？麻煩幫忙解釋下怎么計算的。謝謝。
蘇松志-T-廈大(14291414) 2015/5/31 22:04:40
指的是libsvm？優化完之后得到每個支持向量的alph_i,然后，計算輸入的x和各個支持向量的核函數距離ki，sum(ki*alph_i*yi) for all SUPPORT VECTORS,+b,就是按照教科書上的公式
說明：以上understand completely,對應楊光正教材P28公式(2.54)
胥志偉I-Rising(285308540) 2015/5/31 22:08:30
多類的問題也是這樣嗎？
蘇松志-T-廈大(14291414) 2015/5/31 22:13:41
是的，多類采用的是1vs1，所有里面的sv_coef是一個mxn的矩陣，m：支持向量的數目，n： 類別數目-1，然后有一個rho向量，套用公式，計算
摘自libsvm-mat-3.0-1的README
The function 'svmpredict' has three outputs. The first one, predictd_label, is a vector of predicted labels. The second output, accuracy, is a vector including accuracy (for classification), mean squared error, and squared correlation coefficient (for regression). The third is a matrix containing decision values or probability estimates (if '-b 1' is specified).
If k is the number of classes, for decision values, each row includes results of predicting
k(k-1)/2 binary-class SVMs.
For probabilities, each row contains k values indicating the probability that the testing instance is in each class. Note that the order of classes here is the same as 'Label' field in the model structure.
(9)LibSVM是如何采用one-versus-rest和one-verse-one實現多類分類的？one-versus-rest和one-verse-one的定義見模式識別筆記第四頁反面(同時見孫即祥教材P47)。找libing wang和junge zhang,他們都講沒對這個深究過。根據“If k is the number of classes, for decision values, each row includes results of predicting
k(k-1)/2 binary-class SVMs.
For probabilities, each row contains k values indicating the probability that the testing instance is in each class. ”，我覺得應該是
probabilities實現的是one-versus-rest，即采用-b 1這個選項，他倆都覺得我理解應該是正確的。junge講參加pascal競賽和imagenet，他們都是訓練k個SVM(即one-versus-rest,沒用one-versus-one,后者太慢，而且估計效果差不多)，沒有直接采用SVM做多類問題。
20130910 LibSVM作者回信：
Libsvm implements only 1vs1.For 1vsrest, you can check the followinglibsvm faqQ: LIBSVM supports 1-vs-1 multi-class classification. If instead I wouldlike to use 1-vs-rest, how to implement it using MATLAB interface?
網址：http://www.csie.ntu.edu.tw/~cjlin/libsvm/faq.html#f808
Q: LIBSVM supports 1-vs-1 multi-class classification. If instead I would like to use 1-vs-rest, how to implement it using MATLAB interface?
Please use code in the following directory. The following example shows how to train and test the problem dna (training and testing).
Load, train and predict data:
[trainY trainX] = libsvmread('./dna.scale');
[testY testX] = libsvmread('./dna.scale.t');
model = ovrtrain(trainY, trainX, '-c 8 -g 4');
[pred ac decv] = ovrpredict(testY, testX, model);
fprintf('Accuracy = %g%%\n', ac * 100); Conduct CV on a grid of parametersbestcv = 0;
for log2c = -1:2:3,
for log2g = -4:2:1,
cmd = ['-q -c ', num2str(2^log2c), ' -g ', num2str(2^log2g)];
cv = get_cv_ac(trainY, trainX, cmd, 3);
if (cv >= bestcv),
bestcv = cv; bestc = 2^log2c; bestg = 2^log2g;
end
fprintf('%g %g %g (best c=%g, g=%g, rate=%g)\n', log2c, log2g, cv, bestc, bestg, bestcv);
end
end
(9)如何實現驗證模式下的準確率？見我寫的程序RVM\code\Yale\SVM\TestYale_SVM_2classes
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MATLAB自帶的svm實現函數與libsvm差別小議
1 MATLAB自帶的svm實現函數僅有的模型是C-SVC(C-support vector classification)； 而libsvm工具箱有C-SVC(C-support vector classification),nu-SVC(nu-support vector classification),one-class SVM(distribution estimation),epsilon-SVR(epsilon-support vector regression),nu-SVR(nu-support vector regression)等多種模型可供使用。 2 MATLAB自帶的svm實現函數僅支持分類問題，不支持回歸問題；而libsvm不僅支持分類問題，亦支持回歸問題。 3 MATLAB自帶的svm實現函數僅支持二分類問題，多分類問題需按照多分類的相應算法編程實現；而libsvm采用1v1算法支持多分類。 4 MATLAB自帶的svm實現函數采用RBF核函數時無法調節核函數的參數gamma，貌似僅能用默認的；而libsvm可以進行該參數的調節。 5 libsvm中的二次規劃問題的解決算法是SMO；而MATLAB自帶的svm實現函數中二次規劃問題的解法有三種可以選擇：經典二次方法；SMO；最小二乘。（這個是我目前發現的MATLAB自帶的svm實現函數唯一的優點~） SVM 理論部分
SVM下面推導核化形式(Eric Xing教材)+M. Belkin, P. Niyogi, and V. Sindhwani, “Manifold Regularization: AGeometric Framework for Learning from Labeled and Unlabeled Examples,” J. Machine Learning Research, vol. 7, pp. 2399-2434, 2006的4.3和4.4節.+Ensemble Manifold Regularization (TPAMI 2012)
電腦里的"ZhuMLSS14.pdf
"是很好的入門材料