rbf预测matlab代码-SSVM-demo:SSVM演示

# Smooth Support Vector Machine Toolbox ## Introduction SSVM toolbox is an implementation of Smooth Support Vector Machine in Matlab. SSVM is a reformulation of conventional SVM and can be solved by a fast Newton-Armijo algorithm. Besides, choosing a good parameter setting for a better performance in a learning task is an important issue. We also provide an automatic model selection tool to help users to get a good parameter setting. SSVM toolbox now includes [smooth support vector machine](paper/ssvm.pdf) for classification, [epsilon-insensitive smooth support vector regression](paper/SSVR_TKDE.pdf) and an automatic [model selection tool using uniform design](paper/UD4SVM013006.pdf). ## Key Features * Solve classification ([SSVM](src/SSVM_M.m)) and regression ([SSVR](src/SSVR_M.m)) problems * Support linear, polynomial and radial basis kernels * Provide an automatic model selection for SSVM and SSVR with RBF kernels * Can handle large scale problems by using reduced kernel (RSVM) * Provide cross validation evaluation * Provide an alternative initial point other than zero using regularized least squares ## Download SSVM Toolbox * [Matlab implementation](src/SSVMtoolbox/matlab) * [Python implementation](src/SSVMtoolbox/python) * [R implementation](src/SSVMtoolbox/r) ## Data Format SSVM toolbox is implemented in Matlab. Use a data format which can be loaded into Matlab. The instances are represented by a matrix (rows for instances and columns for variables) and the labels (1 or -1) or responses are represented by a column vector. For classification <p align="center"> </p> For regression <p align="center"> </p> Here are some sample datasets. ## Code Usage SSVM toolbox contains three main functions： ssvm_train for SVMs training, ssvm_predict for SVMs prediction and hibiscus for automatic model selection. ### Usage of ssvm_train `model = ssvm_train(label, inst, 'options')` #### Input of ssvm_train: Variable | Description ---- | ---- label | training data class label or response inst | training data inputs #### Options: Variable | Description ---- | ---- -s | learning algorithm (default: 0)<br/> 0-SSVM<br/> 1-SSVR -t | kernel type (default: 2)<br/> 0-linear <br/> 1-polynomial <br/> 2-radial basis (Gaussian kernel) -c | the weight parameter C of SVMs (default: 100) -e | epsilon-insensitive value in epsilon-SVR (default: 0.1) -g | gamma in kernel function (default: 0.1) -d | degree of polynomial kernel function (default: 2) -b | constant term of polynomial kernel function (default: 0) -m | scalar factor of polynomial kernel function (default: 1) -r | ratio of random subset size to the full data size (default: 1) -i | alternatives initial point (default: 0) <br/> 0-using zero vector (w = 0, b = 0)<br/> 1-using an initial point obtained from regularized least squares -v | number of cross-validation folds (default: 0) #### Output of ssvm_train: Variable | Description ---- | ---- model | learning model (a structure in Matlab) .w | normal vector of separating (or response) hyperplane .b | bias term .RS | reduced set .Err | error rate (a structure in Matlab) .Training | training error .Validation | validation error .Final | final model error <br/> in classification, it returns the error rate <br/> in regression, it returns the relative 2-norm error and the mean absolute error .params | parameters specified by the user inputs #### Example: * Classification using a Gaussian kernel `model = ssvm_train(label, inst, 'options')` * Classification using a polynomial kernel and an initial point by regularized least squares `model_two = ssvm_train(label, inst, '-s 0 -t 1 -c 23.71 -d 2 -m 3 -b 2 -i 1')` * SClassification using a Gaussian kernel and a 10% reduced set `model_three = ssvm_train(label, inst, '-s 0 -t 2 -c 421 -g 0.31 -r 0.1')` * Classification using a Gaussian kernel in a 5-fold cross validation `model_four = ssvm_train(label, inst, '-s 0 -t 2 -c 23.71 -g 0.0625 -v 5')` * Regression using the Gaussian kernel `model_five = ssvm_train(label, inst, '-s 1 -t 2 -c 10000 -g 0.71')` ### Usage of ssvm_predict `[PredictedLabel, ErrRate ]= ssvm_predict(label, inst, model)` #### Input of ssvm_predict: Variable | Description ---- | ---- label | testing data class label or response inst | testing data inputs model | model learned from ssvm_train or user-specified #### Output of ssvm_predict: Variable | Description ---- | ---- Predicted | Labelpredicted label or response ErrRate | error rate (for classification) or relative 2-norm error (for regression) #### Example: * prediction using model_one (classification problem) `[PredictedLabel, ErrRate]=ssvm_predict(label, inst, model_one)` (Note: In this case, the error rate is meaningless.) * prediction using model_one without testing labels(classification problem) `[PredictedLabel, ErrRate]=ssvm_predict(zeros(NumOfInstm,1), inst, model_one)` * prediction using model_five (regression problem) `[PredictedLabel, ErrRate]=ssvm_predict(label, inst, model_five)` ### Usage of hibiscus `Result = hibiscus(label, inst, 'method', 'type', 'command')` Note：only for Gaussian kernel #### Input of hibiscus: Variable | Description ---- | ---- label | training data class label or response inst | training data inputs method | learning algorithm (default: 'SSVM') <br/> It must be {'SSVM', 'SSVR'} (case insensitive) type | model selection methods (default: 'UD') <br/> It must be {'UD', 'GRID'} (case insensitive) command | (optional) <br/> -v: number of cross-validation folds (default: 5)<br/> -r: ratio of random subset size to full data size (default: 1) #### Output of hibiscus: Variable | Description ---- | ---- Result | Include all returned information (a structure in Matlab) .TErr | Training Error .VErr | Validation Error .Best_C | The best C in our model selection method .Best_Gamma | The best gamma in our model selection method .Elapse | CPU time in seconds .Points | Trying points .Ratio | Ratio of random subset size to full data size #### Example: * Determine C and Gamma by a 5-fold cross-validation and the full kernel for classification `Result = hibiscus(label, inst, 'SSVM', 'UD', '-v 5 -r 1')` * Determine C and Gamma by a 10-fold cross-validation and a 10% reduced kernel for classification `Result = hibiscus(label, inst, 'SSVM', 'UD', '-v 10 -r 0.1')` * Determine C and Gamma by a 10-fold cross-validation and 10% reduced kernel for regression `Result = hibiscus(label, inst, 'SSVR', 'UD', '-v 10 -r 0.1')` ### Training and Testing Procedure #### Classification procedure 1. Change your current directory to SSVMtoolbox folder 2. Load dataset from Ionosphere_dataset.mat (can be found in SSVMtoolbox) ``` load Ionosphere_dataset.mat ``` 3. Determine good C and gamma via a 5-fold cross validation using full kernel ``` Result = hibiscus(label, inst, 'SSVM', 'UD', '-v 5 -r 1'); ``` 4. Read the contents of Result (Best_C, Best_Gamma, ...etc) ``` Result Result.Best_C ``` 5. Training a model by using Best_C and Best_Gamma in Result ``` model = ssvm_train(label, inst, '-s 0 -t 2 -c 10 -g 0.0856'); ``` 6. Read the contents of model (w, b, parameters, ...etc) ``` model model.w ``` 7. Prediction using the model obtained from the training process (here, we use the training set as the testing set) ``` [PredictedLabel, ErrRate]=ssvm_predict(label, inst, model); ``` #### Regression procedure 1. Change your current directory to SSVMtoolbox folder 2. Load dataset from housing_dataset.txt (can be found in SSVMtoolbox) ``` load housing_dataset.txt ``` 3. Split the housing data into inst and label ``` inst = housing_dataset(:,1:13); label = housing_dataset(:,14); ``` 4. Determine good C and gamma via a 5-fold cross validation and 10% reduced kernel ``` Result = hibiscus(label, inst, 'SSVR', 'UD', '-v 5 -r 0.1'); ``` 5. Read the contents of