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Merge remote-tracking branch 'upstream/3.4' into merge-3.4
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Alexander Alekhin
@@ -92,81 +92,175 @@ You may also find the source code in `samples/cpp/tutorial_code/ml/non_linear_sv
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@note The following code has been implemented with OpenCV 3.0 classes and functions. An equivalent version of the code
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using OpenCV 2.4 can be found in [this page.](http://docs.opencv.org/2.4/doc/tutorials/ml/non_linear_svms/non_linear_svms.html#nonlinearsvms)
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@include cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp
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@add_toggle_cpp
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- **Downloadable code**: Click
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[here](https://github.com/opencv/opencv/tree/master/samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp)
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- **Code at glance:**
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@include samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp
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@end_toggle
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@add_toggle_java
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- **Downloadable code**: Click
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[here](https://github.com/opencv/opencv/tree/master/samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java)
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- **Code at glance:**
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@include samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java
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@end_toggle
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@add_toggle_python
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- **Downloadable code**: Click
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[here](https://github.com/opencv/opencv/tree/master/samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py)
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- **Code at glance:**
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@include samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py
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@end_toggle
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Explanation
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-----------
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-# __Set up the training data__
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- __Set up the training data__
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The training data of this exercise is formed by a set of labeled 2D-points that belong to one of
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two different classes. To make the exercise more appealing, the training data is generated
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randomly using a uniform probability density functions (PDFs).
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The training data of this exercise is formed by a set of labeled 2D-points that belong to one of
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two different classes. To make the exercise more appealing, the training data is generated
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randomly using a uniform probability density functions (PDFs).
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We have divided the generation of the training data into two main parts.
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We have divided the generation of the training data into two main parts.
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In the first part we generate data for both classes that is linearly separable.
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp setup1
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In the first part we generate data for both classes that is linearly separable.
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In the second part we create data for both classes that is non-linearly separable, data that
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overlaps.
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp setup2
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp setup1
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@end_toggle
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-# __Set up SVM's parameters__
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java setup1
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@end_toggle
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@note In the previous tutorial @ref tutorial_introduction_to_svm there is an explanation of the
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attributes of the class @ref cv::ml::SVM that we configure here before training the SVM.
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py setup1
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@end_toggle
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp init
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In the second part we create data for both classes that is non-linearly separable, data that
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overlaps.
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There are just two differences between the configuration we do here and the one that was done in
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the previous tutorial (@ref tutorial_introduction_to_svm) that we use as reference.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp setup2
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@end_toggle
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- _C_. We chose here a small value of this parameter in order not to punish too much the
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misclassification errors in the optimization. The idea of doing this stems from the will of
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obtaining a solution close to the one intuitively expected. However, we recommend to get a
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better insight of the problem by making adjustments to this parameter.
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java setup2
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@end_toggle
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@note In this case there are just very few points in the overlapping region between classes.
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By giving a smaller value to __FRAC_LINEAR_SEP__ the density of points can be incremented and the
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impact of the parameter _C_ explored deeply.
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py setup2
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@end_toggle
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- _Termination Criteria of the algorithm_. The maximum number of iterations has to be
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increased considerably in order to solve correctly a problem with non-linearly separable
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training data. In particular, we have increased in five orders of magnitude this value.
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- __Set up SVM's parameters__
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-# __Train the SVM__
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@note In the previous tutorial @ref tutorial_introduction_to_svm there is an explanation of the
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attributes of the class @ref cv::ml::SVM that we configure here before training the SVM.
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We call the method @ref cv::ml::SVM::train to build the SVM model. Watch out that the training
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process may take a quite long time. Have patiance when your run the program.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp init
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@end_toggle
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp train
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java init
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@end_toggle
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-# __Show the Decision Regions__
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py init
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@end_toggle
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The method @ref cv::ml::SVM::predict is used to classify an input sample using a trained SVM. In
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this example we have used this method in order to color the space depending on the prediction done
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by the SVM. In other words, an image is traversed interpreting its pixels as points of the
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Cartesian plane. Each of the points is colored depending on the class predicted by the SVM; in
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dark green if it is the class with label 1 and in dark blue if it is the class with label 2.
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There are just two differences between the configuration we do here and the one that was done in
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the previous tutorial (@ref tutorial_introduction_to_svm) that we use as reference.
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show
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- _C_. We chose here a small value of this parameter in order not to punish too much the
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misclassification errors in the optimization. The idea of doing this stems from the will of
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obtaining a solution close to the one intuitively expected. However, we recommend to get a
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better insight of the problem by making adjustments to this parameter.
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-# __Show the training data__
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@note In this case there are just very few points in the overlapping region between classes.
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By giving a smaller value to __FRAC_LINEAR_SEP__ the density of points can be incremented and the
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impact of the parameter _C_ explored deeply.
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The method @ref cv::circle is used to show the samples that compose the training data. The samples
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of the class labeled with 1 are shown in light green and in light blue the samples of the class
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labeled with 2.
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- _Termination Criteria of the algorithm_. The maximum number of iterations has to be
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increased considerably in order to solve correctly a problem with non-linearly separable
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training data. In particular, we have increased in five orders of magnitude this value.
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show_data
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- __Train the SVM__
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-# __Support vectors__
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We call the method @ref cv::ml::SVM::train to build the SVM model. Watch out that the training
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process may take a quite long time. Have patiance when your run the program.
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We use here a couple of methods to obtain information about the support vectors. The method
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@ref cv::ml::SVM::getSupportVectors obtain all support vectors. We have used this methods here
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to find the training examples that are support vectors and highlight them.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp train
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@end_toggle
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@snippet cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show_vectors
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java train
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py train
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@end_toggle
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- __Show the Decision Regions__
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The method @ref cv::ml::SVM::predict is used to classify an input sample using a trained SVM. In
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this example we have used this method in order to color the space depending on the prediction done
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by the SVM. In other words, an image is traversed interpreting its pixels as points of the
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Cartesian plane. Each of the points is colored depending on the class predicted by the SVM; in
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dark green if it is the class with label 1 and in dark blue if it is the class with label 2.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java show
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py show
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@end_toggle
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- __Show the training data__
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The method @ref cv::circle is used to show the samples that compose the training data. The samples
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of the class labeled with 1 are shown in light green and in light blue the samples of the class
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labeled with 2.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show_data
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java show_data
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py show_data
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@end_toggle
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- __Support vectors__
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We use here a couple of methods to obtain information about the support vectors. The method
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@ref cv::ml::SVM::getSupportVectors obtain all support vectors. We have used this methods here
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to find the training examples that are support vectors and highlight them.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp show_vectors
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ml/non_linear_svms/NonLinearSVMsDemo.java show_vectors
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ml/non_linear_svms/non_linear_svms.py show_vectors
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@end_toggle
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Results
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-------
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