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Doxygen tutorials: cpp done

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Maksim Shabunin
2014-11-28 16:21:28 +03:00
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doc/tutorials/ml/introduction_to_svm/introduction_to_svm.markdown
+17 -13
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@@ -23,26 +23,28 @@ In which sense is the hyperplane obtained optimal? Let's consider the following
For a linearly separable set of 2D-points which belong to one of two classes, find a separating
straight line.
![image](images/separating-lines.png)
![](images/separating-lines.png)
@note In this example we deal with lines and points in the Cartesian plane instead of hyperplanes
and vectors in a high dimensional space. This is a simplification of the problem.It is important to
understand that this is done only because our intuition is better built from examples that are easy
to imagine. However, the same concepts apply to tasks where the examples to classify lie in a space
whose dimension is higher than two. In the above picture you can see that there exists multiple
whose dimension is higher than two.
In the above picture you can see that there exists multiple
lines that offer a solution to the problem. Is any of them better than the others? We can
intuitively define a criterion to estimate the worth of the lines:
A line is bad if it passes too close to the points because it will be noise sensitive and it will
not generalize correctly. Therefore, our goal should be to find the line passing as far as
possible from all points.
- A line is bad if it passes too close to the points because it will be noise sensitive and it will
not generalize correctly. Therefore, our goal should be to find the line passing as far as
possible from all points.
Then, the operation of the SVM algorithm is based on finding the hyperplane that gives the largest
minimum distance to the training examples. Twice, this distance receives the important name of
**margin** within SVM's theory. Therefore, the optimal separating hyperplane *maximizes* the margin
of the training data.
![image](images/optimal-hyperplane.png)
![](images/optimal-hyperplane.png)
How is the optimal hyperplane computed?
---------------------------------------
@@ -55,7 +57,9 @@ where \f$\beta\f$ is known as the *weight vector* and \f$\beta_{0}\f$ as the *bi
@sa A more in depth description of this and hyperplanes you can find in the section 4.5 (*Seperating
Hyperplanes*) of the book: *Elements of Statistical Learning* by T. Hastie, R. Tibshirani and J. H.
Friedman. The optimal hyperplane can be represented in an infinite number of different ways by
Friedman.
The optimal hyperplane can be represented in an infinite number of different ways by
scaling of \f$\beta\f$ and \f$\beta_{0}\f$. As a matter of convention, among all the possible
representations of the hyperplane, the one chosen is
@@ -99,7 +103,7 @@ Source Code
Explanation
-----------
1. **Set up the training data**
-# **Set up the training data**
The training data of this exercise is formed by a set of labeled 2D-points that belong to one of
two different classes; one of the classes consists of one point and the other of three points.
@@ -115,7 +119,7 @@ Explanation
Mat labelsMat (4, 1, CV_32FC1, labels);
@endcode
2. **Set up SVM's parameters**
-# **Set up SVM's parameters**
In this tutorial we have introduced the theory of SVMs in the most simple case, when the
training examples are spread into two classes that are linearly separable. However, SVMs can be
@@ -149,7 +153,7 @@ Explanation
less number of steps even if the optimal hyperplane has not been computed yet. This
parameter is defined in a structure @ref cv::cvTermCriteria .
3. **Train the SVM**
-# **Train the SVM**
We call the method
[CvSVM::train](http://docs.opencv.org/modules/ml/doc/support_vector_machines.html#cvsvm-train)
@@ -159,7 +163,7 @@ Explanation
SVM.train(trainingDataMat, labelsMat, Mat(), Mat(), params);
@endcode
4. **Regions classified by the SVM**
-# **Regions classified by the SVM**
The method @ref cv::ml::SVM::predict is used to classify an input sample using a trained SVM. In
this example we have used this method in order to color the space depending on the prediction done
@@ -183,7 +187,7 @@ Explanation
}
@endcode
5. **Support vectors**
-# **Support vectors**
We use here a couple of methods to obtain information about the support vectors.
The method @ref cv::ml::SVM::getSupportVectors obtain all of the support
@@ -209,4 +213,4 @@ Results
optimal separating hyperplane.
- Finally the support vectors are shown using gray rings around the training examples.
![image](images/svm_intro_result.png)
![](images/svm_intro_result.png)
doc/tutorials/ml/non_linear_svms/non_linear_svms.markdown
+16 -16
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@@ -61,11 +61,13 @@ region. The following picture shows non-linearly separable training data from tw
separating hyperplane and the distances to their correct regions of the samples that are
misclassified.
![image](images/sample-errors-dist.png)
![](images/sample-errors-dist.png)
@note Only the distances of the samples that are misclassified are shown in the picture. The
distances of the rest of the samples are zero since they lay already in their correct decision
region. The red and blue lines that appear on the picture are the margins to each one of the
region.
The red and blue lines that appear on the picture are the margins to each one of the
decision regions. It is very **important** to realize that each of the \f$\xi_{i}\f$ goes from a
misclassified training sample to the margin of its appropriate region.
@@ -93,13 +95,10 @@ or [download it from here ](samples/cpp/tutorial_code/ml/non_linear_svms/non_lin
@includelineno cpp/tutorial_code/ml/non_linear_svms/non_linear_svms.cpp
lines
1-12, 23-24, 27-
Explanation
-----------
1. **Set up the training data**
-# **Set up the training data**
The training data of this exercise is formed by a set of labeled 2D-points that belong to one of
two different classes. To make the exercise more appealing, the training data is generated
@@ -140,7 +139,7 @@ Explanation
rng.fill(c, RNG::UNIFORM, Scalar(1), Scalar(HEIGHT));
@endcode
2. **Set up SVM's parameters**
-# **Set up SVM's parameters**
@sa
In the previous tutorial @ref tutorial_introduction_to_svm there is an explanation of the atributes of the
@@ -161,12 +160,13 @@ Explanation
of obtaining a solution close to the one intuitively expected. However, we recommend to get a
better insight of the problem by making adjustments to this parameter.
@note Here there are just very few points in the overlapping region between classes, giving a smaller value to **FRAC_LINEAR_SEP** the density of points can be incremented and the impact of the parameter **CvSVM::C_SVC** explored deeply.
- *Termination Criteria of the algorithm*. The maximum number of iterations has to be
increased considerably in order to solve correctly a problem with non-linearly separable
training data. In particular, we have increased in five orders of magnitude this value.
@note Here there are just very few points in the overlapping region between classes, giving a smaller value to **FRAC_LINEAR_SEP** the density of points can be incremented and the impact of the parameter **CvSVM::C_SVC** explored deeply.
3. **Train the SVM**
- *Termination Criteria of the algorithm*. The maximum number of iterations has to be
increased considerably in order to solve correctly a problem with non-linearly separable
training data. In particular, we have increased in five orders of magnitude this value.
-# **Train the SVM**
We call the method @ref cv::ml::SVM::train to build the SVM model. Watch out that the training
process may take a quite long time. Have patiance when your run the program.
@@ -175,7 +175,7 @@ Explanation
svm.train(trainData, labels, Mat(), Mat(), params);
@endcode
4. **Show the Decision Regions**
-# **Show the Decision Regions**
The method @ref cv::ml::SVM::predict is used to classify an input sample using a trained SVM. In
this example we have used this method in order to color the space depending on the prediction done
@@ -195,7 +195,7 @@ Explanation
}
@endcode
5. **Show the training data**
-# **Show the training data**
The method @ref cv::circle is used to show the samples that compose the training data. The samples
of the class labeled with 1 are shown in light green and in light blue the samples of the class
@@ -220,7 +220,7 @@ Explanation
}
@endcode
6. **Support vectors**
-# **Support vectors**
We use here a couple of methods to obtain information about the support vectors. The method
@ref cv::ml::SVM::getSupportVectors obtain all support vectors.
@@ -250,7 +250,7 @@ Results
and some blue points lay on the green one.
- Finally the support vectors are shown using gray rings around the training examples.
![image](images/svm_non_linear_result.png)
![](images/svm_non_linear_result.png)
You may observe a runtime instance of this on the [YouTube here](https://www.youtube.com/watch?v=vFv2yPcSo-Q).