k最近邻

K-Nearest Neighbors 
该算法存储所有的训练样本（已知标签），然后通过分析新给的样本（标签未知）与已知标签的训练样本的相似度，选出其中的K个最相似的训练样本进行投票得到新样本的标签，并计算加权和等。 该方法有时被称为是“learning by example”，因为他总是根据新样本的特征向量与已知标签的样本特征向量的相似度来判断新样本的类别。

CvKNearest 
class CvKNearest : public CvStatModel 
该类实现了 K-Nearest Neighbors 模型

CvKNearest::CvKNearest

构造函数

默认构造函数. 

Default and training constructors.
C++: CvKNearest::CvKNearest()
C++: CvKNearest::CvKNearest(const Mat& trainData, const Mat& responses, const Mat& sampleIdx=Mat(), bool isRegression=false, int max_k=32 )
C++: CvKNearest::CvKNearest(const CvMat* trainData, const CvMat* responses, const CvMat* sampleIdx=0, bool isRegression=false, int max_k=32 )

训练函数
CvKNearest::trainC++: bool CvKNearest::train(const Mat& trainData, const Mat& responses, const Mat& sampleIdx=Mat(), bool isRegression=false, int maxK=32, bool updateBase=false )
C++: bool CvKNearest::train(const CvMat* trainData, const CvMat* responses, const CvMat* sampleIdx=0, bool is_regression=false, int maxK=32, bool updateBase=false)
Python: cv2.KNearest.train(trainData, responses[, sampleIdx[, isRegression[, maxK[, updateBase]]]]) ---> retval

参数：

    isRegression – Type of the problem: true for regression and false for classification.
    maxK – Number of maximum neighbors that may be passed to the method CvKNearest::find_nearest()
    updateBase – Specifies whether the model is trained from scratch (update_base=false), or it is updated using the new training data (update_base=true). In the latter case, the parameter maxK must not be larger than the original value.

The method trains the K-Nearest model. It follows the conventions of the generic CvStatModel::train() approach with the following limitations:

    • Only CV_ROW_SAMPLE data layout is supported.
    • Input variables are all ordered.
    • Output variables can be either categorical ( is_regression=false ) or ordered ( is_regression=true ).

    • Variable subsets (var_idx) and missing measurements are not supported.

找到邻居并预测输入向量的响应

CvKNearest::find_nearest

Finds the neighbors and predicts responses for input vectors.
C++: float CvKNearest::find_nearest(const Mat& samples, int k, Mat* results=0, const float** neighbors=0, Mat* neighborResponses=0, Mat* dist=0 ) const
C++: float CvKNearest::find_nearest(const Mat& samples, int k, Mat& results, Mat& neighborResponses, Mat& dists) const
C++: float CvKNearest::find_nearest(const CvMat* samples, int k, CvMat* results=0, const float** neighbors=0, CvMat* neighborResponses=0, CvMat* dist=0) const
Python: cv2.KNearest.find_nearest(samples, k[, results[, neighborResponses[, dists]]]) ----> retval, results, neighborResponses, dists

Parameters
samples – Input samples stored by rows. It is a single-precision floating-point matrix of number_of_samples × number_of_features size
k – Number of used nearest neighbors. 
results – Vector with results of prediction (regression or classification) for each input sample. It is a single-precision floating-point vector with number_of_samples elements.
neighbors – Optional output pointers to the neighbor vectors themselves. It is an array of k*samples->rows pointers.
neighborResponses – Optional output values for corresponding neighbors. It is a singleprecision floating-point matrix of number_of_samples × k size.
dist – Optional output distances from the input vectors to the corresponding neighbors. It is a single-precision floating-point matrix of number_of_samples × k size.
For each input vector (a row of the matrix samples), the method finds the k nearest neighbors. In case of regression,
the predicted result is a mean value of the particular vector’s neighbor responses. In case of classification, the class is
determined by voting.
For each input vector, the neighbors are sorted by their distances to the vector.
In case of C++ interface you can use output pointers to empty matrices and the function will allocate memory itself.
If only a single input vector is passed, all output matrices are optional and the predicted value is returned by the method.
The function is parallelized with the TBB library.

例程：

Ptr<ml::KNearest>  knn(ml::KNearest::create());
Mat_<float> trainFeatures(6,4);
trainFeatures << 2,2,2,2,
                 3,3,3,3,
                 4,4,4,4,
                 5,5,5,5,
                 6,6,6,6,
                 7,7,7,7;

Mat_<int> trainLabels(1,6);
trainLabels << 2,3,4,5,6,7;

knn->train(trainFeatures, ml::ROW_SAMPLE, trainLabels);

Mat_<float> testFeature(1,4);
testFeature<< 3,3,3,3;

int K=1;
Mat response,dist;
knn->findNearest(testFeature, K, noArray(), response, dist);
cerr << response << endl;
cerr << dist<< endl;