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# K-Nearest Neighbors

The algorithm caches all training samples and predicts the response for a new sample by analyzing a certain number (K) of the nearest neighbors of the sample using voting, calculating weighted sum, and so on. The method is sometimes referred to as “learning by example” because for prediction it looks for the feature vector with a known response that is closest to the given vector.

## CvKNearest

class `CvKNearest` : public `CvStatModel`

The class implements K-Nearest Neighbors model as described in the beginning of this section.

## CvKNearest::CvKNearest

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 )

See `CvKNearest::train()` for additional parameters descriptions.

## CvKNearest::train

Trains the model.

C++:`` 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

  Parameters:

  - 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.

## 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 \times number\_of\_features size.
  - k – Number of used nearest neighbors. It must satisfy constraint: k \le `CvKNearest::get_max_k()`.
  - 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 single-precision floating-point matrix of number\_of\_samples \times 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 \times 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.

## CvKNearest::get_max_k

Returns the number of maximum neighbors that may be passed to the method `CvKNearest::find_nearest()`.

C++:`` int `CvKNearest::``get_max_k`()`const`

## CvKNearest::get_var_count

Returns the number of used features (variables count).

C++:`` int `CvKNearest::``get_var_count`()`const`

## CvKNearest::get_sample_count

Returns the total number of train samples.

C++:`` int `CvKNearest::``get_sample_count`()`const`

## CvKNearest::is_regression

Returns type of the problem: `true` for regression and `false` for classification.

C++:`` bool `CvKNearest::``is_regression`()`const`

The sample below (currently using the obsolete `CvMat` structures) demonstrates the use of the k-nearest classifier for 2D point classification:

    #include "ml.h"
    #include "highgui.h"

    int main( int argc, char** argv )
    {
        const int K = 10;
        int i, j, k, accuracy;
        float response;
        int train_sample_count = 100;
        CvRNG rng_state = cvRNG(-1);
        CvMat* trainData = cvCreateMat( train_sample_count, 2, CV_32FC1 );
        CvMat* trainClasses = cvCreateMat( train_sample_count, 1, CV_32FC1 );
        IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );
        float _sample[2];
        CvMat sample = cvMat( 1, 2, CV_32FC1, _sample );
        cvZero( img );

        CvMat trainData1, trainData2, trainClasses1, trainClasses2;

        // form the training samples
        cvGetRows( trainData, &trainData1, 0, train_sample_count/2 );
        cvRandArr( &rng_state, &trainData1, CV_RAND_NORMAL, cvScalar(200,200), cvScalar(50,50) );

        cvGetRows( trainData, &trainData2, train_sample_count/2, train_sample_count );
        cvRandArr( &rng_state, &trainData2, CV_RAND_NORMAL, cvScalar(300,300), cvScalar(50,50) );

        cvGetRows( trainClasses, &trainClasses1, 0, train_sample_count/2 );
        cvSet( &trainClasses1, cvScalar(1) );

        cvGetRows( trainClasses, &trainClasses2, train_sample_count/2, train_sample_count );
        cvSet( &trainClasses2, cvScalar(2) );

        // learn classifier
        CvKNearest knn( trainData, trainClasses, 0, false, K );
        CvMat* nearests = cvCreateMat( 1, K, CV_32FC1);

        for( i = 0; i < img->height; i++ )
        {
            for( j = 0; j < img->width; j++ )
            {
                sample.data.fl[0] = (float)j;
                sample.data.fl[1] = (float)i;

                // estimate the response and get the neighbors' labels
                response = knn.find_nearest(&sample,K,0,0,nearests,0);

                // compute the number of neighbors representing the majority
                for( k = 0, accuracy = 0; k < K; k++ )
                {
                    if( nearests->data.fl[k] == response)
                        accuracy++;
                }
                // highlight the pixel depending on the accuracy (or confidence)
                cvSet2D( img, i, j, response == 1 ?
                    (accuracy > 5 ? CV_RGB(180,0,0) : CV_RGB(180,120,0)) :
                    (accuracy > 5 ? CV_RGB(0,180,0) : CV_RGB(120,120,0)) );
            }
        }

        // display the original training samples
        for( i = 0; i < train_sample_count/2; i++ )
        {
            CvPoint pt;
            pt.x = cvRound(trainData1.data.fl[i*2]);
            pt.y = cvRound(trainData1.data.fl[i*2+1]);
            cvCircle( img, pt, 2, CV_RGB(255,0,0), CV_FILLED );
            pt.x = cvRound(trainData2.data.fl[i*2]);
            pt.y = cvRound(trainData2.data.fl[i*2+1]);
            cvCircle( img, pt, 2, CV_RGB(0,255,0), CV_FILLED );
        }

        cvNamedWindow( "classifier result", 1 );
        cvShowImage( "classifier result", img );
        cvWaitKey(0);

        cvReleaseMat( &trainClasses );
        cvReleaseMat( &trainData );
        return 0;
    }

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