knn in scala

• nearest neighbor algorithm -- greedy

1开始的点A(不同则答案不同)

2选择cost最小的点D 重复

3最后回到A，加总

• knn in scala --intuition

• /** @author  wyq
   *  @version 1.0
   *  @date    Sun Sep 22 18:45:44 EDT 2013
   */

  package scalation.analytics
  
  import util.control.Breaks.{breakable, break}
  import collection.mutable.Set
  
  import scalation.linalgebra.{MatrixD, VectorD}
  import scalation.linalgebra_gen.VectorN
  import scalation.linalgebra_gen.Vectors.VectorI
  import scalation.math.DoubleWithExp._
  import scalation.util.Error
  

  /*
   *  @param x    the vectors/points of classified data stored as rows of a matrix (also can be in List[Array[Double]])
   *  @param y    the classification of each vector in x
   *  @param fn   the names for all features/variables
   *  @param k    the number of classes
   *  @param cn   the names for all classes
   *  @param knn  the number of nearest neighbors to consider
   */
  class KNN_Classifier (x: MatrixD, y: VectorI, fn: Array [String], k: Int, cn: Array [String],
                        knn: Int = 3)
        extends ClassifierReal (x, y, fn, k, cn)
  {
      private val DEBUG      = true                                        // degug flag
      private val MAX_DOUBLE = Double.PositiveInfinity                     // infinity
      private val topK       = Array.ofDim [Tuple2 [Int, Double]] (knn)    // top-knn nearest points (in reserve order)    ofDim
      private val count      = new VectorI (k)                             // how many nearest neighbors in each class.
  
      //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
      /** Compute a distance metric between vectors/points u and v.
       *  @param u  the first vector/point
       *  @param v  the second vector/point
       *///always prepare the distance function
      def distance (u: VectorD, v: VectorD): Double =
      {
          (u - v).normSq
      } 
  
      //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
      /** Find the knn nearest neighbors (top-knn) to vector ‘z‘.
       *  @param z  the vector to be classified
       */
      def kNearest (z: VectorD)
      {
          var dk = MAX_DOUBLE
          for (i <- 0 until x.dim1) {
              val di = distance (z, x(i))                   // compute distance to z
              if (di < dk) dk = replace (i, di)             // if closer, adjust top-knn
          }
          if (DEBUG) println ("topK = " + topK.deep)
      } 
  
      //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
      /** Remove the most distant neighbor and add new neighbor ‘i‘.  Maintain the
       *  ‘topK‘ nearest neighbors in sorted order farthest to nearest.
       */
      def replace (i: Int, di: Double): Double =
      {
          var j = 0
          while (j < knn-1 && di < topK(j)._2) { topK(j) = topK(j+1); j += 1 }
          topK(j) = (i, di)
          topK(0)._2                      // the distance of the new farthest neighbor
      } // replace
  
      //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
      /** Training involves resetting the data structures before each classification.
       *  KNN uses lazy training, so most of it is done during classification.
       */
      def train ()
      {
          for (i <- 0 until knn) topK(i)  = (-1, MAX_DOUBLE)   // intialize top-knn
          for (j <- 0 until k) count(j) = 0                    // initilize counters
      } // train
  
      //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
      /** Given a new point/vector ‘z‘, determine which class it belongs to (i.e.,
       *  the class getting the most votes from its ‘knn‘ nearest neighbors.
       *  @param z  the vector to classify
       */
      def classify (z: VectorD): Tuple2 [Int, String] =
      {
          kNearest (z)                                         // set top-knn to knn nearest
          for (i <- 0 until knn) count(y(topK(i)._1)) += 1     // tally per class
          println ("count = " + count)
          val best = count.argmax ()                           // class with maximal count
          (best, cn(best))                                     // return the best class and its name
      } // classify
  
  } // KNN_Classifier class
  
  //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
  /** The `KNN_ClassifierTest` object is used to test the `KNN_Classifier` class.
   */
  object KNN_ClassifierTest extends App
  {
      val x = new MatrixD ((6, 2), 1.0, 2.0,      // data/feature matrix
                                   2.0, 1.0,
                                   5.0, 4.0,
                                   4.0, 5.0,
                                   9.0, 8.0,
                                   8.0, 9.0)
      val y  = VectorN (0, 0, 0, 1, 1, 1)         // classification for each vector in x
      val fn = Array ("x1", "x2")                 // feature/variable names
      val cn = Array ("No", "Yes")                // class names
  
      println ("----------------------------------------------------")
      println ("x = " + x)
      println ("y = " + y)
      val cl = new KNN_Classifier (x, y, fn, 2, cn)
  
      cl.train ()
      val z1 = VectorD (10.0, 10.0)
      println ("----------------------------------------------------")
      println ("z1 = " + z1)
      println ("class = " + cl.classify (z1))
  
      cl.train ()
      val z2 = VectorD ( 3.0,  3.0)
      println ("----------------------------------------------------")
      println ("z2 = " + z2)
      println ("class = " + cl.classify (z2))
  
  } // KNN_ClassifierTest object