相关系数计算

来源：互联网发布：2016淘宝运营视频编辑：程序博客网时间：2024/06/06 00:02

Pearson(皮尔逊), Kendall（肯德尔）和Spearman（斯伯曼/斯皮尔曼）三种相关分析方法

具体公式就不Copy了，一般认为：

使用Pearson积差相关系数:
      两个连续变量间呈线性相关时;
      数据呈现正态分布时；
Spearman和Kendall相关系数：
       对分类变量的数据或变量值的分布明显非正态或分布不明时，计算时先对离散数据进行排序或对定距变量值排（求）秩。

直接上计算代码：

public static double pearson(double x[], double y[]) {
       int size = x.length;
       if (size == 0 || size != y.length) {
           return 0;
       } else {
           double xavg = avg(x);
           double yavg = avg(y);
           double numerator = 0.0;
           double denominatorx = 0.0;
           double denominatory = 0.0;
           for (int i = 0; i < size; i++) {
               numerator += (x[i] - xavg) * (y[i] - yavg);
               denominatorx += Math.pow((x[i] - xavg), 2);
               denominatory += Math.pow((y[i] - yavg), 2);
           }
           return numerator / Math.sqrt(denominatorx * denominatory);
       }
   }

   public static double avg(double x[]) {
       double sum = 0;
       for (int i = 0; i < x.length; i++) {
           sum += x[i];
       }
       return sum / x.length;
   }

/** 要求X按小至大顺序 */

    public static double spearman(double x[], double y[]) {
       double rx[] = getRank(x);
       double ry[] = getRank(y);
       return pearson(rx, ry);
   }

   public static double[] getRank(double x[]) {
       double r[] = new double[x.length];
       for (int i = 0; i < x.length; i++) {
           int cnt_lt = 0, cnt_eq = 0;
           for (int j = 0; j < x.length; j++) {
               if (x[i] < x[j]) {
                   cnt_lt++;
               }
               if (x[i] == x[j]) {
                   cnt_eq++;
               }
           }
           r[i] = cnt_lt + (1 + cnt_eq) / 2;
       }
       return r;
   }
/** 要求X按小至大顺序 */
   public static double kendall(double x[], double y[]) {
       int cnt_bt = 0;
       for (int i = 0; i < y.length; i++) {
           for (int j = i; j < y.length; j++) {
               if (y[i] < y[j]) {
                   cnt_bt++;
               }
           }
       }
       return 4.0 * cnt_bt / ((x.length) * (x.length - 1)) - 1;
   }

public static void sortAsX(double x[], double y[]) {
       List list = new ArrayList();
       for (int i = 0; i < x.length; i++) {
           list.add(new Point(x[i], y[i]));
       }
       Collections.sort(list, new Comparator() {
           @Override
           public int compare(Object o1, Object o2) {
               Point obj1 = (Point) o1;
               Point obj2 = (Point) o2;
               return ((Double) obj1.x).compareTo((Double) obj2.x);
           }
       });

       for (int i = 0; i < x.length; i++) {
           Point p = (Point) list.get(i);
           x[i] = p.x;
           y[i] = p.y;
       }

   }

    public static double calcCorr(double x[], double y[], int type) {
       if (type == 1) {
           return pearson(x, y);
       } else if (type == 2) {
           sortAsX(x, y);
           return spearman(x, y);
       } else {
           sortAsX(x, y);
           return kendall(x, y);
       }

   }

当然代码没有考虑很多异常情况(例如缺失值)，同时Kendall相关系数也是采用了最简单明了的方式，仅供参考。

用Excel / R / Spss 等都可以计算出来

R计算方法为：

  cor(x, y = NULL, use = "everything",    method = c("pearson", "kendall", "spearman"))

0 0