关于归一化算法的简单实践

算法的简单实践"/>

关于归一化算法的简单实践

需求来源

前段时间有个需求要对矩阵数据做归一化处理，之后在对数据做一致性校验，并获取数据对应的权重。

需求分析

1、了解归一化算法
2、通过数据构建矩阵信息
3、数据处理
4、获取权重

实现方案

1、简单说一下概念：
归一化是一种数据处理方式，能将数据经过处理后限制在某个固定范围内。当前的需求是将数据处理为[0,1]之间的小数。

2、计算方法
2.1、归一化算法公式：

2.2、权重算法公式：

2.3、一致性校验公式：

2.4、一致性比例计算：

注：当CR<0.1时，具有一致性；否则不具有一致性。

代码实现

代码如下，做个记录：

package com.***.***.**;import com.alibaba.fastjson.JSON;
import org.apachemons.lang3.StringUtils;
import org.apachemons.lang3.math.NumberUtils;import java.text.DecimalFormat;
import java.util.HashMap;public class MatrixSet {/*** 矩阵横向编码*/private static final String MATRIX_X = "X";/*** 矩阵纵向编码*/private static final String MATRIX_Y = "Y";/*** 对应的平均随机一致性指标 RI，目前存放15阶*/private static final HashMap<Integer, Double> RI_MAP = new HashMap<>();private static final DecimalFormat DF = new DecimalFormat("######0.00");static {RI_MAP.put(1, 0d);RI_MAP.put(2, 0d);RI_MAP.put(3, 0.52d);RI_MAP.put(4, 0.89d);RI_MAP.put(5, 1.12d);RI_MAP.put(6, 1.26d);RI_MAP.put(7, 1.36d);RI_MAP.put(8, 1.41d);RI_MAP.put(9, 1.46d);RI_MAP.put(10, 1.49d);RI_MAP.put(11, 1.52d);RI_MAP.put(12, 1.54d);RI_MAP.put(13, 1.56d);RI_MAP.put(14, 1.58d);RI_MAP.put(15, 1.59d);}public static void main(String[] args) {try {// 存放权重HashMap<String, String> weightMap = new HashMap<>();// 矩阵信息String matrixData = "[[\"A\",\"1\",\"2\",\"3\"],[\"B\",\"1\",\"5\",\"1/3\"],[\"C\",\"1/5\",\"1\",\"1/7\"],[\"D\",\"3\",\"7\",\"1\"]]";// 获取矩阵数据String[][] data = JSON.parseObject(matrixData, String[][].class);if (data.length > 0) {// 获取double精度的二维数组// 原数据数组double[][] arr = getDoubleArrData(data);// 数据校验(可对数据做其他逻辑处理)boolean flag = dataCheck(arr);// sumColumn值计算// parameter="X"--横向// parameter="Y"--纵向double[] sumColumn = getSumData(arr, "Y");// 归一化矩阵double[][] normalizationArr = getNormalizationArrData(arr, sumColumn);// sumRowColumn值计算double[] sumRowColumn = getSumData(normalizationArr, "X");// ω（权重）double[] weightColumn = getWeightData(sumRowColumn, arr.length);System.out.println("权重为：" + JSON.toJSON(weightColumn));// 𝛼ωdouble[] aWeightColumn = getAWeightdata(arr, weightColumn);// λmax = sum(每个𝛼ω/每个ω)double λmax = getAmax(aWeightColumn, weightColumn);// CI=(λmax-n)/(n-1)double ci = (λmax - arr.length) / (arr.length - 1);// RIdouble ri = RI_MAP.get(arr.length);// CR=CI/RIdouble cr = ci / ri;if (cr >= 0.1) {System.out.println("当前矩阵不具有一致性");}else {// 存放指标权重for (int i = 0; i < weightColumn.length; i++) {// 可根据需要做数据处理weightMap.put(i + "", DF.format(weightColumn[i]));}}}else {System.out.println("当前矩阵值为空");}}catch (Exception e) {System.out.println("矩阵数据处理异常,consistencyCheck:" + e.getMessage());}}/*** 获取double精度的二维数组** @param orginArr 原始矩阵数据* @return 结果*/private static double[][] getDoubleArrData(String[][] orginArr) {double[][] data = new double[orginArr.length - 1][orginArr.length - 1];for (int i = 1; i < orginArr.length; i++) {for (int j = 1; j < orginArr.length; j++) {if (orginArr[i][j].indexOf("/") > 0) {if (StringUtils.isNotBlank(orginArr[i][j].split("/")[1])&& NumberUtils.toDouble(orginArr[i][j].split("/")[1]) != 0) {double newDoubleData = NumberUtils.toDouble(orginArr[i][j].split("/")[0], 0d)/ NumberUtils.toDouble(orginArr[i][j].split("/")[1]);data[i - 1][j - 1] = newDoubleData;}else {System.out.println("填写的数据不能为空！");}}else {data[i - 1][j - 1] = NumberUtils.toDouble(orginArr[i][j]);}}}return data;}/*** 数据校验** @param arr 原数组* @return 结果*/private static boolean dataCheck(double[][] arr) {boolean result = false;for (int i = 0; i < arr.length; i++) {for (int j = 0; j < arr.length; j++) {if (arr[i][j] == 0) {result = true;}}}return result;}/*** 获取矩阵每行或者每列数据之和** @param arr 矩阵参数* @param arr 矩阵参数* @return 结果*/private static double[] getSumData(double[][] arr, String parameter) {double[] result = new double[arr.length];for (int i = 0; i < arr.length; i++) {double column = 0d;for (int j = 0; j < arr.length; j++) {if (StringUtils.equals(MATRIX_X, parameter)) {column += arr[i][j];}else if (StringUtils.equals(MATRIX_Y, parameter)) {column += arr[j][i];}}result[i] = column;}return result;}/*** 获取归一化矩阵** @param arr 原数组* @param sumColumn 原数组纵向之和数组* @return 结果*/private static double[][] getNormalizationArrData(double[][] arr, double[] sumColumn) {double[][] normalizationArr = new double[arr.length][arr.length];for (int i = 0; i < arr.length; i++) {for (int j = 0; j < arr.length; j++) {normalizationArr[i][j] = arr[i][j] / sumColumn[j];}}return normalizationArr;}/*** 获取权重数组** @param sumRowColumn* @param length* @return*/private static double[] getWeightData(double[] sumRowColumn, int length) {double[] weightColumn = new double[sumRowColumn.length];for (int i = 0; i < weightColumn.length; i++) {weightColumn[i] = sumRowColumn[i] / length;}return weightColumn;}/*** 获取𝛼ω** @param arr 原数组* @param weightColumn 权重* @return 结果*/private static double[] getAWeightdata(double[][] arr, double[] weightColumn) {double[] aWeightColumn = new double[arr.length];for (int i = 0; i < arr.length; i++) {double temp = 0d;for (int j = 0; j < arr.length; j++) {temp += arr[i][j] * weightColumn[j];}aWeightColumn[i] = temp;}return aWeightColumn;}/*** 获取λmax** @param aWeightColumn 𝛼ω列表* @param weightColumn ω列表* @return 结果*/private static double getAmax(double[] aWeightColumn, double[] weightColumn) {double λmax = 0d;for (int i = 0; i < weightColumn.length; i++) {λmax += aWeightColumn[i] / weightColumn[i];}return λmax / aWeightColumn.length;}
}