日撸 Java 三百行（51-60天，kNN 与 NB）

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目录

第 51 天: kNN 分类器

kNN 的原始论文为: T. Cover and P. Hart. Nearest neighbor pattern classification. IEEE Transactions in Information Theory, IT-13, pages 21–27, 1967.

1. 简单. 没有学习过程, 也被称为惰性学习 lazy learning. 类似于开卷考试, 在已有数据中去找答案.
2. 本源. 找相似, 正是人类认识事物的常用方法, 隐藏于人类或者其他动物的基因里面. 当然, 人类也会上当, 例如有人把邻居的滴水观音误认为是芋头, 偷食后中毒.
3. 效果好. 永远不要小视 kNN, 对于很多数据, 你很难设计算法超越它.
4. 适应性强. 可用于分类, 回归. 可用于各种数据.
5. 可扩展性强. 设计不同的度量, 可获得意想不到的效果.
6. 一般需要对数据归一化.
7. 复杂度高. 这也是 kNN 最重要的缺点. 对于每一个测试数据, 复杂度为 $O((m+k)n)$, 其中 $n$ 为训练数据个数, $m$ 为条件属性个数, $k$ 为邻居个数. 代码见 computeNearests().

代码说明:
8. 两种距离度量.
9. 数据随机分割方式.
10. 间址的灵活使用: trainingSet 和 testingSet 都是整数数组, 表示下标.
11. arff 文件的读取. 需要 weka.jar 包.
12. 求邻居.
13. 投票.

package machinelearning.knn; import java.io.FileReader; import java.util.Arrays; import java.util.Random; import weka.core.*; / * kNN classification. * * @author Fan Min . */ public class KnnClassification { / * Manhattan distance. */ public static final int MANHATTAN = 0; / * Euclidean distance. */ public static final int EUCLIDEAN = 1; / * The distance measure. */ public int distanceMeasure = EUCLIDEAN; / * A random instance; */ public static final Random random = new Random(); / * The number of neighbors. */ int numNeighbors = 7; / * The whole dataset. */ Instances dataset; / * The training set. Represented by the indices of the data. */ int[] trainingSet; / * The testing set. Represented by the indices of the data. */ int[] testingSet; / * The predictions. */ int[] predictions; / * * The first constructor. * * @param paraFilename * The arff filename. * */ public KnnClassification(String paraFilename) { try { FileReader fileReader = new FileReader(paraFilename); dataset = new Instances(fileReader); // The last attribute is the decision class. dataset.setClassIndex(dataset.numAttributes() - 1); fileReader.close(); } catch (Exception ee) { System.out.println("Error occurred while trying to read \'" + paraFilename + "\' in KnnClassification constructor.\r\n" + ee); System.exit(0); } // Of try }// Of the first constructor / * * Get a random indices for data randomization. * * @param paraLength * The length of the sequence. * @return An array of indices, e.g., {4, 3, 1, 5, 0, 2} with length 6. * */ public static int[] getRandomIndices(int paraLength) { int[] resultIndices = new int[paraLength]; // Step 1. Initialize. for (int i = 0; i < paraLength; i++) { resultIndices[i] = i; } // Of for i // Step 2. Randomly swap. int tempFirst, tempSecond, tempValue; for (int i = 0; i < paraLength; i++) { // Generate two random indices. tempFirst = random.nextInt(paraLength); tempSecond = random.nextInt(paraLength); // Swap. tempValue = resultIndices[tempFirst]; resultIndices[tempFirst] = resultIndices[tempSecond]; resultIndices[tempSecond] = tempValue; } // Of for i return resultIndices; }// Of getRandomIndices / * * Split the data into training and testing parts. * * @param paraTrainingFraction * The fraction of the training set. * */ public void splitTrainingTesting(double paraTrainingFraction) { int tempSize = dataset.numInstances(); int[] tempIndices = getRandomIndices(tempSize); int tempTrainingSize = (int) (tempSize * paraTrainingFraction); trainingSet = new int[tempTrainingSize]; testingSet = new int[tempSize - tempTrainingSize]; for (int i = 0; i < tempTrainingSize; i++) { trainingSet[i] = tempIndices[i]; } // Of for i for (int i = 0; i < tempSize - tempTrainingSize; i++) { testingSet[i] = tempIndices[tempTrainingSize + i]; } // Of for i }// Of splitTrainingTesting / * * Predict for the whole testing set. The results are stored in predictions. * #see predictions. * */ public void predict() { predictions = new int[testingSet.length]; for (int i = 0; i < predictions.length; i++) { predictions[i] = predict(testingSet[i]); } // Of for i }// Of predict / * * Predict for given instance. * * @return The prediction. * */ public int predict(int paraIndex) { int[] tempNeighbors = computeNearests(paraIndex); int resultPrediction = simpleVoting(tempNeighbors); return resultPrediction; }// Of predict / * * The distance between two instances. * * @param paraI * The index of the first instance. * @param paraJ * The index of the second instance. * @return The distance. * */ public double distance(int paraI, int paraJ) { double resultDistance = 0; double tempDifference; switch (distanceMeasure) { case MANHATTAN: for (int i = 0; i < dataset.numAttributes() - 1; i++) { tempDifference = dataset.instance(paraI).value(i) - dataset.instance(paraJ).value(i); if (tempDifference < 0) { resultDistance -= tempDifference; } else { resultDistance += tempDifference; } // Of if } // Of for i break; case EUCLIDEAN: for (int i = 0; i < dataset.numAttributes() - 1; i++) { tempDifference = dataset.instance(paraI).value(i) - dataset.instance(paraJ).value(i); resultDistance += tempDifference * tempDifference; } // Of for i break; default: System.out.println("Unsupported distance measure: " + distanceMeasure); }// Of switch return resultDistance; }// Of distance / * * Get the accuracy of the classifier. * * @return The accuracy. * */ public double getAccuracy() { // A double divides an int gets another double. double tempCorrect = 0; for (int i = 0; i < predictions.length; i++) { if (predictions[i] == dataset.instance(testingSet[i]).classValue()) { tempCorrect++; } // Of if } // Of for i return tempCorrect / testingSet.length; }// Of getAccuracy / * Compute the nearest k neighbors. Select one neighbor in each scan. In * fact we can scan only once. You may implement it by yourself. * * @param paraK * the k value for kNN. * @param paraCurrent * current instance. We are comparing it with all others. * @return the indices of the nearest instances. */ public int[] computeNearests(int paraCurrent) { int[] resultNearests = new int[numNeighbors]; boolean[] tempSelected = new boolean[trainingSet.length]; double tempMinimalDistance; int tempMinimalIndex = 0; // Compute all distances to avoid redundant computation. double[] tempDistances = new double[trainingSet.length]; for (int i = 0; i < trainingSet.length; i ++) { tempDistances[i] = distance(paraCurrent, trainingSet[i]); }//Of for i // Select the nearest paraK indices. for (int i = 0; i < numNeighbors; i++) { tempMinimalDistance = Double.MAX_VALUE; for (int j = 0; j < trainingSet.length; j++) { if (tempSelected[j]) { continue; } // Of if if (tempDistances[j] < tempMinimalDistance) { tempMinimalDistance = tempDistances[j]; tempMinimalIndex = j; } // Of if } // Of for j resultNearests[i] = trainingSet[tempMinimalIndex]; tempSelected[tempMinimalIndex] = true; } // Of for i System.out.println("The nearest of " + paraCurrent + " are: " + Arrays.toString(resultNearests)); return resultNearests; }// Of computeNearests / * Voting using the instances. * * @param paraNeighbors * The indices of the neighbors. * @return The predicted label. */ public int simpleVoting(int[] paraNeighbors) { int[] tempVotes = new int[dataset.numClasses()]; for (int i = 0; i < paraNeighbors.length; i++) { tempVotes[(int) dataset.instance(paraNeighbors[i]).classValue()]++; } // Of for i int tempMaximalVotingIndex = 0; int tempMaximalVoting = 0; for (int i = 0; i < dataset.numClasses(); i++) { if (tempVotes[i] > tempMaximalVoting) { tempMaximalVoting = tempVotes[i]; tempMaximalVotingIndex = i; } // Of if } // Of for i return tempMaximalVotingIndex; }// Of simpleVoting / * * The entrance of the program. * * @param args * Not used now. * */ public static void main(String args[]) { KnnClassification tempClassifier = new KnnClassification("D:/data/iris.arff"); tempClassifier.splitTrainingTesting(0.8); tempClassifier.predict(); System.out.println("The accuracy of the classifier is: " + tempClassifier.getAccuracy()); }// Of main }// Of class KnnClassification 

在 https://github.com/FanSmale/sampledata/ 可下载 iris.arff. 万一访问不畅, 把下面的内容拷贝另存成 iris.arff 即可.

@RELATION iris @ATTRIBUTE sepallength REAL @ATTRIBUTE sepalwidth REAL @ATTRIBUTE petallength REAL @ATTRIBUTE petalwidth REAL @ATTRIBUTE class {Iris-setosa,Iris-versicolor,Iris-virginica} @DATA 5.1,3.5,1.4,0.2,Iris-setosa 4.9,3.0,1.4,0.2,Iris-setosa 4.7,3.2,1.3,0.2,Iris-setosa 4.6,3.1,1.5,0.2,Iris-setosa 5.0,3.6,1.4,0.2,Iris-setosa 5.4,3.9,1.7,0.4,Iris-setosa 4.6,3.4,1.4,0.3,Iris-setosa 5.0,3.4,1.5,0.2,Iris-setosa 4.4,2.9,1.4,0.2,Iris-setosa 4.9,3.1,1.5,0.1,Iris-setosa 5.4,3.7,1.5,0.2,Iris-setosa 4.8,3.4,1.6,0.2,Iris-setosa 4.8,3.0,1.4,0.1,Iris-setosa 4.3,3.0,1.1,0.1,Iris-setosa 5.8,4.0,1.2,0.2,Iris-setosa 5.7,4.4,1.5,0.4,Iris-setosa 5.4,3.9,1.3,0.4,Iris-setosa 5.1,3.5,1.4,0.3,Iris-setosa 5.7,3.8,1.7,0.3,Iris-setosa 5.1,3.8,1.5,0.3,Iris-setosa 5.4,3.4,1.7,0.2,Iris-setosa 5.1,3.7,1.5,0.4,Iris-setosa 4.6,3.6,1.0,0.2,Iris-setosa 5.1,3.3,1.7,0.5,Iris-setosa 4.8,3.4,1.9,0.2,Iris-setosa 5.0,3.0,1.6,0.2,Iris-setosa 5.0,3.4,1.6,0.4,Iris-setosa 5.2,3.5,1.5,0.2,Iris-setosa 5.2,3.4,1.4,0.2,Iris-setosa 4.7,3.2,1.6,0.2,Iris-setosa 4.8,3.1,1.6,0.2,Iris-setosa 5.4,3.4,1.5,0.4,Iris-setosa 5.2,4.1,1.5,0.1,Iris-setosa 5.5,4.2,1.4,0.2,Iris-setosa 4.9,3.1,1.5,0.1,Iris-setosa 5.0,3.2,1.2,0.2,Iris-setosa 5.5,3.5,1.3,0.2,Iris-setosa 4.9,3.1,1.5,0.1,Iris-setosa 4.4,3.0,1.3,0.2,Iris-setosa 5.1,3.4,1.5,0.2,Iris-setosa 5.0,3.5,1.3,0.3,Iris-setosa 4.5,2.3,1.3,0.3,Iris-setosa 4.4,3.2,1.3,0.2,Iris-setosa 5.0,3.5,1.6,0.6,Iris-setosa 5.1,3.8,1.9,0.4,Iris-setosa 4.8,3.0,1.4,0.3,Iris-setosa 5.1,3.8,1.6,0.2,Iris-setosa 4.6,3.2,1.4,0.2,Iris-setosa 5.3,3.7,1.5,0.2,Iris-setosa 5.0,3.3,1.4,0.2,Iris-setosa 7.0,3.2,4.7,1.4,Iris-versicolor 6.4,3.2,4.5,1.5,Iris-versicolor 6.9,3.1,4.9,1.5,Iris-versicolor 5.5,2.3,4.0,1.3,Iris-versicolor 6.5,2.8,4.6,1.5,Iris-versicolor 5.7,2.8,4.5,1.3,Iris-versicolor 6.3,3.3,4.7,1.6,Iris-versicolor 4.9,2.4,3.3,1.0,Iris-versicolor 6.6,2.9,4.6,1.3,Iris-versicolor 5.2,2.7,3.9,1.4,Iris-versicolor 5.0,2.0,3.5,1.0,Iris-versicolor 5.9,3.0,4.2,1.5,Iris-versicolor 6.0,2.2,4.0,1.0,Iris-versicolor 6.1,2.9,4.7,1.4,Iris-versicolor 5.6,2.9,3.6,1.3,Iris-versicolor 6.7,3.1,4.4,1.4,Iris-versicolor 5.6,3.0,4.5,1.5,Iris-versicolor 5.8,2.7,4.1,1.0,Iris-versicolor 6.2,2.2,4.5,1.5,Iris-versicolor 5.6,2.5,3.9,1.1,Iris-versicolor 5.9,3.2,4.8,1.8,Iris-versicolor 6.1,2.8,4.0,1.3,Iris-versicolor 6.3,2.5,4.9,1.5,Iris-versicolor 6.1,2.8,4.7,1.2,Iris-versicolor 6.4,2.9,4.3,1.3,Iris-versicolor 6.6,3.0,4.4,1.4,Iris-versicolor 6.8,2.8,4.8,1.4,Iris-versicolor 6.7,3.0,5.0,1.7,Iris-versicolor 6.0,2.9,4.5,1.5,Iris-versicolor 5.7,2.6,3.5,1.0,Iris-versicolor 5.5,2.4,3.8,1.1,Iris-versicolor 5.5,2.4,3.7,1.0,Iris-versicolor 5.8,2.7,3.9,1.2,Iris-versicolor 6.0,2.7,5.1,1.6,Iris-versicolor 5.4,3.0,4.5,1.5,Iris-versicolor 6.0,3.4,4.5,1.6,Iris-versicolor 6.7,3.1,4.7,1.5,Iris-versicolor 6.3,2.3,4.4,1.3,Iris-versicolor 5.6,3.0,4.1,1.3,Iris-versicolor 5.5,2.5,4.0,1.3,Iris-versicolor 5.5,2.6,4.4,1.2,Iris-versicolor 6.1,3.0,4.6,1.4,Iris-versicolor 5.8,2.6,4.0,1.2,Iris-versicolor 5.0,2.3,3.3,1.0,Iris-versicolor 5.6,2.7,4.2,1.3,Iris-versicolor 5.7,3.0,4.2,1.2,Iris-versicolor 5.7,2.9,4.2,1.3,Iris-versicolor 6.2,2.9,4.3,1.3,Iris-versicolor 5.1,2.5,3.0,1.1,Iris-versicolor 5.7,2.8,4.1,1.3,Iris-versicolor 6.3,3.3,6.0,2.5,Iris-virginica 5.8,2.7,5.1,1.9,Iris-virginica 7.1,3.0,5.9,2.1,Iris-virginica 6.3,2.9,5.6,1.8,Iris-virginica 6.5,3.0,5.8,2.2,Iris-virginica 7.6,3.0,6.6,2.1,Iris-virginica 4.9,2.5,4.5,1.7,Iris-virginica 7.3,2.9,6.3,1.8,Iris-virginica 6.7,2.5,5.8,1.8,Iris-virginica 7.2,3.6,6.1,2.5,Iris-virginica 6.5,3.2,5.1,2.0,Iris-virginica 6.4,2.7,5.3,1.9,Iris-virginica 6.8,3.0,5.5,2.1,Iris-virginica 5.7,2.5,5.0,2.0,Iris-virginica 5.8,2.8,5.1,2.4,Iris-virginica 6.4,3.2,5.3,2.3,Iris-virginica 6.5,3.0,5.5,1.8,Iris-virginica 7.7,3.8,6.7,2.2,Iris-virginica 7.7,2.6,6.9,2.3,Iris-virginica 6.0,2.2,5.0,1.5,Iris-virginica 6.9,3.2,5.7,2.3,Iris-virginica 5.6,2.8,4.9,2.0,Iris-virginica 7.7,2.8,6.7,2.0,Iris-virginica 6.3,2.7,4.9,1.8,Iris-virginica 6.7,3.3,5.7,2.1,Iris-virginica 7.2,3.2,6.0,1.8,Iris-virginica 6.2,2.8,4.8,1.8,Iris-virginica 6.1,3.0,4.9,1.8,Iris-virginica 6.4,2.8,5.6,2.1,Iris-virginica 7.2,3.0,5.8,1.6,Iris-virginica 7.4,2.8,6.1,1.9,Iris-virginica 7.9,3.8,6.4,2.0,Iris-virginica 6.4,2.8,5.6,2.2,Iris-virginica 6.3,2.8,5.1,1.5,Iris-virginica 6.1,2.6,5.6,1.4,Iris-virginica 7.7,3.0,6.1,2.3,Iris-virginica 6.3,3.4,5.6,2.4,Iris-virginica 6.4,3.1,5.5,1.8,Iris-virginica 6.0,3.0,4.8,1.8,Iris-virginica 6.9,3.1,5.4,2.1,Iris-virginica 6.7,3.1,5.6,2.4,Iris-virginica 6.9,3.1,5.1,2.3,Iris-virginica 5.8,2.7,5.1,1.9,Iris-virginica 6.8,3.2,5.9,2.3,Iris-virginica 6.7,3.3,5.7,2.5,Iris-virginica 6.7,3.0,5.2,2.3,Iris-virginica 6.3,2.5,5.0,1.9,Iris-virginica 6.5,3.0,5.2,2.0,Iris-virginica 6.2,3.4,5.4,2.3,Iris-virginica 5.9,3.0,5.1,1.8,Iris-virginica 

第 52 天: kNN 分类器 (续)

1. 重新实现 computeNearests, 仅需要扫描一遍训练集, 即可获得 $k$ 个邻居. 提示: 现代码与插入排序思想相结合. 其时间复杂度为 $O(kn)$, 其中 $O(n)$ 用于扫描训练集, $O(k)$ 用于插入.
2. 增加 setDistanceMeasure() 方法.
3. 增加 setNumNeighors() 方法.

第 53 天: kNN 分类器 (续)

1. 增加 weightedVoting() 方法, 距离越短话语权越大. 支持两种以上的加权方式.
2. 实现 leave-one-out 测试.

第 54 天: 基于 M-distance 的推荐

这里夹带一点私货, 即论文 Mei Zheng, Fan Min, Heng-Ru Zhang, Wen-Bin Chen, Fast recommendations with the M-distance, IEEE Access 4 (2016) 1464–1468 的源代码. 点击下载论文.

1. 评分表 (用户, 项目, 评分) 的压缩方式给出. 见 https://github.com/FanSmale/sampledata/ 中 movielens-943u1682m.txt.
   前几行数据为:
   0,0,5
   0,1,3
   0,2,4
   0,3,3
   0,4,3
   0,5,5
   0,6,4
   …
   1,0,4
   1,9,2
   1,12,4
   其中, “0,2,4” 表示用户 0 对项目 2 的评分为 4. 用户 1 对项目 1、2 等的评分没有, 表示没看过该电影. 在用户数、项目数很多时, 必须使用压缩存储.
   
   
   
   
   
   
   
   
   
   
   
   
   
2. 一篇论文的代码就这么一点点. 当然, 这篇论文本身很简单. 所谓 M-distance, 就是根据平均分来计算两个用户 (或项目) 之间的距离.
   炫一下数学表达式. 令项目 $j$ 的平均分为 $x_{\cdot j}$,
   采用 item-based recommendation, 则第 $j$ 个项目关于第 $i$ 个用户的邻居项目集合为
   N i j = { 1 ≤ j ′ ≤ m ∣ j ′ ≠ j , p i j ′ ≠ 0 , ∣ r ⋅ j ‾ − r ⋅ j ′ ‾ ∣ < ϵ } (1) N_{ij} = \{1 \leq j’ \leq m | j’ \neq j, p_{ij’} \neq 0, |\overline{r_{\cdot j}} – \overline{r_{\cdot j’}}| < \epsilon\} \tag{1} Nij​={
   1≤j′≤m∣j′=j,pij′​=0,∣r⋅j​​−r⋅j′​​∣<ϵ}(1)
   第 $i$ 个用户对 $j$ 个项目的评分预测为:
   $$p_{ij}=\frac{{\sum }_{j^{\prime }\in N_{ij}}{r}_{i{j}^{\prime }}}{|N_{ij}|}\text{\hspace{1em}(2)}$$
   
   
   
   
   
3. 邻居不用 $k$ 控制. 距离小于 radius (即 $ϵ$) 的都是邻居. 使用 M-distance 时, 这种方式效果更好.
4. 使用 leave-one-out 的测试方式, 很高效的算法才能使用这种方式.

package machinelearning.knn; / * Recommendation with M-distance. * @author Fan Min . */ import java.io.*; public class MBR { / * Default rating for 1-5 points. */ public static final double DEFAULT_RATING = 3.0; / * The total number of users. */ private int numUsers; / * The total number of items. */ private int numItems; / * The total number of ratings (non-zero values) */ private int numRatings; / * The predictions. */ private double[] predictions; / * Compressed rating matrix. User-item-rating triples. */ private int[][] compressedRatingMatrix; / * The degree of users (how many item he has rated). */ private int[] userDegrees; / * The average rating of the current user. */ private double[] userAverageRatings; / * The degree of users (how many item he has rated). */ private int[] itemDegrees; / * The average rating of the current item. */ private double[] itemAverageRatings; / * The first user start from 0. Let the first user has x ratings, the second * user will start from x. */ private int[] userStartingIndices; / * Number of non-neighbor objects. */ private int numNonNeighbors; / * The radius (delta) for determining the neighborhood. */ private double radius; / * * Construct the rating matrix. * * @param paraRatingFilename * the rating filename. * @param paraNumUsers * number of users * @param paraNumItems * number of items * @param paraNumRatings * number of ratings * */ public MBR(String paraFilename, int paraNumUsers, int paraNumItems, int paraNumRatings) throws Exception { // Step 1. Initialize these arrays numItems = paraNumItems; numUsers = paraNumUsers; numRatings = paraNumRatings; userDegrees = new int[numUsers]; userStartingIndices = new int[numUsers + 1]; userAverageRatings = new double[numUsers]; itemDegrees = new int[numItems]; compressedRatingMatrix = new int[numRatings][3]; itemAverageRatings = new double[numItems]; predictions = new double[numRatings]; System.out.println("Reading " + paraFilename); // Step 2. Read the data file. File tempFile = new File(paraFilename); if (!tempFile.exists()) { System.out.println("File " + paraFilename + " does not exists."); System.exit(0); } // Of if BufferedReader tempBufReader = new BufferedReader(new FileReader(tempFile)); String tempString; String[] tempStrArray; int tempIndex = 0; userStartingIndices[0] = 0; userStartingIndices[numUsers] = numRatings; while ((tempString = tempBufReader.readLine()) != null) { // Each line has three values tempStrArray = tempString.split(","); compressedRatingMatrix[tempIndex][0] = Integer.parseInt(tempStrArray[0]); compressedRatingMatrix[tempIndex][1] = Integer.parseInt(tempStrArray[1]); compressedRatingMatrix[tempIndex][2] = Integer.parseInt(tempStrArray[2]); userDegrees[compressedRatingMatrix[tempIndex][0]]++; itemDegrees[compressedRatingMatrix[tempIndex][1]]++; if (tempIndex > 0) { // Starting to read the data of a new user. if (compressedRatingMatrix[tempIndex][0] != compressedRatingMatrix[tempIndex - 1][0]) { userStartingIndices[compressedRatingMatrix[tempIndex][0]] = tempIndex; } // Of if } // Of if tempIndex++; } // Of while tempBufReader.close(); double[] tempUserTotalScore = new double[numUsers]; double[] tempItemTotalScore = new double[numItems]; for (int i = 0; i < numRatings; i++) { tempUserTotalScore[compressedRatingMatrix[i][0]] += compressedRatingMatrix[i][2]; tempItemTotalScore[compressedRatingMatrix[i][1]] += compressedRatingMatrix[i][2]; } // Of for i for (int i = 0; i < numUsers; i++) { userAverageRatings[i] = tempUserTotalScore[i] / userDegrees[i]; } // Of for i for (int i = 0; i < numItems; i++) { itemAverageRatings[i] = tempItemTotalScore[i] / itemDegrees[i]; } // Of for i }// Of the first constructor / * * Set the radius (delta). * * @param paraRadius * The given radius. * */ public void setRadius(double paraRadius) { if (paraRadius > 0) { radius = paraRadius; } else { radius = 0.1; } // Of if }// Of setRadius / * * Leave-one-out prediction. The predicted values are stored in predictions. * * @see predictions * */ public void leaveOneOutPrediction() { double tempItemAverageRating; // Make each line of the code shorter. int tempUser, tempItem, tempRating; System.out.println("\r\nLeaveOneOutPrediction for radius " + radius); numNonNeighbors = 0; for (int i = 0; i < numRatings; i++) { tempUser = compressedRatingMatrix[i][0]; tempItem = compressedRatingMatrix[i][1]; tempRating = compressedRatingMatrix[i][2]; // Step 1. Recompute average rating of the current item. tempItemAverageRating = (itemAverageRatings[tempItem] * itemDegrees[tempItem] - tempRating) / (itemDegrees[tempItem] - 1); // Step 2. Recompute neighbors, at the same time obtain the ratings // Of neighbors. int tempNeighbors = 0; double tempTotal = 0; int tempComparedItem; for (int j = userStartingIndices[tempUser]; j < userStartingIndices[tempUser + 1]; j++) { tempComparedItem = compressedRatingMatrix[j][1]; if (tempItem == tempComparedItem) { continue;// Ignore itself. } // Of if if (Math.abs(tempItemAverageRating - itemAverageRatings[tempComparedItem]) < radius) { tempTotal += compressedRatingMatrix[j][2]; tempNeighbors++; } // Of if } // Of for j // Step 3. Predict as the average value of neighbors. if (tempNeighbors > 0) { predictions[i] = tempTotal / tempNeighbors; } else { predictions[i] = DEFAULT_RATING; numNonNeighbors++; } // Of if } // Of for i }// Of leaveOneOutPrediction / * * Compute the MAE based on the deviation of each leave-one-out. * * @author Fan Min * */ public double computeMAE() throws Exception { double tempTotalError = 0; for (int i = 0; i < predictions.length; i++) { tempTotalError += Math.abs(predictions[i] - compressedRatingMatrix[i][2]); } // Of for i return tempTotalError / predictions.length; }// Of computeMAE / * * Compute the MAE based on the deviation of each leave-one-out. * * @author Fan Min * */ public double computeRSME() throws Exception { double tempTotalError = 0; for (int i = 0; i < predictions.length; i++) { tempTotalError += (predictions[i] - compressedRatingMatrix[i][2]) * (predictions[i] - compressedRatingMatrix[i][2]); } // Of for i double tempAverage = tempTotalError / predictions.length; return Math.sqrt(tempAverage); }// Of computeRSME / * * The entrance of the program. * * @param args * Not used now. * */ public static void main(String[] args) { try { MBR tempRecommender = new MBR("D:/data/movielens-943u1682m.txt", 943, 1682, ); for (double tempRadius = 0.2; tempRadius < 0.6; tempRadius += 0.1) { tempRecommender.setRadius(tempRadius); tempRecommender.leaveOneOutPrediction(); double tempMAE = tempRecommender.computeMAE(); double tempRSME = tempRecommender.computeRSME(); System.out.println("Radius = " + tempRadius + ", MAE = " + tempMAE + ", RSME = " + tempRSME + ", numNonNeighbors = " + tempRecommender.numNonNeighbors); } // Of for tempRadius } catch (Exception ee) { System.out.println(ee); } // Of try }// Of main }// Of class MBR 

第 55 天: 基于 M-distance 的推荐 (续)

j = userStartingIndices[tempUser]; j < userStartingIndices[tempUser + 1]; j++ 

就可将 tempUser 的所有评分信息读入. 然而, user-based recommendation 没有这样的便利. 为解决该问题, 可以有两种方案:

1. 将压缩矩阵转置, 用户与项目关系互换. 这种方案要增加相应的代码, 但复杂度低. 推荐使用.
2. 扫描时不仅仅是连续的数据, 而是需要整个数据集. 这种方案实现简单, 但复杂度高.

第 56 天: kMeans 聚类

kMeans 是最常用的聚类算法.

1. kMeans 聚类需要中心点收敛时结束. 偷懒使用了 Arrays.equals()
2. 数据集为 iris, 所以最后一个属性没使用. 如果对于没有决策属性的数据集, 需要进行相应修改.
3. 数据没有归一化.
4. getRandomIndices() 和 kMeans 的完全相同, 拷贝过来. 本来应该写在 SimpleTools.java 里面的, 代码不多, 为保证独立性就放这里了.
5. distance() 和 kMeans 的相似, 注意不要用决策属性, 而且参数不同. 第 2 个参数为实数向量, 这是类为中心可能为虚拟的, 而中心点那里并没有对象.

package machinelearning.kmeans; import java.io.FileReader; import java.util.Arrays; import java.util.Random; import weka.core.Instances; / * kMeans clustering. * @author Fan Min . */ public class KMeans { / * Manhattan distance. */ public static final int MANHATTAN = 0; / * Euclidean distance. */ public static final int EUCLIDEAN = 1; / * The distance measure. */ public int distanceMeasure = EUCLIDEAN; / * A random instance; */ public static final Random random = new Random(); / * The data. */ Instances dataset; / * The number of clusters. */ int numClusters = 2; / * The clusters. */ int[][] clusters; / * * The first constructor. * * @param paraFilename * The data filename. * */ public KMeans(String paraFilename) { dataset = null; try { FileReader fileReader = new FileReader(paraFilename); dataset = new Instances(fileReader); fileReader.close(); } catch (Exception ee) { System.out.println("Cannot read the file: " + paraFilename + "\r\n" + ee); System.exit(0); } // Of try }// Of the first constructor / * * A setter. * */ public void setNumClusters(int paraNumClusters) { numClusters = paraNumClusters; }// Of the setter / * * Get a random indices for data randomization. * * @param paraLength * The length of the sequence. * @return An array of indices, e.g., {4, 3, 1, 5, 0, 2} with length 6. * */ public static int[] getRandomIndices(int paraLength) { int[] resultIndices = new int[paraLength]; // Step 1. Initialize. for (int i = 0; i < paraLength; i++) { resultIndices[i] = i; } // Of for i // Step 2. Randomly swap. int tempFirst, tempSecond, tempValue; for (int i = 0; i < paraLength; i++) { // Generate two random indices. tempFirst = random.nextInt(paraLength); tempSecond = random.nextInt(paraLength); // Swap. tempValue = resultIndices[tempFirst]; resultIndices[tempFirst] = resultIndices[tempSecond]; resultIndices[tempSecond] = tempValue; } // Of for i return resultIndices; }// Of getRandomIndices / * * The distance between two instances. * * @param paraI * The index of the first instance. * @param paraArray * The array representing a point in the space. * @return The distance. * */ public double distance(int paraI, double[] paraArray) { int resultDistance = 0; double tempDifference; switch (distanceMeasure) { case MANHATTAN: for (int i = 0; i < dataset.numAttributes() - 1; i++) { tempDifference = dataset.instance(paraI).value(i) - paraArray[i]; if (tempDifference < 0) { resultDistance -= tempDifference; } else { resultDistance += tempDifference; } // Of if } // Of for i break; case EUCLIDEAN: for (int i = 0; i < dataset.numAttributes() - 1; i++) { tempDifference = dataset.instance(paraI).value(i) - paraArray[i]; resultDistance += tempDifference * tempDifference; } // Of for i break; default: System.out.println("Unsupported distance measure: " + distanceMeasure); }// Of switch return resultDistance; }// Of distance / * * Clustering. * */ public void clustering() { int[] tempOldClusterArray = new int[dataset.numInstances()]; tempOldClusterArray[0] = -1; int[] tempClusterArray = new int[dataset.numInstances()]; Arrays.fill(tempClusterArray, 0); double[][] tempCenters = new double[numClusters][dataset.numAttributes() - 1]; // Step 1. Initialize centers. int[] tempRandomOrders = getRandomIndices(dataset.numInstances()); for (int i = 0; i < numClusters; i++) { for (int j = 0; j < tempCenters[0].length; j++) { tempCenters[i][j] = dataset.instance(tempRandomOrders[i]).value(j); } // Of for j } // Of for i int[] tempClusterLengths = null; while (!Arrays.equals(tempOldClusterArray, tempClusterArray)) { System.out.println("New loop ..."); tempOldClusterArray = tempClusterArray; tempClusterArray = new int[dataset.numInstances()]; // Step 2.1 Minimization. Assign cluster to each instance. int tempNearestCenter; double tempNearestDistance; double tempDistance; for (int i = 0; i < dataset.numInstances(); i++) { tempNearestCenter = -1; tempNearestDistance = Double.MAX_VALUE; for (int j = 0; j < numClusters; j++) { tempDistance = distance(i, tempCenters[j]); if (tempNearestDistance > tempDistance) { tempNearestDistance = tempDistance; tempNearestCenter = j; } // Of if } // Of for j tempClusterArray[i] = tempNearestCenter; } // Of for i // Step 2.2 Mean. Find new centers. tempClusterLengths = new int[numClusters]; Arrays.fill(tempClusterLengths, 0); double[][] tempNewCenters = new double[numClusters][dataset.numAttributes() - 1]; // Arrays.fill(tempNewCenters, 0); for (int i = 0; i < dataset.numInstances(); i++) { for (int j = 0; j < tempNewCenters[0].length; j++) { tempNewCenters[tempClusterArray[i]][j] += dataset.instance(i).value(j); } // Of for j tempClusterLengths[tempClusterArray[i]]++; } // Of for i // Step 2.3 Now average for (int i = 0; i < tempNewCenters.length; i++) { for (int j = 0; j < tempNewCenters[0].length; j++) { tempNewCenters[i][j] /= tempClusterLengths[i]; } // Of for j } // Of for i System.out.println("Now the new centers are: " + Arrays.deepToString(tempNewCenters)); tempCenters = tempNewCenters; } // Of while // Step 3. Form clusters. clusters = new int[numClusters][]; int[] tempCounters = new int[numClusters]; for (int i = 0; i < numClusters; i++) { clusters[i] = new int[tempClusterLengths[i]]; } // Of for i for (int i = 0; i < tempClusterArray.length; i++) { clusters[tempClusterArray[i]][tempCounters[tempClusterArray[i]]] = i; tempCounters[tempClusterArray[i]]++; } // Of for i System.out.println("The clusters are: " + Arrays.deepToString(clusters)); }// Of clustering / * * Clustering. * */ public static void testClustering() { KMeans tempKMeans = new KMeans("D:/data/iris.arff"); tempKMeans.setNumClusters(3); tempKMeans.clustering(); }// Of testClustering / * * A testing method. * */ public static void main(String arags[]) { testClustering(); }// Of main }// Of class KMeans 

第 57 天: kMeans 聚类 (续)

第 58 天: 符号型数据的 NB 算法

Naive Bayes 是一种用后验概率公式推导出的算法. 它有一个独立性假设, 从数学上看起来不靠谱. 但从机器学习效果来说是不错的. 写程序之前, 先点击NB 算法 (包括符号型与数值型, 结合 Java 程序分析)进行学习.

1. 所有的程序都在今天列出, 但今天只研究符号型数据的分类. 为此, 可以只抄符号型数据相关的方法 (从 main() 顺藤摸瓜开始有选择性地抄), 明天再抄数值型数据处理算法. 421 行的代码仅仅是测试训练与测试集不同的情况, 没有必要抄.
2. 必须自己举一个小的例子 (如 10 个对象, 3 个条件属性, 2 个类别) 来辅助理解.
3. 需要查阅相关基础知识.
4. 需要理解三维数组每个维度的涵义: The conditional probabilities for all classes over all attributes on all values. 注意到三维数组不是规则的, 例如, 不同属性的属性值个数可能不同.
5. 这里使用同样的数据进行训练和测试. 如果要划分训练集和测试集, 可参考 kNN 代码.
6. tempPseudoProbability 初始化为 0 就错了. 对于类平衡数据集没影响, 但不平衡的话效果就不对了. 在这个问题上输了 50 块钱, 害!

package datastructure.nb; import java.io.FileReader; import java.util.Arrays; import java.util.Random; import weka.core.*; / * The Naive Bayes algorithm. * * @author Fan Min . */ public class NaiveBayes { / * * An inner class to store parameters. * */ private class GaussianParamters { double mu; double sigma; public GaussianParamters(double paraMu, double paraSigma) { mu = paraMu; sigma = paraSigma; }// Of the constructor public String toString() { return "(" + mu + ", " + sigma + ")"; }// Of toString }// Of GaussianParamters / * The data. */ Instances dataset; / * The number of classes. For binary classification it is 2. */ int numClasses; / * The number of instances. */ int numInstances; / * The number of conditional attributes. */ int numConditions; / * The prediction, including queried and predicted labels. */ int[] predicts; / * Class distribution. */ double[] classDistribution; / * Class distribution with Laplacian smooth. */ double[] classDistributionLaplacian; / * To calculate the conditional probabilities for all classes over all * attributes on all values. */ double[][][] conditionalCounts; / * The conditional probabilities with Laplacian smooth. */ double[][][] conditionalProbabilitiesLaplacian; / * The Guassian parameters. */ GaussianParamters[][] gaussianParameters; / * Data type. */ int dataType; / * Nominal. */ public static final int NOMINAL = 0; / * Numerical. */ public static final int NUMERICAL = 1; / * The constructor. * * @param paraFilename * The given file. */ public NaiveBayes(String paraFilename) { dataset = null; try { FileReader fileReader = new FileReader(paraFilename); dataset = new Instances(fileReader); fileReader.close(); } catch (Exception ee) { System.out.println("Cannot read the file: " + paraFilename + "\r\n" + ee); System.exit(0); } // Of try dataset.setClassIndex(dataset.numAttributes() - 1); numConditions = dataset.numAttributes() - 1; numInstances = dataset.numInstances(); numClasses = dataset.attribute(numConditions).numValues(); }// Of the constructor / * The constructor. * * @param paraFilename * The given file. */ public NaiveBayes(Instances paraInstances) { dataset = paraInstances; dataset.setClassIndex(dataset.numAttributes() - 1); numConditions = dataset.numAttributes() - 1; numInstances = dataset.numInstances(); numClasses = dataset.attribute(numConditions).numValues(); }// Of the constructor / * Set the data type. */ public void setDataType(int paraDataType) { dataType = paraDataType; }// Of setDataType / * Calculate the class distribution with Laplacian smooth. */ public void calculateClassDistribution() { classDistribution = new double[numClasses]; classDistributionLaplacian = new double[numClasses]; double[] tempCounts = new double[numClasses]; for (int i = 0; i < numInstances; i++) { int tempClassValue = (int) dataset.instance(i).classValue(); tempCounts[tempClassValue]++; } // Of for i for (int i = 0; i < numClasses; i++) { classDistribution[i] = tempCounts[i] / numInstances; classDistributionLaplacian[i] = (tempCounts[i] + 1) / (numInstances + numClasses); } // Of for i System.out.println("Class distribution: " + Arrays.toString(classDistribution)); System.out.println("Class distribution Laplacian: " + Arrays.toString(classDistributionLaplacian)); }// Of calculateClassDistribution / * Calculate the conditional probabilities with Laplacian smooth. ONLY scan * the dataset once. There was a simpler one, I have removed it because the * time complexity is higher. */ public void calculateConditionalProbabilities() { conditionalCounts = new double[numClasses][numConditions][]; conditionalProbabilitiesLaplacian = new double[numClasses][numConditions][]; // Allocate space for (int i = 0; i < numClasses; i++) { for (int j = 0; j < numConditions; j++) { int tempNumValues = (int) dataset.attribute(j).numValues(); conditionalCounts[i][j] = new double[tempNumValues]; conditionalProbabilitiesLaplacian[i][j] = new double[tempNumValues]; } // Of for j } // Of for i // Count the numbers int[] tempClassCounts = new int[numClasses]; for (int i = 0; i < numInstances; i++) { int tempClass = (int) dataset.instance(i).classValue(); tempClassCounts[tempClass]++; for (int j = 0; j < numConditions; j++) { int tempValue = (int) dataset.instance(i).value(j); conditionalCounts[tempClass][j][tempValue]++; } // Of for j } // Of for i // Now for the real probability with Laplacian for (int i = 0; i < numClasses; i++) { for (int j = 0; j < numConditions; j++) { int tempNumValues = (int) dataset.attribute(j).numValues(); for (int k = 0; k < tempNumValues; k++) { conditionalProbabilitiesLaplacian[i][j][k] = (conditionalCounts[i][j][k] + 1) / (tempClassCounts[i] + tempNumValues); // I wrote a bug here. This is an alternative approach, // however its performance is better in the mushroom dataset. // conditionalProbabilitiesLaplacian[i][j][k] = // (numInstances * conditionalCounts[i][j][k] + 1) // / (numInstances * tempClassCounts[i] + tempNumValues); } // Of for k } // Of for j } // Of for i System.out.println("Conditional probabilities: " + Arrays.deepToString(conditionalCounts)); }// Of calculateConditionalProbabilities / * Calculate the conditional probabilities with Laplacian smooth. */ public void calculateGausssianParameters() { gaussianParameters = new GaussianParamters[numClasses][numConditions]; double[] tempValuesArray = new double[numInstances]; int tempNumValues = 0; double tempSum = 0; for (int i = 0; i < numClasses; i++) { for (int j = 0; j < numConditions; j++) { tempSum = 0; // Obtain values for this class. tempNumValues = 0; for (int k = 0; k < numInstances; k++) { if ((int) dataset.instance(k).classValue() != i) { continue; } // Of if tempValuesArray[tempNumValues] = dataset.instance(k).value(j); tempSum += tempValuesArray[tempNumValues]; tempNumValues++; } // Of for k // Obtain parameters. double tempMu = tempSum / tempNumValues; double tempSigma = 0; for (int k = 0; k < tempNumValues; k++) { tempSigma += (tempValuesArray[k] - tempMu) * (tempValuesArray[k] - tempMu); } // Of for k tempSigma /= tempNumValues; tempSigma = Math.sqrt(tempSigma); gaussianParameters[i][j] = new GaussianParamters(tempMu, tempSigma); } // Of for j } // Of for i System.out.println(Arrays.deepToString(gaussianParameters)); }// Of calculateGausssianParameters / * Classify all instances, the results are stored in predicts[]. */ public void classify() { predicts = new int[numInstances]; for (int i = 0; i < numInstances; i++) { predicts[i] = classify(dataset.instance(i)); } // Of for i }// Of classify / * Classify an instances. */ public int classify(Instance paraInstance) { if (dataType == NOMINAL) { return classifyNominal(paraInstance); } else if (dataType == NUMERICAL) { return classifyNumerical(paraInstance); } // Of if return -1; }// Of classify / * Classify an instances with nominal data. */ public int classifyNominal(Instance paraInstance) { // Find the biggest one double tempBiggest = -10000; int resultBestIndex = 0; for (int i = 0; i < numClasses; i++) { double tempPseudoProbability = Math.log(classDistributionLaplacian[i]); for (int j = 0; j < numConditions; j++) { int tempAttributeValue = (int) paraInstance.value(j); tempPseudoProbability += Math.log(conditionalProbabilitiesLaplacian[i][j][tempAttributeValue]); } // Of for j if (tempBiggest < tempPseudoProbability) { tempBiggest = tempPseudoProbability; resultBestIndex = i; } // Of if } // Of for i return resultBestIndex; }// Of classifyNominal / * Classify an instances with numerical data. */ public int classifyNumerical(Instance paraInstance) { // Find the biggest one double tempBiggest = -10000; int resultBestIndex = 0; for (int i = 0; i < numClasses; i++) { double tempPseudoProbability = Math.log(classDistributionLaplacian[i]); for (int j = 0; j < numConditions; j++) { double tempAttributeValue = paraInstance.value(j); double tempSigma = gaussianParameters[i][j].sigma; double tempMu = gaussianParameters[i][j].mu; tempPseudoProbability += -Math.log(tempSigma) - (tempAttributeValue - tempMu) * (tempAttributeValue - tempMu) / (2 * tempSigma * tempSigma); } // Of for j if (tempBiggest < tempPseudoProbability) { tempBiggest = tempPseudoProbability; resultBestIndex = i; } // Of if } // Of for i return resultBestIndex; }// Of classifyNumerical / * Compute accuracy. */ public double computeAccuracy() { double tempCorrect = 0; for (int i = 0; i < numInstances; i++) { if (predicts[i] == (int) dataset.instance(i).classValue()) { tempCorrect++; } // Of if } // Of for i double resultAccuracy = tempCorrect / numInstances; return resultAccuracy; }// Of computeAccuracy / * * Test nominal data. * */ public static void testNominal() { System.out.println("Hello, Naive Bayes. I only want to test the nominal data."); String tempFilename = "D:/data/mushroom.arff"; NaiveBayes tempLearner = new NaiveBayes(tempFilename); tempLearner.setDataType(NOMINAL); tempLearner.calculateClassDistribution(); tempLearner.calculateConditionalProbabilities(); tempLearner.classify(); System.out.println("The accuracy is: " + tempLearner.computeAccuracy()); }// Of testNominal / * * Test numerical data. * */ public static void testNumerical() { System.out.println("Hello, Naive Bayes. I only want to test the numerical data with Gaussian assumption."); // String tempFilename = "D:/data/iris.arff"; String tempFilename = "D:/data/iris-imbalance.arff"; NaiveBayes tempLearner = new NaiveBayes(tempFilename); tempLearner.setDataType(NUMERICAL); tempLearner.calculateClassDistribution(); tempLearner.calculateGausssianParameters(); tempLearner.classify(); System.out.println("The accuracy is: " + tempLearner.computeAccuracy()); }// Of testNumerical / * * Test this class. * * @param args * Not used now. * */ public static void main(String[] args) { testNominal(); testNumerical(); // testNominal(0.8); }// Of main / * * Get a random indices for data randomization. * * @param paraLength * The length of the sequence. * @return An array of indices, e.g., {4, 3, 1, 5, 0, 2} with length 6. * */ public static int[] getRandomIndices(int paraLength) { Random random = new Random(); int[] resultIndices = new int[paraLength]; // Step 1. Initialize. for (int i = 0; i < paraLength; i++) { resultIndices[i] = i; } // Of for i // Step 2. Randomly swap. int tempFirst, tempSecond, tempValue; for (int i = 0; i < paraLength; i++) { // Generate two random indices. tempFirst = random.nextInt(paraLength); tempSecond = random.nextInt(paraLength); // Swap. tempValue = resultIndices[tempFirst]; resultIndices[tempFirst] = resultIndices[tempSecond]; resultIndices[tempSecond] = tempValue; } // Of for i return resultIndices; }// Of getRandomIndices / * * Split the data into training and testing parts. * * @param paraTrainingFraction * The fraction of the training set. * */ public static Instances[] splitTrainingTesting(Instances paraDataset, double paraTrainingFraction) { int tempSize = paraDataset.numInstances(); int[] tempIndices = getRandomIndices(tempSize); int tempTrainingSize = (int) (tempSize * paraTrainingFraction); // Empty datasets. Instances tempTrainingSet = new Instances(paraDataset); tempTrainingSet.delete(); Instances tempTestingSet = new Instances(tempTrainingSet); for (int i = 0; i < tempTrainingSize; i++) { tempTrainingSet.add(paraDataset.instance(tempIndices[i])); } // Of for i for (int i = 0; i < tempSize - tempTrainingSize; i++) { tempTestingSet.add(paraDataset.instance(tempIndices[tempTrainingSize + i])); } // Of for i tempTrainingSet.setClassIndex(tempTrainingSet.numAttributes() - 1); tempTestingSet.setClassIndex(tempTestingSet.numAttributes() - 1); Instances[] resultInstanesArray = new Instances[2]; resultInstanesArray[0] = tempTrainingSet; resultInstanesArray[1] = tempTestingSet; return resultInstanesArray; }// Of splitTrainingTesting / * Classify all instances, the results are stored in predicts[]. */ public double classify(Instances paraTestingSet) { double tempCorrect = 0; int[] tempPredicts = new int[paraTestingSet.numInstances()]; for (int i = 0; i < tempPredicts.length; i++) { tempPredicts[i] = classify(paraTestingSet.instance(i)); if (tempPredicts[i] == (int) paraTestingSet.instance(i).classValue()) { tempCorrect++; } // Of if } // Of for i System.out.println("" + tempCorrect + " correct over " + tempPredicts.length + " instances."); double resultAccuracy = tempCorrect / tempPredicts.length; return resultAccuracy; }// Of classify / * * Test nominal data. * */ public static void testNominal(double paraTrainingFraction) { System.out.println("Hello, Naive Bayes. I only want to test the nominal data."); String tempFilename = "D:/data/mushroom.arff"; // String tempFilename = "D:/data/voting.arff"; Instances tempDataset = null; try { FileReader fileReader = new FileReader(tempFilename); tempDataset = new Instances(fileReader); fileReader.close(); } catch (Exception ee) { System.out.println("Cannot read the file: " + tempFilename + "\r\n" + ee); System.exit(0); } // Of try Instances[] tempDatasets = splitTrainingTesting(tempDataset, paraTrainingFraction); NaiveBayes tempLearner = new NaiveBayes(tempDatasets[0]); tempLearner.setDataType(NOMINAL); tempLearner.calculateClassDistribution(); tempLearner.calculateConditionalProbabilities(); double tempAccuracy = tempLearner.classify(tempDatasets[1]); System.out.println("The accuracy is: " + tempAccuracy); }// Of testNominal }// Of class NaiveBayes 

第 59 天: 数值型数据的 NB 算法

1. 今天把数值型数据处理的代码加上去.
2. 假设所有属性的属性值都服从高斯分布. 也可以做其它假设.
3. 将概率密度当成概率值直接使用 Bayes 公式.
4. 可以看到, 数值型数据的处理并不会比符号型的复杂.

第 60 天: 小结

描述这 10 天的学习体会, 不少于 10 条.