em算法Java代码，MapReduce实现EM算法步骤+代码

EM算法是一种迭代算法，用于在含有隐变量的概率模型中进行参数估计。以下是EM算法的Java代码实现：

public class EMAlgorithm {

    // E-step：计算隐变量的后验概率
    public double[][] getPosterior(double[][] data, double[] weights, double[] means, double[] variances) {
        int numPoints = data.length;
        int numClusters = means.length;

        double[][] posterior = new double[numPoints][numClusters];
        for (int i = 0; i < numPoints; i++) {
            double sum = 0.0;
            for (int j = 0; j < numClusters; j++) {
                posterior[i][j] = weights[j] * Gaussian(data[i], means[j], variances[j]);
                sum += posterior[i][j];
            }
            for (int j = 0; j < numClusters; j++) {
                posterior[i][j] /= sum;
            }
        }
        return posterior;
    }

    // M-step：计算新的参数
    public double[] getWeights(double[][] posterior) {
        int numPoints = posterior.length;
        int numClusters = posterior[0].length;

        double[] weights = new double[numClusters];
        for (int j = 0; j < numClusters; j++) {
            double sum = 0.0;
            for (int i = 0; i < numPoints; i++) {
                sum += posterior[i][j];
            }
            weights[j] = sum / numPoints;
        }
        return weights;
    }

    public double[] getMeans(double[][] data, double[][] posterior) {
        int numClusters = posterior[0].length;
        int numDimensions = data[0].length;
        double[] means = new double[numClusters];

        for (int j = 0; j < numClusters; j++) {
            double sum = 0.0;
            double totalWeight = 0.0;
            for (int i = 0; i < data.length; i++) {
                sum += posterior[i][j] * data[i][j];
                totalWeight += posterior[i][j];
            }
            means[j] = sum / totalWeight;
        }
        return means;
    }

    public double[] getVariances(double[][] data, double[][] posterior, double[] means) {
        int numClusters = posterior[0].length;
        int numDimensions = data[0].length;
        double[] variances = new double[numClusters];

        for (int j = 0; j < numClusters; j++) {
            double sum = 0.0;
            double totalWeight = 0.0;
            for (int i = 0; i < data.length; i++) {
                sum += posterior[i][j] * Math.pow(data[i][j] - means[j], 2);
                totalWeight += posterior[i][j];
            }
            variances[j] = sum / totalWeight;
        }
        return variances;
    }

    private double Gaussian(double[] dataPoint, double mean, double variance) {
        double stdDev = Math.sqrt(variance);
        return (1.0 / (stdDev * Math.sqrt(2 * Math.PI))) * Math.exp(-Math.pow(dataPoint[0] - mean, 2) / (2 * variance));
    }
}

下面是MapReduce实现EM算法的步骤：

1. Map阶段：对每个数据点，计算它对每个聚类中心的后验概率，输出键值对\<聚类中心, 后验概率\>；
2. Reduce阶段：对每个聚类中心，计算它的新的权重、均值和方差，并输出键值对\<聚类中心, 参数\>；
3. 迭代以上步骤，直到收敛为止。

以下是MapReduce实现EM算法的Java代码：

public class KMeansMR {

    public static class Map extends Mapper<LongWritable, Text, IntWritable, DoubleWritable> {

        private final static IntWritable cluster = new IntWritable();
        private final static DoubleWritable posterior = new DoubleWritable();

        public void map(LongWritable key, Text value, Context context) throws IOException, InterruptedException {
            // 读取数据点
            double[] dataPoint = parseDataPoint(value.toString());

            // 计算数据点对每个聚类中心的后验概率
            for (int i = 0; i < numClusters; i++) {
                double posterior = weights[i] * Gaussian(dataPoint, means[i], variances[i]);
                cluster.set(i);
                posterior.set(posterior);
                context.write(cluster, posterior);
            }
        }
    }

    public static class Reduce extends Reducer<IntWritable, DoubleWritable, IntWritable, Text> {

        private final static DecimalFormat df = new DecimalFormat("#.####");

        public void reduce(IntWritable key, Iterable<DoubleWritable> values, Context context) throws IOException, InterruptedException {
            double sum = 0.0;
            int count = 0;
            for (DoubleWritable value : values) {
                sum += value.get();
                count++;
            }

            // 计算新的权重、均值和方差
            double newWeight = sum / numPoints;
            double[] newMeans = getNewMeans(key.get());
            double[] newVariances = getNewVariances(key.get(), newMeans);

            // 输出键值对<聚类中心, 参数>
            Text outputValue = new Text(df.format(newWeight) + "," + Arrays.toString(newMeans) + "," + Arrays.toString(newVariances));
            context.write(key, outputValue);
        }
    }

    public static void main(String[] args) throws Exception {
        Configuration conf = new Configuration();
        Job job = Job.getInstance(conf, "KMeansMR");
        job.setJarByClass(KMeansMR.class);
        job.setMapperClass(Map.class);
        job.setReducerClass(Reduce.class);
        job.setOutputKeyClass(IntWritable.class);
        job.setOutputValueClass(DoubleWritable.class);
        FileInputFormat.addInputPath(job, new Path(args[0]));
        FileOutputFormat.setOutputPath(job, new Path(args[1]));
        System.exit(job.waitForCompletion(true) ? 0 : 1);
    }
}