Median and standard deviation
中值和标准差的计算比前面的例子复杂一点。因为这种运算是非关联的，它们不是那么容易的能从combiner中获益。中值是将数据集一分为两等份的数值类型，一份比中值大，一部分比中值小。这需要数据集按顺序完成清洗。数据必须是排序的，但存在一定障碍，因为MapReduce不会根据values排序。
方差告诉我们数据跟平均值之间的差异程度。这就要求我们之前要先找到平均值。执行这种操作最容易的方法是复制值得列表到临时列表，以便找到中值，或者再一次迭代集合所有数据得到标准差。对大的数据量，这种实现可能导致java堆空间的问题，引文每个输入组的每个值都放进内存处理。下一个例子就是针对这种问题的。
问题：给出用户评论，计算一天中每个小时评论长度的中值和标准差。
Mapper code。Mapper会处理每条输入记录计算一天内每个小时评论长度的中值（貌似事实不是这样）。输出键是小时，输出值是评论长度。
public static class MedianStdDevMapper extends Mapper<Object, Text, IntWritable, IntWritable> {
private IntWritable outHour = new IntWritable();
private IntWritable outCommentLength = new IntWritable();
private final static SimpleDateFormat frmt = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSS");
public void map(Object key, Text value, Context context) throws IOException, InterruptedException {
Map<String, String> parsed = MRDPUtils.transformXmlToMap(value.toString());
// Grab the "CreationDate" field,
// since it is what we are grouping by
String strDate = parsed.get("CreationDate");
// Grab the comment to find the length
String text = parsed.get("Text");
// get the hour this comment was posted in
Date creationDate = null;
try {
creationDate = frmt.parse(strDate);
} catch (ParseException e) {
e.printStackTrace();
}
outHour.set(creationDate.getHours());
// set the comment length
outCommentLength.set(text.length());
// write out the user ID with min max dates and count
context.write(outHour, outCommentLength);
}
}
Reducer code。Reducer会迭代给定值得集合，并把每个值加到内存列表里。同时也会计算一个动态的sum和count。迭代之后，评论长度被排序，以便找出中值。如果数量是偶数，中值是中间两个数的平均值。下面，根据动态的sum和count计算出平均值，然后迭代排序的列表计算出标准差。每个数跟平均值的差的平方累加求和保存在一个动态sum中，这个sum的平方根就是标准差。最后输出key，中值和标准差。
public static class MedianStdDevReducer extends Reducer<IntWritable, IntWritable, IntWritable, MedianStdDevTuple> {
private MedianStdDevTuple result = new MedianStdDevTuple();
private ArrayList<Double> commentLengths = new ArrayList<Double>();
public void reduce(IntWritable key, Iterable<IntWritable> values, Context context) throws IOException, InterruptedException {
double sum = 0;
double count = 0;
commentLengths.clear();
result.setStdDev(0d);
// Iterate through all input values for this key
for (IntWritable val : values) {
commentLengths.add((double) val.get());
sum += val.get();
++count;
}
// sort commentLengths to calculate median
Collections.sort(commentLengths);
// if commentLengths is an even value, average middle two elements
if (count % 2 == 0) {
result.setMedian((commentLengths.get((int) count / 2 - 1) +
commentLengths.get((int) count / 2)) / 2.0f);
} else {
// else, set median to middle value
result.setMedian(commentLengths.get((int) count / 2));
}
// calculate standard deviation
double mean = sum / count;
double sumOfSquares = 0.0f;
for (double f : commentLengths) {
sumOfSquares += (f - mean) * (f - mean);
}
result.setStdDev((double) Math.sqrt(sumOfSquares / (count - 1)));
context.write(key, result);
}
}
Combiner optimization。这种情况下不能用combiner。reducer需要所有的值去计算中值和标准差。因为combiner仅仅在一个map本地处理中间键值对。计算完整的中值，和标准值是不可能的。下面的例子是一种复杂一点的使用自定义的combiner的实现。
Memory-conscious median and standard deviation
下面的例子跟前一个不同，并减少了内存的使用。把值放进列表会导致很多重复的元素。一种去重的方法是标记元素的个数。例如，对于列表< 1, 1, 1, 1, 2, 2, 3,4, 5, 5, 5 >,可以用一个sorted map保存：(1→4, 2→2, 3→1, 4→1, 5→3)。核心的原理是一样的：reduce阶段会迭代所有值并放入内存数据结构中。数据结构和搜索的方式是改变的地方。Map很大程度上减少了内存的使用。前一个例子使用list，复杂度为O（n），n是评论条数，本例使用map，使用键值对，为O（max（m）），m是评论长度的最大值。作为额外的补充，combiner的使用能帮助聚合评论长度的数目，并通过writable对象输出reducer端将要使用的这个map。
问题：同前一个。
Mapper code。Mapper处理输入记录，输出键是小时，值是sortedmapwritable对象，包含一个元素：评论长度和计数1.这个map在reducer和combiner里多处用到。
public static class MedianStdDevMapper extends Mapper<Object, Text, IntWritable, SortedMapWritable> {
private IntWritable commentLength = new IntWritable();
private static final LongWritable ONE = new LongWritable(1);
private IntWritable outHour = new IntWritable();
private final static SimpleDateFormat frmt = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSS");
public void map(Object key, Text value, Context context) throws IOException, InterruptedException {
Map<String, String> parsed = MRDPUtils.transformXmlToMap(value.toString());
// Grab the "CreationDate" field,
// since it is what we are grouping by
String strDate = parsed.get("CreationDate");
// Grab the comment to find the length
String text = parsed.get("Text");
// Get the hour this comment was posted in
Date creationDate = null;
try {
creationDate = frmt.parse(strDate);
} catch (ParseException e) {
e.printStackTrace();
}
outHour.set(creationDate.getHours());
commentLength.set(text.length());
SortedMapWritable outCommentLength = new SortedMapWritable();
outCommentLength.put(commentLength, ONE);
// Write out the user ID with min max dates and count
context.write(outHour, outCommentLength);
}
}
Reducer code。Reducer通过迭代上面的map生成一个大的treemap，key是评论长度，value是这个长度的评论的数目。
迭代以后，中值被计算出来。中值的索引由评论总数除以2得出。然后迭代treemap的entrySet找到key，需满足条件为：previousCommentCount≤ medianIndex < commentCount，把treeMap的值加到每一步迭代的评论里。一旦条件满足，如果有偶数条评论且中值索引等于前一条评论的，中值取前一个的长度和当前长度的平均值。否则，中值就是当前评论的长度。
接下来，再一次迭代treemap,计算出平方和，确保相关联的评论长度和数目相乘。标准差就根据平方和算出来了。中值和标准差就随着key一块输出。
public static class MedianStdDevReducer extends
Reducer<IntWritable, SortedMapWritable,
IntWritable, MedianStdDevTuple> {
private MedianStdDevTuple result = new MedianStdDevTuple();
private TreeMap<Integer, Long> commentLengthCounts =
new TreeMap<Integer, Long>();
public void reduce(IntWritable key, Iterable<SortedMapWritable>values,
Context context) throws IOException, InterruptedException {
float sum = 0;
long totalComments = 0;
commentLengthCounts.clear();
result.setMedian(0);
result.setStdDev(0);
for (SortedMapWritable v : values) {
for (Entry<WritableComparable, Writable> entry : v.entrySet()) {
int length = ((IntWritable) entry.getKey()).get();
long count = ((LongWritable) entry.getValue()).get();
totalComments += count;
sum += length * count;
Long storedCount = commentLengthCounts.get(length);
if (storedCount == null) {
commentLengthCounts.put(length, count);
} else {
commentLengthCounts.put(length, storedCount + count);
}
}
}
long medianIndex = totalComments / 2L;
long previousComments = 0;
long comments = 0;
int prevKey = 0;
for (Entry<Integer, Long> entry : commentLengthCounts.entrySet()) {
comments = previousComments + entry.getValue();
if (previousComments ≤ medianIndex && medianIndex < comments) {
if (totalComments % 2 == 0 &&previousComments == medianIndex) {
result.setMedian((float) (entry.getKey() + prevKey) / 2.0f);
} else {
result.setMedian(entry.getKey());
}
break;
}
previousComments = comments;
prevKey = entry.getKey();
}
// calculate standard deviation
float mean = sum / totalComments;
float sumOfSquares = 0.0f;
for (Entry<Integer, Long> entry : commentLengthCounts.entrySet()) {
sumOfSquares += (entry.getKey() - mean) * (entry.getKey() - mean) *
entry.getValue();
}
result.setStdDev((float) Math.sqrt(sumOfSquares / (totalComments - 1)));
context.write(key, result);
}
}
Combiner optimization。跟前面的例子不同，这里combiner的逻辑跟reducer不同。Reducer计算中值和标准差，而combiner对每个本地map的中间键值对聚合sortedMapWritable条目。代码解析这些条目并在本地map聚合它们，这跟前面部分的reducer代码是相同的。这里用一个hashmap替换treemap，因为不需要排序，且hashmap更快。Reducer使用map计算中值和标准差，而combiner是用sortedMapWritable序列化为reduce阶段做准备。
public static class MedianStdDevCombiner extends
Reducer<IntWritable, SortedMapWritable, IntWritable, SortedMapWritable> {
protected void reduce(IntWritable key,
Iterable<SortedMapWritable>values, Context context)
throws IOException, InterruptedException {
SortedMapWritable outValue = new SortedMapWritable();
for (SortedMapWritable v : values) {
for (Entry<WritableComparable, Writable> entry : v.entrySet()) {
LongWritable count = (LongWritable) outValue.get(entry.getKey());
if (count != null) {
count.set(count.get()
+ ((LongWritable) entry.getValue()).get());
} else {
outValue.put(entry.getKey(), new LongWritable(
((LongWritable) entry.getValue()).get()));
}
}
}
context.write(key, outValue);
}
}
Data flow diagram。图2-4展示了例子的数据流程图
Figure 2-4. Data flow for the standard deviation example