How to Efficiently Calculate Median and Quantiles in Apache Spark?

Finding Median and Quantiles in Apache Spark

Introduction

When dealing with large datasets, finding the median and quantiles can be a computationally expensive task. Spark's distributed computing capabilities make it well-suited for handling such computations.

Spark 2.0

Approximation with approxQuantile:

Spark 2.0 and above provide the approxQuantile method, which leverages the Greenwald-Khanna algorithm for efficient quantile estimation. It returns the quantile value for a given probability p with an optional relative error threshold.

Example:

<code class="python"># DataFrame:
df.approxQuantile("x", [0.5], 0.25)

# RDD:
rdd.map(lambda x: (x,)).toDF().approxQuantile("x", [0.5], 0.25)</code>

SQL:

In SQL aggregation, you can use the approx_percentile function to estimate the quantile:

<code class="sql">SELECT approx_percentile(column, 0.5) FROM table;</code>

Pre-Spark 2.0

Sampling and Local Computation:

For smaller datasets or when exact quantiles are not required, sampling the data and computing the quantiles locally can be a viable option. This avoids the overhead of sorting and distributing the data.

Example:

<code class="python">from numpy import median

sampled_rdd = rdd.sample(False, 0.1)  # Sample 10% of the data
sampled_quantiles = median(sampled_rdd.collect())</code>

Sorting and Partitioning:

If sampling is not feasible, sorting the data and finding the median or other quantiles can be done directly on the RDD. However, this approach can be slower and less efficient compared to sampling.

Example:

<code class="python">import numpy as np

# Sort and compute quantiles
sorted_rdd = rdd.sortBy(lambda x: x)
partition_index = int(len(rdd.collect()) * p)
partition_value = sorted_rdd.collect()[partition_index]

# Compute quantiles by splitting the partitions
if p == 0.5:
    median = partition_value
else:
    partition_value_left = sorted_rdd.collect()[partition_index - 1]
    median = partition_value_left + (p - 0.5) * (partition_value - partition_value_left)</code>

Hive UDAFs:

If using HiveContext, you can leverage Hive UDAFs for calculating quantiles:

<code class="python"># Continuous values:
sqlContext.sql("SELECT percentile(x, 0.5) FROM table")

# Integral values:
sqlContext.sql("SELECT percentile_approx(x, 0.5) FROM table")</code>

Conclusion

Spark provides various options for finding median and quantiles. The choice of method depends on factors such as data size, accuracy requirements, and the availability of HiveContext.

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