# Basic Statistics

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## Correlation

Calculating the correlation between two series of data is a common operation in Statistics. In spark.ml we provide the flexibility to calculate pairwise correlations among many series. The supported correlation methods are currently Pearson’s and Spearman’s correlation.

Correlation computes the correlation matrix for the input Dataset of Vectors using the specified method. The output will be a DataFrame that contains the correlation matrix of the column of vectors.

import org.apache.spark.ml.linalg.{Matrix, Vectors}
import org.apache.spark.ml.stat.Correlation
import org.apache.spark.sql.Row

val data = Seq(
Vectors.sparse(4, Seq((0, 1.0), (3, -2.0))),
Vectors.dense(4.0, 5.0, 0.0, 3.0),
Vectors.dense(6.0, 7.0, 0.0, 8.0),
Vectors.sparse(4, Seq((0, 9.0), (3, 1.0)))
)

val df = data.map(Tuple1.apply).toDF("features")
val Row(coeff1: Matrix) = Correlation.corr(df, "features").head
println(s"Pearson correlation matrix:\n $coeff1") val Row(coeff2: Matrix) = Correlation.corr(df, "features", "spearman").head println(s"Spearman correlation matrix:\n$coeff2")

Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/CorrelationExample.scala" in the Spark repo.

Correlation computes the correlation matrix for the input Dataset of Vectors using the specified method. The output will be a DataFrame that contains the correlation matrix of the column of vectors.

import java.util.Arrays;
import java.util.List;

import org.apache.spark.ml.linalg.Vectors;
import org.apache.spark.ml.linalg.VectorUDT;
import org.apache.spark.ml.stat.Correlation;
import org.apache.spark.sql.Dataset;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;

List<Row> data = Arrays.asList(
RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{1.0, -2.0})),
RowFactory.create(Vectors.dense(4.0, 5.0, 0.0, 3.0)),
RowFactory.create(Vectors.dense(6.0, 7.0, 0.0, 8.0)),
RowFactory.create(Vectors.sparse(4, new int[]{0, 3}, new double[]{9.0, 1.0}))
);

StructType schema = new StructType(new StructField[]{
new StructField("features", new VectorUDT(), false, Metadata.empty()),
});

Dataset<Row> df = spark.createDataFrame(data, schema);
System.out.println("Pearson correlation matrix:\n" + r1.get(0).toString());

Row r2 = Correlation.corr(df, "features", "spearman").head();
System.out.println("Spearman correlation matrix:\n" + r2.get(0).toString());

Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaCorrelationExample.java" in the Spark repo.

Correlation computes the correlation matrix for the input Dataset of Vectors using the specified method. The output will be a DataFrame that contains the correlation matrix of the column of vectors.

from pyspark.ml.linalg import Vectors
from pyspark.ml.stat import Correlation

data = [(Vectors.sparse(4, [(0, 1.0), (3, -2.0)]),),
(Vectors.dense([4.0, 5.0, 0.0, 3.0]),),
(Vectors.dense([6.0, 7.0, 0.0, 8.0]),),
(Vectors.sparse(4, [(0, 9.0), (3, 1.0)]),)]
df = spark.createDataFrame(data, ["features"])

print("Pearson correlation matrix:\n" + str(r1[0]))

print("Spearman correlation matrix:\n" + str(r2[0]))

Find full example code at "examples/src/main/python/ml/correlation_example.py" in the Spark repo.

## Hypothesis testing

Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically significant, whether this result occurred by chance or not. spark.ml currently supports Pearson’s Chi-squared ( $\chi^2$) tests for independence.

ChiSquareTest conducts Pearson’s independence test for every feature against the label. For each feature, the (feature, label) pairs are converted into a contingency matrix for which the Chi-squared statistic is computed. All label and feature values must be categorical.

Refer to the ChiSquareTest Scala docs for details on the API.

import org.apache.spark.ml.linalg.{Vector, Vectors}
import org.apache.spark.ml.stat.ChiSquareTest

val data = Seq(
(0.0, Vectors.dense(0.5, 10.0)),
(0.0, Vectors.dense(1.5, 20.0)),
(1.0, Vectors.dense(1.5, 30.0)),
(0.0, Vectors.dense(3.5, 30.0)),
(0.0, Vectors.dense(3.5, 40.0)),
(1.0, Vectors.dense(3.5, 40.0))
)

val df = data.toDF("label", "features")
val chi = ChiSquareTest.test(df, "features", "label").head
println(s"pValues = ${chi.getAs[Vector](0)}") println(s"degreesOfFreedom${chi.getSeq[Int](1).mkString("[", ",", "]")}")
println(s"statistics \${chi.getAs[Vector](2)}")

Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/ChiSquareTestExample.scala" in the Spark repo.

Refer to the ChiSquareTest Java docs for details on the API.

import java.util.Arrays;
import java.util.List;

import org.apache.spark.ml.linalg.Vectors;
import org.apache.spark.ml.linalg.VectorUDT;
import org.apache.spark.ml.stat.ChiSquareTest;
import org.apache.spark.sql.Dataset;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.RowFactory;
import org.apache.spark.sql.types.*;

List<Row> data = Arrays.asList(
RowFactory.create(0.0, Vectors.dense(0.5, 10.0)),
RowFactory.create(0.0, Vectors.dense(1.5, 20.0)),
RowFactory.create(1.0, Vectors.dense(1.5, 30.0)),
RowFactory.create(0.0, Vectors.dense(3.5, 30.0)),
RowFactory.create(0.0, Vectors.dense(3.5, 40.0)),
RowFactory.create(1.0, Vectors.dense(3.5, 40.0))
);

StructType schema = new StructType(new StructField[]{
new StructField("features", new VectorUDT(), false, Metadata.empty()),
});

Dataset<Row> df = spark.createDataFrame(data, schema);
Row r = ChiSquareTest.test(df, "features", "label").head();
System.out.println("pValues: " + r.get(0).toString());
System.out.println("degreesOfFreedom: " + r.getList(1).toString());
System.out.println("statistics: " + r.get(2).toString());

Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaChiSquareTestExample.java" in the Spark repo.

Refer to the ChiSquareTest Python docs for details on the API.

from pyspark.ml.linalg import Vectors
from pyspark.ml.stat import ChiSquareTest

data = [(0.0, Vectors.dense(0.5, 10.0)),
(0.0, Vectors.dense(1.5, 20.0)),
(1.0, Vectors.dense(1.5, 30.0)),
(0.0, Vectors.dense(3.5, 30.0)),
(0.0, Vectors.dense(3.5, 40.0)),
(1.0, Vectors.dense(3.5, 40.0))]
df = spark.createDataFrame(data, ["label", "features"])