[SPARK-20423][ML] fix MLOR coeffs centering when reg == 0

## What changes were proposed in this pull request?

When reg == 0, MLOR has multiple solutions and we need to centralize the coeffs to get identical result.
BUT current implementation centralize the `coefficientMatrix` by the global coeffs means.

In fact the `coefficientMatrix` should be centralized on each feature index itself.
Because, according to the MLOR probability distribution function, it can be proven easily that:
suppose `{ w0, w1, .. w(K-1) }` make up the `coefficientMatrix`,
then `{ w0 + c, w1 + c, ... w(K - 1) + c}` will also be the equivalent solution.
`c` is an arbitrary vector of `numFeatures` dimension.
reference
https://core.ac.uk/download/pdf/6287975.pdf

So that we need to centralize the `coefficientMatrix` on each feature dimension separately.

**We can also confirm this through R library `glmnet`, that MLOR in `glmnet` always generate coefficients result that the sum of each dimension is all `zero`, when reg == 0.**

## How was this patch tested?

Tests added.

Author: WeichenXu <WeichenXu123@outlook.com>

Closes #17706 from WeichenXu123/mlor_center.

2 files changed, 14 insertions, 3 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/ml/classification/LogisticRegression.scala b/mllib/src/main/scala/org/apache/spark/ml/classification/LogisticRegression.scala
index 965ce3d6f2..bc8154692e 100644
--- a/mllib/src/main/scala/org/apache/spark/ml/classification/LogisticRegression.scala
+++ b/mllib/src/main/scala/org/apache/spark/ml/classification/LogisticRegression.scala
@@ -609,9 +609,14 @@ class LogisticRegression @Since("1.2.0") (
             Friedman, et al. "Regularization Paths for Generalized Linear Models via
               Coordinate Descent," https://core.ac.uk/download/files/153/6287975.pdf
            */
-          val denseValues = denseCoefficientMatrix.values
-          val coefficientMean = denseValues.sum / denseValues.length
-          denseCoefficientMatrix.update(_ - coefficientMean)
+          val centers = Array.fill(numFeatures)(0.0)
+          denseCoefficientMatrix.foreachActive { case (i, j, v) =>
+            centers(j) += v
+          }
+          centers.transform(_ / numCoefficientSets)
+          denseCoefficientMatrix.foreachActive { case (i, j, v) =>
+            denseCoefficientMatrix.update(i, j, v - centers(j))
+          }
         }
 
         // center the intercepts when using multinomial algorithm
diff --git a/mllib/src/test/scala/org/apache/spark/ml/classification/LogisticRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/ml/classification/LogisticRegressionSuite.scala
index c858b9bbfc..83f575e838 100644
--- a/mllib/src/test/scala/org/apache/spark/ml/classification/LogisticRegressionSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/ml/classification/LogisticRegressionSuite.scala
@@ -1139,6 +1139,9 @@ class LogisticRegressionSuite
       0.10095851, -0.85897154, 0.08392798, 0.07904499), isTransposed = true)
     val interceptsR = Vectors.dense(-2.10320093, 0.3394473, 1.76375361)
 
+    model1.coefficientMatrix.colIter.foreach(v => assert(v.toArray.sum ~== 0.0 absTol eps))
+    model2.coefficientMatrix.colIter.foreach(v => assert(v.toArray.sum ~== 0.0 absTol eps))
+
     assert(model1.coefficientMatrix ~== coefficientsR relTol 0.05)
     assert(model1.coefficientMatrix.toArray.sum ~== 0.0 absTol eps)
     assert(model1.interceptVector ~== interceptsR relTol 0.05)
@@ -1204,6 +1207,9 @@ class LogisticRegressionSuite
       -0.3180040, 0.9679074, -0.2252219, -0.4319914,
       0.2452411, -0.6046524, 0.1050710, 0.1180180), isTransposed = true)
 
+    model1.coefficientMatrix.colIter.foreach(v => assert(v.toArray.sum ~== 0.0 absTol eps))
+    model2.coefficientMatrix.colIter.foreach(v => assert(v.toArray.sum ~== 0.0 absTol eps))
+
     assert(model1.coefficientMatrix ~== coefficientsR relTol 0.05)
     assert(model1.coefficientMatrix.toArray.sum ~== 0.0 absTol eps)
     assert(model1.interceptVector.toArray === Array.fill(3)(0.0))