convert Dense Vector to Sparse Vector in PySpark - pyspark

Is there a built in way to create a sparse vector from a dense vector in PySpark? The way I am doing this is the following:
Vectors.sparse(len(denseVector), [(i,j) for i,j in enumerate(denseVector) if j != 0 ])
That satisfies the [size, (index, data)] format. Seems kinda hacky. Is there a more efficient way to do it?

import scipy.sparse
from pyspark.ml.linalg import Vectors, _convert_to_vector, VectorUDT
from pyspark.sql.functions import udf, col
If you have just one dense vector this will do it:
def dense_to_sparse(vector):
return _convert_to_vector(scipy.sparse.csc_matrix(vector.toArray()).T)
dense_to_sparse(densevector)
The trick here is that csc_matrix.shape[1] has to equal 1, so transpose the vector. Have a look at the source of _convert_to_vector: https://people.eecs.berkeley.edu/~jegonzal/pyspark/_modules/pyspark/mllib/linalg.html
The more likely scenario is you have a DF with a column of densevectors:
to_sparse = udf(dense_to_sparse, VectorUDT())
DF.withColumn("sparse", to_sparse(col("densevector"))

I'm not sure whether you're using mllib or ml. Anyway, You can convert like this:
from pyspark.mllib.linalg import Vectors as mllib_vectors
from pyspark.ml.linalg import Vectors as ml_vectors
# Construct dense vectors in mllib and ml
v1 = mllib_vectors.dense([1.0, 1.0, 0, 0, 0])
v2 = ml_vectors.dense([1.0, 1.0, 0, 0, 0])
# Convert ml dense vector to sparse vector
arr2 = v2.toArray()
print('arr2', arr2)
d = {i:arr2[i] for i in np.nonzero(arr2)[0]}
print('d', d)
v4 = ml_vectors.sparse(len(arr2), d)
print('v4: %s' % v4)
# Convert mllib dense vector to sparse vector
v6 = ml_vectors.sparse(len(arr2), d)
print('v6: %s' % v6)

Related

Cosine similarity of two sparse vectors in Scala Spark

I have a dataframe with two columns where each row has a Sparse Vector. I try to find a proper way to calculate the cosine similarity (or just the dot product) of the two vectors in each row.
However, I haven't been able to find any library or tutorial to do it for Sparse vectors.
The only way I found is the following:
Create a k X n matrix, where n items are described as k-dimensioned vectors. For representing each item as a k dimension vector, you can use ALS which represents each entity in a latent factor space. The dimension of this space (k) can be chosen by you. This k X n matrix can be represented as RDD[Vector].
Convert this k X n matrix to RowMatrix.
Use columnSimilarities() function to get a n X n matrix of similarities between n items.
I feel it is an overkill to calculate all the cosine similarities for each pair while I need it only for the specific pairs in my (quite big) dataframe.
In Spark 3 there is now method dot for a SparseVector object, which takes another vector as its argument.
If you want to do this in earlier versions, you could create a user defined function that follows this algorithm:
Take intersection of your vectors' indices.
Get two subarrays of your vectors' values based on the indices from the intersection.
Do pairwise multiplication of the elements of those two subarrays.
Sum the values resulting values from such pairwise multiplication.
Here's my realization of it:
import org.apache.spark.ml.linalg.SparseVector
def dotProduct(vec: SparseVector, vecOther: SparseVector) = {
val commonIndices = vec.indices intersect vecOther.indices
commonIndices.map(x => vec(x) * vecOther(x)).reduce(_+_)
}
I guess you know how to turn it into a Spark UDF from here and apply it to your dataframe's columns.
And if you normalize your sparse vectors with org.apache.spark.ml.feature.Normalizer before computing your dot product, you'll get cosine similarity in the end (by definition).
Great answer above #Sergey-Zakharov +1.
A few adds-on:
The reduce doesn't work on empty sequences.
Make sure computing L2 normalization.
val normalizer = new Normalizer()
.setInputCol("features")
.setOutputCol("normFeatures")
.setP(2.0)
val l2NormData = normalizer.transform(df_features)
and
val dotProduct = udf {(v1: SparseVector, v2: SparseVector) =>
v1.indices.intersect(v2.indices).map(x => v1(x) * v2(x)).reduceOption(_ + _).getOrElse(0.0)
}
and then
val df = dfA.crossJoin(broadcast(dfB))
.withColumn("dot", dotProduct(col("featuresA"), col("featuresB")))
If the number of vectors you want to calculate the dot product with is small, cache the RDD[Vector] table. Create a new table [cosine_vectors] that is a filter on the original table to only select the vectors you want the cosine similarities for. Broadcast join those two together and calculate.

Efficient way to extract a row and do cosine similarity

In the code below, I get a dense Matrix V after doing SVD. What I want is
Given a set of values(say 3,7,9).
I want to extract the 3,7 and 9th row of Matrix V.
I want to calculate cosine similarity of these 3 rows with each row of Matrix V
I need to add the three cosine similarities obtained for of each row.
I finally need the index of row which have the maximum summation.
val data = Array(
Vectors.sparse(5, Seq((1, 1.0), (3, 7.0))),
Vectors.dense(2.0, 0.0, 3.0, 4.0, 5.0),
Vectors.dense(4.0, 0.0, 0.0, 6.0, 7.0))
val dataRDD = sc.parallelize(data)
val mat: RowMatrix = new RowMatrix(dataRDD)
// Compute the top 4 singular values and corresponding singular vectors.
val svd: SingularValueDecomposition[RowMatrix, Matrix] = mat.computeSVD(4, computeU = true)
val U: RowMatrix = svd.U // The U factor is a RowMatrix.
val s: Vector = svd.s // The singular values are stored in a local dense vector.
val V: Matrix = svd.V // The V factor is a local dense matrix.
Please advise an efficient method to do the same. I have been thinking of converting Matrix V to Indexed Row Matrix, But when I do use row iterator on V, How do I keep track of index of rows? Is there a better way to do it?

Matrix multiplication in py-spark using RDD

I have two matrices
# 3x3 matrix
X = [[10,7,3],[3 ,2,6],[5 ,8,7]]
# 3x4 matrix
Y = [[3,7,11,2],[2,7,4,10],[8,7,6,11]]
I want to multiply these two in spark using RDD. Can some one help me on this. This multiplication should not use any inbuilt function.
I was able to multiply the 2 using for loop in python as follows
for i in range(len(X)):
# iterate through columns of Y
for j in range(len(Y[0])):
# iterate through rows of Y
for k in range(len(Y)):
Output[i][j] += X[i][k] * Y[k][j]
#output is a 3*4 empty matrix
I am new to spark and using pyspark.
It is not so hard, you just have to write your matrix using a different notation.
X = [[10,7,3],[3 ,2,6],[5 ,8,7]]
Can be written as
X = (0,0,10),(0,1,7),(0,2,3)...
rdd_x = sc.parallelize((0,0,10),(0,1,7),(0,2,3)...)
rdd_y = sc.parallelize((0,0,3),(0,1,7),(0,2,11)...)
Now you can make the multiplication both using join or cartesian.
E.g.,
rdd_x.cartesian(rdd_y)\
.filter(lambda x: x [0][0] == x[1][1] and x[0][1] == x[1][0])\
.map(lambda x: (x[0][0],x[0][2] * x[1][2])).reduceByKey(lambda x,y: x+y).collect()
Your code works, but you should initialize Output, and only once,
Output=[[0]*4]*3
You're not using RDDs though, your teacher won't be happy.
Based on Andrea's answer, I came up with this solution:
rdd_x.cartesian(rdd_y)\
.filter(lambda x: (x[0][1] == x[1][0]))\
.map(lambda x: ((x[0][0],x[1][1]),x[0][2] * x[1][2])).reduceByKey(lambda x,y: x+y).collect()

Concatenate Sparse Vectors in Spark?

Say you have two Sparse Vectors. As an example:
val vec1 = Vectors.sparse(2, List(0), List(1)) // [1, 0]
val vec2 = Vectors.sparse(2, List(1), List(1)) // [0, 1]
I want to concatenate these two vectors so that the result is equivalent to:
val vec3 = Vectors.sparse(4, List(0, 2), List(1, 1)) // [1, 0, 0, 1]
Does Spark have any such convenience method to do this?
If you have the data in a DataFrame, then VectorAssembler would be the right thing to use. For example:
from pyspark.ml.feature import VectorAssembler
dataset = spark.createDataFrame(
[(0, Vectors.sparse(10, {0: 0.6931, 5: 0.0, 7: 0.5754, 9: 0.2877}), Vectors.sparse(10, {3: 0.2877, 4: 0.6931, 5: 0.0, 6: 0.6931, 8: 0.6931}))],
["label", "userFeatures1", "userFeatures2"])
assembler = VectorAssembler(
inputCols=["userFeatures1", "userFeatures2"],
outputCol="features")
output = assembler.transform(dataset)
output.select("features", "label").show(truncate=False)
You would get the following output for this:
+---------------------------------------------------------------------------+-----+
|features |label|
+---------------------------------------------------------------------------+-----+
|(20,[0,7,9,13,14,16,18], [0.6931,0.5754,0.2877,0.2877,0.6931,0.6931,0.6931])|0|
+---------------------------------------------------------------------------+-----+
I think you have a slight problem understanding SparseVectors. Therefore I will make a little explanation about them, the first argument is the number of features | columns | dimensions of the data, besides every entry of the List in the second argument represent the position of the feature, and the values in the the third List represent the value for that column, therefore SparseVectors are locality sensitive, and from my point of view your approach is incorrect.
If you pay more attention you are summing or combining two vectors that have the same dimensions, hence the real result would be different, the first argument tells us that the vector has only 2 dimensions, so [1,0] + [0,1] => [1,1] and the correct representation would be Vectors.sparse(2, [0,1], [1,1]), not four dimensions.
In the other hand if each vector has two different dimensions and you are trying to combine them and represent them in a higher dimensional space, let's say four then your operation might be valid, however this functionality isn't provided by the SparseVector class, and you would have to program a function to do that, something like (a bit imperative but I accept suggestions):
def combine(v1:SparseVector, v2:SparseVector):SparseVector = {
val size = v1.size + v2.size
val maxIndex = v1.size
val indices = v1.indices ++ v2.indices.map(e => e + maxIndex)
val values = v1.values ++ v2.values
new SparseVector(size, indices, values)
}
If your vectors represent different columns of a dataframe, you can use VectorAssembler. Just need to set setInputcols (your 2 vectors) and Spark will make your wish come true ;)

spark conversion from RowMatrix to CoordinateMatrix in scala

I am trying to perform some operations in Distributed matrix space in Scala Spark, and I am wondering if there is any straightforward way to convert a distributed RowMatrix to a distributed CoordinateMatrix?
For example, if
rdd_input = Array[org.apache.spark.mllib.linalg.Vector] = Array([10], [0], [0], [40])
The conversion of RowMatrix to 2 X 2 dense matrix was accomplished by,
rdd_input.zipWithIndex.groupBy{case (x, i) => i / 2}.map(_._2.map(_._1))
If the Matrix is sparse, how can I convert this matrix to a CoordinateMatrix?
Any help is appreciated.