Spark Jaccard similarity computation by min hashing slow compared to trivial approach - scala

Question

Given 2 huge list of values, I am trying to compute jaccard similarity between them in Spark using Scala.
Assume colHashed1 contains the first list of values and colHashed2 contains the second list.
Approach 1(trivial approach):
val jSimilarity = colHashed1.intersection(colHashed2).distinct.count/(colHashed1.union(colHashed2).distinct.count.toDouble)
Approach 2(using minHashing):
I have used the approach explained here.
import java.util.zip.CRC32
def getCRC32 (s : String) : Int =
{
val crc=new CRC32
crc.update(s.getBytes)
return crc.getValue.toInt & 0xffffffff
}
val maxShingleID = Math.pow(2,32)-1
def pickRandomCoeffs(kIn : Int) : Array[Int] =
{
var k = kIn
val randList = Array.fill(k){0}
while(k > 0)
{
// Get a random shingle ID.
var randIndex = (Math.random()*maxShingleID).toInt
// Ensure that each random number is unique.
while(randList.contains(randIndex))
{
randIndex = (Math.random()*maxShingleID).toInt
}
// Add the random number to the list.
k = k - 1
randList(k) = randIndex
}
return randList
}
val colHashed1 = list1Values.map(a => getCRC32(a))
val colHashed2 = list2Values.map(a => getCRC32(a))
val nextPrime = 4294967311L
val numHashes = 10
val coeffA = pickRandomCoeffs(numHashes)
val coeffB = pickRandomCoeffs(numHashes)
var signature1 = Array.fill(numHashes){0}
for (i <- 0 to numHashes-1)
{
// Evaluate the hash function.
val hashCodeRDD = colHashed1.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
// Track the lowest hash code seen.
signature1(i) = hashCodeRDD.min.toInt
}
var signature2 = Array.fill(numHashes){0}
for (i <- 0 to numHashes-1)
{
// Evaluate the hash function.
val hashCodeRDD = colHashed2.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
// Track the lowest hash code seen.
signature2(i) = hashCodeRDD.min.toInt
}
var count = 0
// Count the number of positions in the minhash signature which are equal.
for(k <- 0 to numHashes-1)
{
if(signature1(k) == signature2(k))
count = count + 1
}
val jSimilarity = count/numHashes.toDouble
Approach 1 seems to outperform Approach 2 in terms of time always. When I analyzed the code, min() function call on the RDD in Approach 2 takes significant time and that function is called many times depending upon how many hash functions are used.
The intersection and union operations used in Approach 1 seems to work faster compared to the repeated min() function calls.
I don't understand why minHashing does not help here. I expected minHashing to work faster compared to trivial approach. Is there anything I am doing wrong here?
Sample data can be viewed here

Answer 1

JaccardSimilarity with MinHash is not giving consistent results:
import java.util.zip.CRC32
object Jaccard {
def getCRC32(s: String): Int = {
val crc = new CRC32
crc.update(s.getBytes)
return crc.getValue.toInt & 0xffffffff
}
def pickRandomCoeffs(kIn: Int, maxShingleID: Double): Array[Int] = {
var k = kIn
val randList = Array.ofDim[Int](k)
while (k > 0) {
// Get a random shingle ID.
var randIndex = (Math.random() * maxShingleID).toInt
// Ensure that each random number is unique.
while (randList.contains(randIndex)) {
randIndex = (Math.random() * maxShingleID).toInt
}
// Add the random number to the list.
k = k - 1
randList(k) = randIndex
}
return randList
}
def approach2(list1Values: List[String], list2Values: List[String]) = {
val maxShingleID = Math.pow(2, 32) - 1
val colHashed1 = list1Values.map(a => getCRC32(a))
val colHashed2 = list2Values.map(a => getCRC32(a))
val nextPrime = 4294967311L
val numHashes = 10
val coeffA = pickRandomCoeffs(numHashes, maxShingleID)
val coeffB = pickRandomCoeffs(numHashes, maxShingleID)
val signature1 = for (i <- 0 until numHashes) yield {
val hashCodeRDD = colHashed1.map(ele => (coeffA(i) * ele + coeffB(i)) % nextPrime)
hashCodeRDD.min.toInt // Track the lowest hash code seen.
}
val signature2 = for (i <- 0 until numHashes) yield {
val hashCodeRDD = colHashed2.map(ele => (coeffA(i) * ele + coeffB(i)) % nextPrime)
hashCodeRDD.min.toInt // Track the lowest hash code seen
}
val count = (0 until numHashes)
.map(k => if (signature1(k) == signature2(k)) 1 else 0)
.fold(0)(_ + _)
val jSimilarity = count / numHashes.toDouble
jSimilarity
}
// def approach1(list1Values: List[String], list2Values: List[String]) = {
// val colHashed1 = list1Values.toSet
// val colHashed2 = list2Values.toSet
//
// val jSimilarity = colHashed1.intersection(colHashed2).distinct.count / (colHashed1.union(colHashed2).distinct.count.toDouble)
// jSimilarity
// }
def approach1(list1Values: List[String], list2Values: List[String]) = {
val colHashed1 = list1Values.toSet
val colHashed2 = list2Values.toSet
val jSimilarity = (colHashed1 & colHashed2).size / (colHashed1 ++ colHashed2).size.toDouble
jSimilarity
}
def main(args: Array[String]) {
val list1Values = List("a", "b", "c")
val list2Values = List("a", "b", "d")
for (i <- 0 until 5) {
println(s"Iteration ${i}")
println(s" - Approach 1: ${approach1(list1Values, list2Values)}")
println(s" - Approach 2: ${approach2(list1Values, list2Values)}")
}
}
}
OUTPUT:
Iteration 0
- Approach 1: 0.5
- Approach 2: 0.5
Iteration 1
- Approach 1: 0.5
- Approach 2: 0.5
Iteration 2
- Approach 1: 0.5
- Approach 2: 0.8
Iteration 3
- Approach 1: 0.5
- Approach 2: 0.8
Iteration 4
- Approach 1: 0.5
- Approach 2: 0.4
Why are you using it?

Answer 2

It seems to me that the overhead cost for minHashing approach just outweighs its functionality in Spark. Especially as numHashes increases.
Here are some observations I've found in your code:
First, while (randList.contains(randIndex)) this part will surely slow down your process as numHashes (which is by the way equal to the size of randList) increases.
Second, You can save some time if you rewrite this code:
var signature1 = Array.fill(numHashes){0}
for (i <- 0 to numHashes-1)
{
// Evaluate the hash function.
val hashCodeRDD = colHashed1.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
// Track the lowest hash code seen.
signature1(i) = hashCodeRDD.min.toInt
}
var signature2 = Array.fill(numHashes){0}
for (i <- 0 to numHashes-1)
{
// Evaluate the hash function.
val hashCodeRDD = colHashed2.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
// Track the lowest hash code seen.
signature2(i) = hashCodeRDD.min.toInt
}
var count = 0
// Count the number of positions in the minhash signature which are equal.
for(k <- 0 to numHashes-1)
{
if(signature1(k) == signature2(k))
count = count + 1
}
into
var count = 0
for (i <- 0 to numHashes - 1)
{
val hashCodeRDD1 = colHashed1.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
val hashCodeRDD2 = colHashed2.map(ele => ((coeffA(i) * ele + coeffB(i)) % nextPrime))
val sig1 = hashCodeRDD1.min.toInt
val sig2 = hashCodeRDD2.min.toInt
if (sig1 == sig2) { count = count + 1 }
}
This method simplifies the three loops into one. However, I am not sure if that would give a huge boost in computational time.
One other suggestion I have, assuming that the first approach still turns out to be much faster is to use the property of sets to modify the first approach:
val colHashed1_dist = colHashed1.distinct
val colHashed2_dist = colHashed2.distinct
val intersect_cnt = colHashed1_dist.intersection(colHashed2_dist).distinct.count
val jSimilarity = intersect_cnt/(colHashed1_dist.count + colHashed2_dist.count - intersect_cnt).toDouble
with that, instead of getting the union, you can just reuse the value of the intersection.

Answer 3

Actually, in LSH apporach you would calculate minHash only once for each of your documents and then compare two minHases for each possible pair of documents. And in case of trivial approach you would perform full comparison of documents for each possible pair of documents. Which is roughly N^2/2 number of comparisons. Hence extra cost of calculating minHashes is negligible for large enough number of documents.
You should actually compare the performance of the trivial approach:
val jSimilarity = colHashed1.intersection(colHashed2).distinct.count/(colHashed1.union(colHashed2).distinct.count.toDouble)
and performance of the Jaccard distance calculation (last lines in your code):
var count = 0
// Count the number of positions in the minhash signature which are equal.
for(k <- 0 to numHashes-1)
{
if(signature1(k) == signature2(k))
count = count + 1
}
val jSimilarity = count/numHashes.toDouble