Github user sethah commented on a diff in the pull request:
https://github.com/apache/spark/pull/15874#discussion_r88753014
--- Diff: mllib/src/main/scala/org/apache/spark/ml/feature/MinHashLSH.scala
---
@@ -31,36 +31,40 @@ import org.apache.spark.sql.types.StructType
/**
* :: Experimental ::
*
- * Model produced by [[MinHash]], where multiple hash functions are
stored. Each hash function is
- * a perfect hash function:
- * `h_i(x) = (x * k_i mod prime) mod numEntries`
- * where `k_i` is the i-th coefficient, and both `x` and `k_i` are from
`Z_prime^*`
+ * Model produced by [[MinHashLSH]], where multiple hash functions are
stored. Each hash function is
+ * picked from a hash family for a specific set `S` with cardinality equal
to `numEntries`:
+ * `h_i(x) = ((x \cdot a_i + b_i) \mod prime) \mod numEntries`
+ *
+ * This hash family is approximately min-wise independent according to the
reference.
*
* Reference:
- * [[https://en.wikipedia.org/wiki/Perfect_hash_function Wikipedia on
Perfect Hash Function]]
+ *
[[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.121.8215&rep=rep1&type=pdf
Min-wise
+ * independent permutations]]
*
* @param numEntries The number of entries of the hash functions.
- * @param randCoefficients An array of random coefficients, each used by
one hash function.
+ * @param randCoefficients Pairs of random coefficients. Each pair is used
by one hash function.
*/
@Experimental
@Since("2.1.0")
-class MinHashModel private[ml] (
+class MinHashLSHModel private[ml](
override val uid: String,
- @Since("2.1.0") val numEntries: Int,
- @Since("2.1.0") val randCoefficients: Array[Int])
- extends LSHModel[MinHashModel] {
+ private[ml] val numEntries: Int,
+ private[ml] val randCoefficients: Array[(Int, Int)])
+ extends LSHModel[MinHashLSHModel] {
@Since("2.1.0")
- override protected[ml] val hashFunction: Vector => Vector = {
- elems: Vector =>
+ override protected[ml] val hashFunction: Vector => Array[Vector] = {
+ elems: Vector => {
require(elems.numNonzeros > 0, "Must have at least 1 non zero
entry.")
val elemsList = elems.toSparse.indices.toList
- val hashValues = randCoefficients.map({ randCoefficient: Int =>
- elemsList.map({elem: Int =>
- (1 + elem) * randCoefficient.toLong % MinHash.prime %
numEntries
- }).min.toDouble
+ val hashValues = randCoefficients.map({ case (a: Int, b: Int) =>
+ elemsList.map { elem: Int =>
+ ((1 + elem) * a + b) % MinHashLSH.HASH_PRIME % numEntries
--- End diff --
I'm still looking at it, but I don't think this is correct. Why do we tack
on `% numEntries` here. Could you point me to a resource? The paper linked
above (and many other references that I've seen) use `(ax + b) mod p` where p
is a large prime.
I see the formula listed under the wiki article for [perfect hashing
functions](https://en.wikipedia.org/wiki/Perfect_hash_function) lists `(kx mod
p) mod n`, but that's not the full picture. They are referencing a paper which
simply uses that formula as the first part of multilevel scheme.
If it's helpful -
[this](http://cs.brown.edu/courses/cs253/papers/nearduplicate.pdf) seems to be
the original paper on MinHash. The author mentions that
````
This is further explored in [5] where it is shown
that random linear transformations are likely to suffice in practice.
````
Reference 5 is
[here](http://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r26/pdf),
which seems to be a more concise version of your reference. In that paper,
they describe `(ax + b mod p)`.
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