nak.space.DMImplicits.scala Maven / Gradle / Ivy
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package nak.space
import breeze.generic.UFunc
import breeze.linalg._
import breeze.linalg.operators.{OpMulInner, OpMulMatrix, OpSub}
import breeze.math.{Semiring, MutableInnerProductModule}
import breeze.numerics._
import scala.reflect.ClassTag
/**
* dialogue
* 6/19/14
* @author Gabriel Schubiner
*
*
*/
object DMImplicits {
type chebyshev = chebyshev.type
type cosine = cosine.type
type euclidean = euclidean.type
type mahalanobis = mahalanobis.type
type manhattan = manhattan.type
type minkowski = minkowski.type
type projectedSquaredNorm = projectedSquaredNorm.type
object projectedSquaredNorm extends UFunc {
implicit def pSqNorm[T, U](implicit mulImpl: OpMulMatrix.Impl2[U, T, T],
subImpl: OpSub.Impl2[T, T, T],
normImpl: norm.Impl[T, Double]): Impl3[T, T, U, Double] =
new Impl3[T, T, U, Double] {
def apply(v: T, v2: T, proj: U): Double = {
pow(norm(subImpl(mulImpl(proj, v), mulImpl(proj, v2))), 2)
}
}
}
object chebyshev extends UFunc {
implicit def chebyshevDistanceFromZippedValues[T, U]
(implicit zipImpl: zipValues.Impl2[T, U, ZippedValues[Double, Double]]): Impl2[T, U, Double] =
new Impl2[T, U, Double] {
def apply(v: T, v2: U): Double = {
var minDist = Double.NegativeInfinity
zipValues(v, v2).foreach {
(a, b) =>
val absdiff = abs(a - b)
if (absdiff > minDist)
minDist = absdiff
}
minDist
}
}
}
object cosine extends UFunc {
implicit def cosineDistanceFromZippedValues[T, U]
(implicit zipImpl: zipValues.Impl2[T, U, ZippedValues[Double, Double]]): Impl2[T, U, Double] =
new Impl2[T, U, Double] {
def apply(v: T, v2: U): Double = {
var numer = 0.0
var denom = 0.0
var denom2 = 0.0
zipValues(v, v2).foreach {
(a, b) =>
numer += a * b
denom += a * a
denom2 += b * b
}
numer / (sqrt(denom) * sqrt(denom2))
}
}
}
object euclidean extends UFunc {
implicit def euclideanDistanceFromZippedValues[T, U]
(implicit zipImpl: zipValues.Impl2[T, U, ZippedValues[Double, Double]]): Impl2[T, U, Double] =
new Impl2[T, U, Double] {
def apply(v: T, v2: U): Double = {
var dist = 0.0
zipValues(v, v2).foreach {
(a, b) =>
val diff = a - b
dist += (diff * diff)
}
sqrt(dist)
}
}
}
object decomposedMahalanobis extends UFunc {
// implicit def decomposedMahalanobisFromLinearTransformationMatrix[T]
// (implicit vspace: MutableInnerProductModule[T,Double],
// ev: T <:< Vector[Double]): Impl3[T,T,DenseMatrix[Double],Double] = {
// import vspace._
// new Impl3[T, T, DenseMatrix[Double], Double] {
// def apply(v: T, v2: T, A: DenseMatrix[Double]): Double = {
// ((A * v) - (A * v2)).t * ((A * v) - (A * v2))
// }
// }
// }
implicit def decomposedMahalanobisFromLinearTransformationDense(implicit vspace: MutableInnerProductModule[DenseVector[Double], Double]):
Impl3[DenseVector[Double], DenseVector[Double], DenseMatrix[Double], Double] = {
import vspace._
new Impl3[DenseVector[Double], DenseVector[Double], DenseMatrix[Double], Double] {
def apply(v: DenseVector[Double], v2: DenseVector[Double], A: DenseMatrix[Double]): Double = {
val c: DenseVector[Double] = (A * v) - (A * v2)
c dot c
}
}
}
implicit def decomposedMahalanobisFromLinTransGen[V, M, T](implicit vspace: MutableInnerProductModule[V, T],
opMulMV: OpMulMatrix.Impl2[M, V, V],
opSubVV: OpSub.Impl2[V, V, V],
opDotVV: OpMulInner.Impl2[V, V, T],
// viewM: M <:< Matrix[T],
// viewV: V <:< Vector[T],
semiring: Semiring[T],
man: ClassTag[T]): Impl3[V, V, M, T] = {
// import vspace._
new Impl3[V, V, M, T] {
def apply(v: V, v2: V, A: M): T = {
val c: V = opSubVV(opMulMV(A, v), opMulMV(A, v2))
opDotVV(c,c)
}
}
}
implicit def decomposedMahalanobisFromLinearTransformationSparse(implicit vspace: MutableInnerProductModule[SparseVector[Double], Double]):
Impl3[SparseVector[Double], SparseVector[Double], CSCMatrix[Double], Double] = {
import vspace._
new Impl3[SparseVector[Double], SparseVector[Double], CSCMatrix[Double], Double] {
def apply(v: SparseVector[Double], v2: SparseVector[Double], A: CSCMatrix[Double]): Double = {
val c = (A * v) - (A * v2)
c dot c
}
}
}
}
object mahalanobis extends UFunc {
def requireSymmetricMatrix[V](mat: Matrix[V]): Unit = {
if (mat.rows != mat.cols)
throw new MatrixNotSquareException
for (i <- 0 until mat.rows; j <- 0 until i)
if (mat(i, j) != mat(j, i))
throw new MatrixNotSymmetricException
}
implicit object mahalanobisDistanceFromRawMeanCovValues_DV_DV_DM
extends Impl3[DenseVector[Double], DenseVector[Double], DenseMatrix[Double], Double] {
override def apply(v: DenseVector[Double], v2: DenseVector[Double], v3: DenseMatrix[Double]): Double = {
requireSymmetricMatrix(v3)
sqrt((v - v2).t * (v3 \ (v - v2)))
}
}
// Assumes rows represent individual data points (i.e. v2 is MxN array comprising M data points in R^N
// implicit object mahalanobisDistanceFromPointDistribution_DV_DM extends Impl2[DenseVector[Double],DenseMatrix[Double], Double] {
// override def apply(v: DenseVector[Double], v2: DenseMatrix[Double]): Double = {
// val means: DenseMatrix[Double] = mean(v2(::, *)) // mean of columns into 1xN Matrix
// val centered: DenseMatrix[Double] = v2(*,::) - means
// val sampleCov = (1 / v2.rows) :* (centered * centered.t)
//
// mahalanobisDistanceFromRawMeanCovValues_DV_DV_DM(v, means.toDenseVector, sampleCov)
// }
// }
}
object manhattan extends UFunc {
implicit def manhattanDistanceFromZippedValues[T, U]
(implicit zipImpl: zipValues.Impl2[T, U, ZippedValues[Double, Double]]): Impl2[T, U, Double] =
new Impl2[T, U, Double] {
def apply(v: T, v2: U): Double = {
var dist = 0.0
zipValues(v, v2).foreach {
(a, b) =>
dist += abs(a - b)
}
dist
}
}
}
object minkowski extends UFunc {
implicit def minkowskiDistanceFromZippedValues[T, U]
(implicit zipImpl: zipValues.Impl2[T, U, ZippedValues[Double, Double]]): Impl3[T, U, Double, Double] =
new Impl3[T, U, Double, Double] {
def apply(v: T, v2: U, v3: Double): Double = {
var cumul = 0.0
zipValues(v, v2).foreach {
(a, b) =>
cumul += pow(abs(a - b), v3)
}
pow(cumul, 1 / v3)
}
}
}
}
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