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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.spark.mllib.optimization
import org.jblas.DoubleMatrix
/**
* Class used to compute the gradient for a loss function, given a single data point.
*/
abstract class Gradient extends Serializable {
/**
* Compute the gradient and loss given the features of a single data point.
*
* @param data - Feature values for one data point. Column matrix of size dx1
* where d is the number of features.
* @param label - Label for this data item.
* @param weights - Column matrix containing weights for every feature.
*
* @return A tuple of 2 elements. The first element is a column matrix containing the computed
* gradient and the second element is the loss computed at this data point.
*
*/
def compute(data: DoubleMatrix, label: Double, weights: DoubleMatrix):
(DoubleMatrix, Double)
}
/**
* Compute gradient and loss for a logistic loss function, as used in binary classification.
* See also the documentation for the precise formulation.
*/
class LogisticGradient extends Gradient {
override def compute(data: DoubleMatrix, label: Double, weights: DoubleMatrix):
(DoubleMatrix, Double) = {
val margin: Double = -1.0 * data.dot(weights)
val gradientMultiplier = (1.0 / (1.0 + math.exp(margin))) - label
val gradient = data.mul(gradientMultiplier)
val loss =
if (label > 0) {
math.log(1 + math.exp(margin))
} else {
math.log(1 + math.exp(margin)) - margin
}
(gradient, loss)
}
}
/**
* Compute gradient and loss for a Least-squared loss function, as used in linear regression.
* This is correct for the averaged least squares loss function (mean squared error)
* L = 1/n ||A weights-y||^2
* See also the documentation for the precise formulation.
*/
class LeastSquaresGradient extends Gradient {
override def compute(data: DoubleMatrix, label: Double, weights: DoubleMatrix):
(DoubleMatrix, Double) = {
val diff: Double = data.dot(weights) - label
val loss = diff * diff
val gradient = data.mul(2.0 * diff)
(gradient, loss)
}
}
/**
* Compute gradient and loss for a Hinge loss function, as used in SVM binary classification.
* See also the documentation for the precise formulation.
* NOTE: This assumes that the labels are {0,1}
*/
class HingeGradient extends Gradient {
override def compute(data: DoubleMatrix, label: Double, weights: DoubleMatrix):
(DoubleMatrix, Double) = {
val dotProduct = data.dot(weights)
// Our loss function with {0, 1} labels is max(0, 1 - (2y – 1) (f_w(x)))
// Therefore the gradient is -(2y - 1)*x
val labelScaled = 2 * label - 1.0
if (1.0 > labelScaled * dotProduct) {
(data.mul(-labelScaled), 1.0 - labelScaled * dotProduct)
} else {
(DoubleMatrix.zeros(1, weights.length), 0.0)
}
}
}
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