def learnParametersClosdFormSolution(inputData, outputData, numberOfClusters,
lambdaRegularization):
# Calculate the design matrix.
clusteredDataInfo = re.calculateM(inputData, numberOfClusters)
clusteredData = re.createDataClusters(inputData, clusteredDataInfo,
numberOfClusters)
covarianceMatrixClusters = re.covariancePerCluster(clusteredData)
designMatrix = re.calculateDesignMatrix(inputData, clusteredDataInfo,
covarianceMatrixClusters,
numberOfClusters)
Wml = computeClosedFormSolution(lambdaRegularization, designMatrix,
outputData)
# Return the parameters.
return Wml
def learnParameterSGD(inputData, inputValidationData, outputData,
outputValidationData, batchSize, numberOfClusters,
lambdaRegularization):
# Learning rate fixed.
learningRate = 1
# Cluster the input data to decide the number of basis functions.
clusteredDataInfo = re.calculateM(inputData, numberOfClusters)
clusteredData = re.createDataClusters(inputData, clusteredDataInfo,
numberOfClusters)
covarianceMatrixClusters = re.covariancePerCluster(clusteredData)
designMatrix = re.calculateDesignMatrix(inputData, clusteredDataInfo,
covarianceMatrixClusters,
numberOfClusters)
# Choose a random w.
randomW = np.random.rand(1, numberOfClusters + 1)
# Run the update on parameters using the stochastic gradient update.
W = stochasticUpdate(inputData, inputValidationData, outputData,
outputValidationData, designMatrix, randomW,
learningRate, batchSize, numberOfClusters,
lambdaRegularization)
return W
def computeTargetSGD(inputData, numberOfClusters, W):
# Compute the design matrix for the input.
clusteredDataInfo = re.calculateM(inputData, numberOfClusters)
clusteredData = re.createDataClusters(inputData, clusteredDataInfo,
numberOfClusters)
covarianceMatrixClusters = re.covariancePerCluster(clusteredData)
designMatrix = re.calculateDesignMatrix(inputData, clusteredDataInfo,
covarianceMatrixClusters,
numberOfClusters)
# Target matrix to be returned.
target = np.empty((
len(inputData),
1,
))
target[:] = np.NAN
target = np.asmatrix(target)
if (W.shape[1] == 1):
# Ensure that the dot product is performed without any errors.
W = W.T
for i in range(0, len(designMatrix)):
target[i][0] = np.matmul(W, designMatrix[i].T)
return target
def stochasticUpdate(inputData, inputValidationData, outputData,
outputValidationData, designMatrix, currentW,
learningRate, batchSize, numberOfClusters,
lambdaRegularization):
idealW = currentW
# Initial minimum error set to a large value.
rmsErrorMin = 9999
# Calculate design matrix for the validation input set.
clusteredDataInfo = re.calculateM(inputValidationData, numberOfClusters)
clusteredData = re.createDataClusters(inputValidationData,
clusteredDataInfo, numberOfClusters)
covarianceMatrixClusters = re.covariancePerCluster(clusteredData)
designMatrixValidation = re.calculateDesignMatrix(
inputValidationData, clusteredDataInfo, covarianceMatrixClusters,
numberOfClusters)
# Run the update step once for each batch.
index = len(inputData) // batchSize
for i in range(0, index):
# Calculate the batch change in E for the batch.
deltaE = calculateBatchDeltaE(designMatrix, outputData, i * batchSize,
(i + 1) * batchSize, currentW,
lambdaRegularization)
# Update the parameters usind the batch gradient and the learning rate.
currentW = np.subtract(currentW, learningRate * deltaE)
# Calculate the new target values with the updated parameters.
predictedTarget = computeTargetValuesSGD(inputValidationData,
designMatrixValidation,
numberOfClusters, currentW)
# Calculate the rms error for the updated parameters.
rmsError = re.calculateRootMeanSquaredError(outputValidationData,
predictedTarget)
if (rmsError < rmsErrorMin):
# Got a new minimum rms error.
# Save the parameters.
idealW = currentW
# Save the minimum rms error till now.
rmsErrorMin = rmsError
return idealW
def computeTargetValuesClosedFormSolution(inputData, numberOfClusters, Wml):
# Calculate the design matrix.
clusteredDataInfo = re.calculateM(inputData, numberOfClusters)
clusteredData = re.createDataClusters(inputData, clusteredDataInfo,
numberOfClusters)
covarianceMatrixClusters = re.covariancePerCluster(clusteredData)
designMatrix = re.calculateDesignMatrix(inputData, clusteredDataInfo,
covarianceMatrixClusters,
numberOfClusters)
# Initialise the output matrix for the number of row vectors in the input.
target = np.empty((
len(inputData),
1,
))
target[:] = np.NAN
target = np.asmatrix(target)
if (Wml.shape[1] == 1):
Wml = Wml.T
# Calculate the output matrix using the learned parameters.
for i in range(0, len(designMatrix)):
target[i][0] = np.matmul(Wml, designMatrix[i].T)
# Return the output matrix.
return target