def pcaTaylorModel(stations, startDate, endDate, \
features, ncomp=None, targetVar='TempMax', \
lag=1, order=0, smooth_window=0, verbose=False):
# build regression model to predict "variable" for a single
# station using training data from multiple stations
# between startdate and enddate.
#
# The set of values of each feature at all stations is converted
# to a truncated list of principal components for purposes of
# feature-reduction and reduction of multicolinearity
#
# Uses a "Taylor expansion" by combining information from
# several days (higher order time derivatives)
#
# stations: a list of station codes, the first entry is
# the station for which forecast is generated
# features: a list of variables to use as predictors
# ncomp: a list of same length as features containing the
# number of PCA to keep for each feature
# lag: the number of days in the future to forecast
# order: the number of days in the past to include
# (also maximum order of time derivative)
import numpy as np
import wUUtils as Util
import wUPCA
reload(wUPCA)
from sklearn import preprocessing
from sklearn import linear_model
# load target variable data
target = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
targetVar, castFloat=True)
if smooth_window > 0:
target = Util.smooth(target, smooth_window)
# shift vector by lag
target = target[lag:]
# load features data and compute PC
pcaData, transform_params = wUPCA.pcaConvert(stations, features, \
startDate, endDate, ncomp)
# flatten featureData into single list of lists, while shortening by lag
featureData = [data[:(-lag)] for dataList in pcaData for data in dataList]
if smooth_window > 0:
for data in featureData:
data = Util.smooth(data,smooth_window)
# number of PC-transformed features
if ncomp == None:
nfeat = len(stations)*len(features)
else:
nfeat = sum(ncomp)
# add in "derivative" terms
for ideriv in range(1,order+1):
for ii in range(nfeat):
# print("Adding " + str(ideriv) + " derivative of " + feature[jfeat])
fd = np.diff(featureData[ii],n=ideriv)
featureData.append(fd)
# shorten vectors to length of highest order derivative
nrows = len(featureData[-1])
for column in range(len(featureData)):
featureData[column] = featureData[column][-nrows:]
target = target[-nrows:]
# convert target and features to np arrays
target = np.array(target)
featureData = (np.array(featureData)).T
# fit regression model
regr = linear_model.LinearRegression()
regr.fit(featureData, target)
model_params = {
'stations': stations, \
'startDate': startDate, \
'endDate': endDate, \
'targetVar': targetVar, \
'features': features, \
'regr': regr, \
'lag': lag, \
'order': order, \
'smooth_window': smooth_window, \
'transform_params': transform_params}
# report regression results:
print("R^2: " + str(regr.score(featureData,target)))
if verbose:
print("Regression coefficients:")
print(" intercept" + ":\t" + str(regr.intercept_))
column = 0
for ideriv in range(order+1):
print(" " + str(ideriv) + "th derivative:")
for ii, feature in enumerate(features):
print(" " + feature)
if ncomp == None:
nc = len(stations)
else:
nc = ncomp[ii]
for jj in range(nc):
print(" PC " + str(jj) + " :\t" + str(regr.coef_[column]))
column += 1
return featureData, target, model_params
def pcaClusterModel(stations, startDate, endDate, \
features, ncomp=None, \
clusterVars=[], nclusters=1, \
targetVar='TempMax', \
lag=1, order=0, ranseed=666, verbose=False):
# build regression model to predict "variable" for a single
# station using training data from multiple stations
# between startdate and enddate.
#
# The set of values of each feature at all stations is converted
# to a truncated list of principal components for purposes of
# feature-reduction and reduction of multicolinearity
#
# Clustering is used to train multiple models for different
# partitions of the data
#
# Uses a "Taylor expansion" by combining information from
# several days (higher order time derivatives)
#
# stations: a list of station codes, the first entry is
# the station for which forecast is generated
# features: a list of variables to use as predictors
# ncomp: a list of same length as features containing the
# number of PCA to keep for each feature
# clusterVars: a list of pairs of form ('feature',npc), where
# where npc is the index of the PC to use for
# clustering
# lag: the number of days in the future to forecast
# order: the number of days in the past to include
# (also maximum order of time derivative)
import numpy as np
import wUUtils as Util
import wUPCA
import wUCluster as Clust
from sklearn import preprocessing
from sklearn import linear_model
# load target variable data
target = Util.loadDailyVariableRange(stations[0], startDate, endDate, \
targetVar, castFloat=True)
# shift vector by lag
target = target[lag:]
# load features data and compute PC
pcaData, transformParams = wUPCA.pcaConvert(stations, features, \
startDate, endDate, ncomp)
# flatten featureData into single list of lists, while shortening by lag
featureData = [data[:(-lag)] for dataList in pcaData for data in dataList]
# number of PC-transformed features
if ncomp == None:
nfeat = len(stations)*len(features)
else:
nfeat = sum(ncomp)
# add in "derivative" terms
for ideriv in range(1,order+1):
for ii in range(nfeat):
# print("Adding " + str(ideriv) + " derivative of " + feature[jfeat])
fd = np.diff(featureData[ii],n=ideriv)
featureData.append(fd)
# shorten vectors to length of highest order derivative
nrows = len(featureData[-1])
for column in range(len(featureData)):
featureData[column] = featureData[column][-nrows:]
target = target[-nrows:]
# apply clustering
# locate columns to be used for clustering
cols = []
for clusterPair in clusterVars:
ifeat = features.index(clusterPair[0]) # index of feature
col = sum(ncomp[:ifeat]) + clusterPair[1]
cols += [col]
if clusterPair[1] >= ncomp[ifeat]:
print('Requested cluster variable out of range')
print(clusterPair[0] + ' ' + str(clusterPair[1]) + ' >= ' + str(ncomp[ifeat]))
return
print('columns for clustering: ' + str(cols))
clusterData = np.array([featureData[ii] for ii in cols]).T
scaler, clusterer = Clust.computeClusters(clusterData, nclusters, ranseed)
classes = Clust.assignClusters(scaler, clusterer, clusterData)
clusterParams = { \
'scaler': scaler, \
'clusterer': clusterer, \
'nclusters': nclusters, \
'ranseed': ranseed, \
'cols': cols }
# separate data into clusters
featureClusters = []
targetClusters = []
for icl in range(nclusters):
# features
clust = [f for i,f in enumerate(zip(*featureData)) if classes[i]==icl]
featureClusters.append( map(list,zip(*clust)) )
# targetVar
clust = [t for i,t in enumerate(target) if classes[i]==icl]
targetClusters.append(clust)
# train separate regression model for each cluster
regrs = []
for icl in range(nclusters):
# convert features and target to arrays
featureClusters[icl] = (np.array(featureClusters[icl])).T
targetClusters[icl] = np.array(targetClusters[icl])
regr = linear_model.LinearRegression()
regr.fit(featureClusters[icl], targetClusters[icl])
regrs.append(regr)
print('Cluster %d, nrows %d, R^2 %f' \
% (icl, \
len(targetClusters[icl]), \
regr.score(featureClusters[icl],targetClusters[icl])) )
if verbose:
print("\nCluster " + str(icl))
print("Regression coefficients:")
print(" intercept" + ":\t" + str(regr.intercept_))
column = 0
for ideriv in range(order+1):
print(" " + str(ideriv) + "th derivative:")
for ii, feature in enumerate(features):
print(" " + feature)
for jj in range(ncomp[ii]):
print(" PC " + str(jj) + " :\t" + str(regr.coef_[column]))
column += 1
modelParams = {
'stations': stations, \
'startDate': startDate, \
'endDate': endDate, \
'targetVar': targetVar, \
'features': features, \
'clusterVars': clusterVars, \
'clusterParams': clusterParams, \
'classes': classes, \
'regrs': regrs, \
'lag': lag, \
'order': order, \
'transformParams': transformParams}
return featureData, target, modelParams
