inital commit

Author: Lucas van Walstijn

1.py

@@ -0,0 +1,30 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+trainCSV = np.genfromtxt('quasar_train.csv',delimiter=",")
+lambdas = trainCSV[0,:]
+train = trainCSV[1:,:]
+test = np.genfromtxt('quasar_test.csv',delimiter=",",skip_header=1)
+
+mm = lambdas.size
+
+y = train[0,:]
+y.reshape(y.size,1)
+
+x1 = np.ones((mm,1))
+x2 = lambdas.reshape((mm,1))
+
+X = np.hstack((x1,x2))
+
+XtX = (X.T).dot(X)
+XtX_inv = np.linalg.inv( XtX )
+
+theta = (XtX_inv).dot(X.T).dot(y)
+
+plt.figure(1, figsize=(8, 4))
+plt.scatter( x2, y, marker="x", c="red", s=2 )
+plt.ylabel('Intensity')
+plt.xlabel("Wavelength")
+plt.title("Some noisy spectrum with an OLS regression")
+plt.plot( x2, X.dot(theta), "b-", )
+plt.show()

2.py

@@ -0,0 +1,37 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from weight import weight
+
+trainCSV = np.genfromtxt('quasar_train.csv',delimiter=",")
+lambdas = trainCSV[0,:]
+train = trainCSV[1:,:]
+test = np.genfromtxt('quasar_test.csv',delimiter=",",skip_header=1)
+
+mm = lambdas.size
+
+y = train[0,:]
+y.reshape(y.size,1)
+
+x1 = np.ones((mm,1))
+x2 = lambdas.reshape((mm,1))
+
+X = np.hstack((x1,x2))
+
+tau = 5
+
+y_hat = np.zeros(mm)
+for i in range(0, mm):
+    W = weight(x2, x2[i], tau)
+    XtWX = (X.T).dot(W).dot(X)
+    XtWX_inv = np.linalg.inv(XtWX)
+    theta_w = (XtWX_inv).dot(X.T).dot(W).dot(y)
+    y_hat[i] = X.dot(theta_w)[i]
+
+plt.figure(1, figsize=(8, 4))
+plt.ylabel('Intensity')
+plt.xlabel("Wavelength")
+plt.title("Smoothing some spectral data with WLS regression")
+plt.scatter(x2, y, marker="x", c="red", s=2 )
+plt.plot(x2, y_hat, "b-")
+plt.legend()
+plt.show()

3.py

@@ -0,0 +1,32 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from weight import weight
+
+trainCSV = np.genfromtxt('quasar_train.csv',delimiter=",")
+lambdas = trainCSV[0,:]
+train = trainCSV[1:,:]
+test = np.genfromtxt('quasar_test.csv',delimiter=",",skip_header=1)
+
+mm = lambdas.size
+
+x1 = np.ones((mm,1))
+x2 = lambdas.reshape((mm,1))
+X = np.hstack((x1,x2))
+
+tau = 5
+
+test_smooth = np.zeros(test.shape)
+for j in range(0, test.shape[0]):
+    y_hat = np.zeros(mm)
+    y = test[j, :]
+    y.reshape(y.size, 1)
+    for i in range(0, mm):
+        W = weight(x2, x2[i], tau)
+        XtWX = (X.T).dot(W).dot(X)
+        XtWX_inv = np.linalg.inv(XtWX)
+        theta_w = (XtWX_inv).dot(X.T).dot(W).dot(y)
+        y_hat[i] = X.dot(theta_w)[i]
+    print("{0}% complete".format(j/test.shape[0]*100))
+    test_smooth[j] = y_hat
+
+np.savetxt("quasar_test_smooth.csv", test_smooth, delimiter=",")

4.py

@@ -0,0 +1,80 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from weight import weight
+from distance import getDistanceMatrix
+from distance import getDistanceMatrixTrainTest
+from distance import distance
+
+def ker(t):
+    return np.max([1-t, 0])
+
+trainCSV = np.genfromtxt('quasar_train.csv',delimiter=",")
+lambdas = trainCSV[0,:]
+lambdas = lambdas.reshape((lambdas.shape[0],1))
+
+train = np.genfromtxt('quasar_train_smooth.csv',delimiter=",")
+test = np.genfromtxt('quasar_test_smooth.csv',delimiter=",")
+
+right_index = np.where(lambdas == 1300)[0][0]
+left_index = np.where(lambdas == 1200)[0][0]
+
+lambdas_right = lambdas[right_index:,:]
+lambdas_left = lambdas[:left_index,:]
+
+train_right = train[:,right_index:]
+test_right = test[:,right_index:]
+train_left = train[:,:left_index]
+test_left = test[:,:left_index]
+
+mm = train.shape[0]
+
+
+
+neighborhood_size = 3
+
+train_right_distance = getDistanceMatrix(train_right)
+train_left_hat = np.zeros(train_left.shape)
+error = np.zeros((mm,1))
+for i in range(0,mm):
+    indices_of_neighbors = train_right_distance[i].argsort()[:neighborhood_size]
+    distance_with_neighbors = train_right_distance[i][indices_of_neighbors]
+    h = np.nanmax(train_right_distance[i])
+    upper = 0
+    lower = 0
+    for j in range(0, neighborhood_size):
+        kernel = ker(distance_with_neighbors[j]/h)
+        upper = upper + kernel * train_left[indices_of_neighbors[j],:]
+        lower = lower + kernel
+    train_left_hat[i] = upper / lower
+    error[i] = distance(train_left[i], train_left_hat[i])
+
+print(np.average(error))
+
+mm_test = test.shape[0]
+distanceM = getDistanceMatrixTrainTest(train_right, test_right)
+test_left_hat = np.zeros(test_left.shape)
+error = np.zeros((mm_test,1))
+for i in range(0,mm_test):
+    indices_of_neighbors = distanceM[i].argsort()[:neighborhood_size]
+    distance_with_neighbors = distanceM[i][indices_of_neighbors]
+    h = np.nanmax(distanceM[i])
+    upper = 0
+    lower = 0
+    for j in range(0, neighborhood_size):
+        #kernel = ker(distance_with_neighbors[j]/h)
+        kernel = ker(distance_with_neighbors[j] / h)
+        upper = upper + kernel * train_left[indices_of_neighbors[j],:]
+        lower = lower + kernel
+        test_left_hat[i] = upper / lower
+    error[i] = distance(test_left[i], test_left_hat[i])
+
+print(np.average(error))
+
+
+plt.figure(1, figsize=(4, 4))
+plt.plot(lambdas, test[5], ".", label="true" )
+plt.plot(lambdas_left, test_left_hat[5], ".", label="true" )
+plt.legend()
+plt.show()
+
+

5.py

@@ -0,0 +1,59 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from weight import weight
+from distance import getDistanceMatrix
+from distance import getDistanceMatrixTrainTest
+from distance import distance
+
+def ker(t):
+    return np.max([1-t, 0])
+
+trainCSV = np.genfromtxt('quasar_train.csv',delimiter=",")
+lambdas = trainCSV[0,:]
+lambdas = lambdas.reshape((lambdas.shape[0],1))
+
+train = np.genfromtxt('quasar_train_smooth.csv',delimiter=",")
+test = np.genfromtxt('quasar_test_smooth.csv',delimiter=",")
+
+right_index = np.where(lambdas == 1300)[0][0]
+left_index = np.where(lambdas == 1200)[0][0]
+
+lambdas_right = lambdas[right_index:,:]
+lambdas_left = lambdas[:left_index,:]
+
+train_right = train[:,right_index:]
+test_right = test[:,right_index:]
+train_left = train[:,:left_index]
+test_left = test[:,:left_index]
+
+mm = train.shape[0]
+
+neighborhood_size = 3
+
+mm_test = test.shape[0]
+distanceM = getDistanceMatrixTrainTest(train_right, test_right)
+test_left_hat = np.zeros(test_left.shape)
+error = np.zeros((mm_test,1))
+for i in range(0,mm_test):
+    indices_of_neighbors = distanceM[i].argsort()[:neighborhood_size]
+    distance_with_neighbors = distanceM[i][indices_of_neighbors]
+    h = np.nanmax(distanceM[i])
+    upper = 0
+    lower = 0
+    for j in range(0, neighborhood_size):
+        kernel = ker(distance_with_neighbors[j] / h)
+        upper = upper + kernel * train_left[indices_of_neighbors[j],:]
+        lower = lower + kernel
+        test_left_hat[i] = upper / lower
+    error[i] = distance(test_left[i], test_left_hat[i])
+
+print(np.average(error))
+
+
+plt.figure(1, figsize=(4, 4))
+plt.plot(lambdas, test[0], ".", label="true" )
+plt.plot(lambdas_left, test_left_hat[0], ".", label="true" )
+plt.legend()
+plt.show()
+
+

distance.py

@@ -0,0 +1,29 @@
+import numpy as np
+
+def distance(f1,f2):
+    diff = f1 - f2
+    return diff.T.dot(diff)
+
+def getDistanceMatrix(X):
+    mm = X.shape[0]
+    nn = X.shape[1]
+    distanceMatrix = np.nan * np.eye(mm)
+    for i in range(0,mm):
+        for j in range(0,mm):
+            if (i==j):
+                continue
+            f1 = X[i,:]
+            f2 = X[j,:]
+            distanceMatrix[i,j] = distance(f1,f2)
+    return distanceMatrix
+
+def getDistanceMatrixTrainTest(train, test):
+    mtrain = train.shape[0]
+    mtest = test.shape[0]
+    distanceMatrix = np.zeros((mtest,mtrain))
+    for i in range(0,mtest):
+        for j in range(0,mtrain):
+            f1 = train[j,:]
+            f2 = test[i,:]
+            distanceMatrix[i,j] = distance(f1,f2)
+    return distanceMatrix