From e4befffe0ba466366066cb77139fc441915e52f2 Mon Sep 17 00:00:00 2001
From: Saniya <saniyaparveez1996@gmail.com>
Date: Mon, 19 Oct 2020 22:05:57 +0530
Subject: [PATCH] Added code related to linear algebra

---
 .../house_price.csv                           |  8 +++
 .../linear_regression.py                      | 59 +++++++++++++++++++
 .../pca_with_python.py                        | 59 +++++++++++++++++++
 3 files changed, 126 insertions(+)
 create mode 100644 linear-algebra-for-ml-and-deep-learning/house_price.csv
 create mode 100644 linear-algebra-for-ml-and-deep-learning/linear_regression.py
 create mode 100644 linear-algebra-for-ml-and-deep-learning/pca_with_python.py

diff --git a/linear-algebra-for-ml-and-deep-learning/house_price.csv b/linear-algebra-for-ml-and-deep-learning/house_price.csv
new file mode 100644
index 0000000..576933b
--- /dev/null
+++ b/linear-algebra-for-ml-and-deep-learning/house_price.csv
@@ -0,0 +1,8 @@
+square_feet,price
+150,6450
+200,7450
+250,8450
+300,9450
+350,11450
+400,15450
+600,18450
diff --git a/linear-algebra-for-ml-and-deep-learning/linear_regression.py b/linear-algebra-for-ml-and-deep-learning/linear_regression.py
new file mode 100644
index 0000000..e4c26c3
--- /dev/null
+++ b/linear-algebra-for-ml-and-deep-learning/linear_regression.py
@@ -0,0 +1,59 @@
+# import important libraries
+
+import pandas as pd
+import numpy as np
+
+df = pd.read_csv('house_price.csv')
+
+print(df.head())
+
+def get_mean(value):
+    total = sum(value)
+    length = len(value)
+    mean = total/length
+    return mean
+
+def get_variance(value):
+    mean = get_mean(value)
+    mean_difference_square = [pow((item - mean), 2) for item in value]
+    variance = sum(mean_difference_square)/float(len(value)-1)
+    return variance
+
+def get_covariance(value1, value2):
+    value1_mean = get_mean(value1)
+    value2_mean = get_mean(value2)
+    values_size = len(value1)
+    covariance = 0.0
+    for i in range(0, values_size):
+        covariance += (value1[i] - value1_mean) * (value2[i] - value2_mean)
+        
+    return covariance / float(values_size - 1)
+
+def linear_regression(df):
+
+    X = df['square_feet']
+    Y = df['price']
+    m = len(X)
+
+    square_feet_mean = get_mean(X)
+    price_mean = get_mean(Y)
+    
+    #variance of X
+    square_feet_variance = get_variance(X)
+    price_variance = get_variance(Y)
+    
+    covariance_of_price_and_square_feet = get_covariance(X, Y)
+    w1 = covariance_of_price_and_square_feet / float(square_feet_variance)
+    w0 = price_mean - w1 * square_feet_mean
+    
+    # prediction --> Linear Equation
+    prediction = w0 + w1 * X
+    
+    df['price (prediction)'] = prediction
+    return df['price (prediction)']
+
+
+    predicted = linear_regression(df)
+
+    print(predicted)
+    
diff --git a/linear-algebra-for-ml-and-deep-learning/pca_with_python.py b/linear-algebra-for-ml-and-deep-learning/pca_with_python.py
new file mode 100644
index 0000000..28fe1a3
--- /dev/null
+++ b/linear-algebra-for-ml-and-deep-learning/pca_with_python.py
@@ -0,0 +1,59 @@
+# Import important libraries
+import numpy as np
+import pylab as plt
+import pandas as pd
+from sklearn import datasets
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import StandardScaler
+
+load_iris = datasets.load_iris()
+iris_df = pd.DataFrame(load_iris.data, columns=[load_iris.feature_names])
+
+print(iris_df.head())
+
+print(load_iris.data.shape)
+
+standardized_x = StandardScaler().fit_transform(load_iris.data)
+print(standardized_x[:2])
+
+print(standardized_x.T)
+
+covariance_matrix_x = np.cov(standardized_x.T)
+print(covariance_matrix_x)
+
+eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix_x)
+
+print(eigenvalues)
+
+print(eigenvectors)
+
+total_of_eigenvalues = sum(eigenvalues)
+varariance = [(i / total_of_eigenvalues)*100 for i in sorted(eigenvalues, reverse=True)]
+
+print(varariance)
+
+eigenpairs = [(np.abs(eigenvalues[i]), eigenvectors[:,i]) for i in range(len(eigenvalues))]
+
+# Sorting from Higher values to lower value
+eigenpairs.sort(key=lambda x: x[0], reverse=True)
+print(eigenpairs)
+
+matrix_weighing = np.hstack((eigenpairs[0][1].reshape(4,1),
+                      eigenpairs[1][1].reshape(4,1)))
+print(matrix_weighing)
+
+Y = standardized_x.dot(matrix_weighing)
+print(Y)
+
+plt.figure()
+target_names = load_iris.target_names
+y = load_iris.target
+for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
+    plt.scatter(Y[y==i,0], Y[y==i,1], c=c, label=target_name)
+
+plt.xlabel('PCA 1')
+plt.ylabel('PCA 2')
+plt.legend()
+plt.title('PCA')
+plt.show()
+