1# NumPy: For mathematical funcations, array, matrices operations
 2import numpy as np 
 3
 4# Graph: Plotting graphs and other visula tools
 5import pandas as pd
 6import seaborn as sns
 7
 8# sns.set_palette("muted")
 9sns.set(color_codes=True)
10
11# color_palette = sns.color_palette()
12# To enable inline plotting graphs
13import matplotlib.pyplot as plt
14%matplotlib inline

1# Remove outliers from data frame
2def remove_outlier(df_in, col_name):
3    q1 = df_in[col_name].quantile(0.25)
4    q3 = df_in[col_name].quantile(0.75)
5    iqr = q3-q1 #Interquartile range
6    fence_low  = q1-1.5*iqr
7    fence_high = q3+1.5*iqr
8    df_out = df_in.loc[(df_in[col_name] > fence_low) & (df_in[col_name] < fence_high)]
9    return df_out

 1# Load data set
 2# Import CSV data using pandas data frame
 3df_original = pd.read_csv('../vehicle-2.csv')
 4
 5# Print total columns
 6print("Total Colums in dataframe: ", len(df_original.columns))
 7
 8# Prepare columns names
 9df_original_columns = []
10for column in df_original.columns:
11    df_original_columns.append(column)
12
13
14    
15print("Columns list {}".format(df_original_columns))
16print("***********************************************************************************************************************")
17
18# Prepare mapping of column names for quick access
19df_original_columns_map = {}
20map_index: int = 0
21for column in df_original_columns:
22    df_original_columns_map[map_index] = column
23    map_index = map_index + 1
24    
25# print("Columns Map {}".format(df_original_columns_map))
26
27# We have separated out columns and its mapping from data, at any point of time during data analysis or cleaning we 
28# can directly refer or get data from either index or column identifier

Total Colums in dataframe:  19
Columns list ['compactness', 'circularity', 'distance_circularity', 'radius_ratio', 'pr.axis_aspect_ratio', 'max.length_aspect_ratio', 'scatter_ratio', 'elongatedness', 'pr.axis_rectangularity', 'max.length_rectangularity', 'scaled_variance', 'scaled_variance.1', 'scaled_radius_of_gyration', 'scaled_radius_of_gyration.1', 'skewness_about', 'skewness_about.1', 'skewness_about.2', 'hollows_ratio', 'class']
***********************************************************************************************************************

1df_original.shape

(846, 19)

1df_original.info()
2# All columns are numeric in nature except target column

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 846 entries, 0 to 845
Data columns (total 19 columns):
 #   Column                       Non-Null Count  Dtype  
---  ------                       --------------  -----  
 0   compactness                  846 non-null    int64  
 1   circularity                  841 non-null    float64
 2   distance_circularity         842 non-null    float64
 3   radius_ratio                 840 non-null    float64
 4   pr.axis_aspect_ratio         844 non-null    float64
 5   max.length_aspect_ratio      846 non-null    int64  
 6   scatter_ratio                845 non-null    float64
 7   elongatedness                845 non-null    float64
 8   pr.axis_rectangularity       843 non-null    float64
 9   max.length_rectangularity    846 non-null    int64  
 10  scaled_variance              843 non-null    float64
 11  scaled_variance.1            844 non-null    float64
 12  scaled_radius_of_gyration    844 non-null    float64
 13  scaled_radius_of_gyration.1  842 non-null    float64
 14  skewness_about               840 non-null    float64
 15  skewness_about.1             845 non-null    float64
 16  skewness_about.2             845 non-null    float64
 17  hollows_ratio                846 non-null    int64  
 18  class                        846 non-null    object 
dtypes: float64(14), int64(4), object(1)
memory usage: 125.7+ KB

1df_original.head()

1# Data Describe 
2df_original.describe().T

1pd.value_counts(df_original['class'])

car    429
bus    218
van    199
Name: class, dtype: int64

1pd.value_counts(df_original["class"]).plot(kind="bar")

<matplotlib.axes._subplots.AxesSubplot at 0x7fc03fd39b50>

1# Loading data in excel sheets quickly tells that there are Blank values in some columns
2# So print count of them as we are sure they exists
3
4df_original.isna().sum()

compactness                    0
circularity                    5
distance_circularity           4
radius_ratio                   6
pr.axis_aspect_ratio           2
max.length_aspect_ratio        0
scatter_ratio                  1
elongatedness                  1
pr.axis_rectangularity         3
max.length_rectangularity      0
scaled_variance                3
scaled_variance.1              2
scaled_radius_of_gyration      2
scaled_radius_of_gyration.1    4
skewness_about                 6
skewness_about.1               1
skewness_about.2               1
hollows_ratio                  0
class                          0
dtype: int64

1df_duplicates = df_original.duplicated()
2
3print('Number of duplicate rows = {}'.format(df_duplicates.sum()))
4
5# No duplicates

Number of duplicate rows = 0

 1# Create a copy for df before operating on it
 2df_main = df_original.copy()
 3
 4# Replace all missing value from thei median
 5for column in df_original_columns:
 6    if df_main[column].isna().sum() > 0:
 7        median = df_main[column].median()
 8        df_main[column] = df_main[column].fillna(df_main[column].median())
 9        
10
11
12# After replacement confirm that there are no mising values
13df_main.isna().sum()

compactness                    0
circularity                    0
distance_circularity           0
radius_ratio                   0
pr.axis_aspect_ratio           0
max.length_aspect_ratio        0
scatter_ratio                  0
elongatedness                  0
pr.axis_rectangularity         0
max.length_rectangularity      0
scaled_variance                0
scaled_variance.1              0
scaled_radius_of_gyration      0
scaled_radius_of_gyration.1    0
skewness_about                 0
skewness_about.1               0
skewness_about.2               0
hollows_ratio                  0
class                          0
dtype: int64

1from sklearn import preprocessing
2target_column = 'class'
3le = preprocessing.LabelEncoder()
4le.fit(df_main[target_column])
5df_main[target_column] = le.transform(df_main[target_column]) 
6
7df_main.head()

1df_main.boxplot(figsize=(16,4))

<matplotlib.axes._subplots.AxesSubplot at 0x7fc03f2ae090>

1sns.pairplot(df_main,diag_kind='kde')

<seaborn.axisgrid.PairGrid at 0x7fc03ef2e2d0>

1
2# Treat outliers by removing them from data frame
3
4for name in df_original_columns:
5    df_main = remove_outlier(df_main, name)
6    
7df_main.boxplot(figsize=(20,3))  

<matplotlib.axes._subplots.AxesSubplot at 0x7fc034d37cd0>

1# Circularity
2pd.crosstab(df_original['class'], df_original['circularity'])

1# elongatedness
2
3pd.crosstab(df_original['class'], df_original['elongatedness'])

1sns.countplot(x='class',data=df_original)

<matplotlib.axes._subplots.AxesSubplot at 0x7fc030238c10>

1my_tab = pd.crosstab(index = df_main["elongatedness"], columns="class")
2my_tab.plot.bar()

<matplotlib.axes._subplots.AxesSubplot at 0x7fc0301faa90>

1sns.catplot(y='elongatedness', x='class', data=df_original)

<seaborn.axisgrid.FacetGrid at 0x7fc03015bbd0>

1sns.boxplot(y="hollows_ratio", x="class", data=df_original)

<matplotlib.axes._subplots.AxesSubplot at 0x7fc0300983d0>

1#Seperating independent and dependent variables
2
3df_main_x = df_main.copy().drop(['class'], axis = 1) 
4
5
6df_main_y = df_main['class']

1from sklearn.preprocessing import StandardScaler
2
3sc = StandardScaler()
4
5main_x_std =  sc.fit_transform(df_main_x)          
6
7cov_matrix = np.cov(main_x_std.T)
8
9print(cov_matrix)

1eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)

 1# Step 3 (continued): Sort eigenvalues in descending order
 2
 3# Make a set of (eigenvalue, eigenvector) pairs
 4eig_pairs = [(eigenvalues[index], eigenvectors[:,index]) for index in range(len(eigenvalues))]
 5
 6# Sort the (eigenvalue, eigenvector) pairs from highest to lowest with respect to eigenvalue
 7eig_pairs.sort()
 8
 9eig_pairs.reverse()
10print(eig_pairs)
11
12# Extract the descending ordered eigenvalues and eigenvectors
13eigvalues_sorted = [eig_pairs[index][0] for index in range(len(eigenvalues))]
14eigvectors_sorted = [eig_pairs[index][1] for index in range(len(eigenvalues))]
15
16# Let's confirm our sorting worked, print out eigenvalues
17print('Eigenvalues in descending order: \n%s' %eigvalues_sorted)

1total = sum(eigenvalues)
2var_exp = [( i /total ) * 100 for i in sorted(eigenvalues, reverse=True)]
3cum_var_exp = np.cumsum(var_exp)
4print("Cumulative Variance Explained", cum_var_exp)

Cumulative Variance Explained [ 54.1414912   72.83734035  79.57484836  85.9546281   90.96781645
  94.67377661  96.49487775  97.7654787   98.40655404  98.83353799
  99.18001751  99.4227584   99.58377841  99.72928046  99.83007959
  99.92588594  99.98250325 100.        ]

1plt.plot(var_exp)

[<matplotlib.lines.Line2D at 0x7fc02bfbb950>]

1plt.bar(range(0,18), var_exp, alpha=0.5, align='center', label='individual explained variance')
2plt.step(range(0,18),cum_var_exp, where= 'mid', label='cumulative explained variance')
3plt.ylabel('Explained variance ratio')
4plt.xlabel('Principal components')
5plt.legend(loc = 'best')
6plt.show()

1# Reducing from 19 to 5 dimension space
2pca_reduced = np.array(eigvectors_sorted[0:5])
3# projecting original data into principal component dimensions
4main_x_4d = np.dot(main_x_std,pca_reduced.T)
5
6#converting array to dataframe for pairplot
7df_main_x_4d = pd.DataFrame(main_x_4d) 

1sns.pairplot(df_main_x_4d,diag_kind='kde')

<seaborn.axisgrid.PairGrid at 0x7fc029f04a90>

 1from sklearn import model_selection
 2
 3test_size = 0.30 # taking 70:30 training and test set
 4seed = 7  # Random numbmer seeding for reapeatability of the code
 5X_train, X_test, y_train, y_test = model_selection.train_test_split(df_main_x, df_main_y, test_size=test_size, random_state=seed)
 6
 7# Let us build a linear regression model on the PCA dimensions 
 8
 9# Import Linear Regression machine learning library
10from sklearn.linear_model import LinearRegression
11
12regression_model = LinearRegression()
13regression_model.fit(X_train, y_train)
14
15regression_model.coef_
16
17regression_model.score(X_test, y_test)

0.6336302682886086