. To build a regression methodology to determine the sales of items at a particular outlet.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn import preprocessing
from statsmodels.stats.outliers_influence import variance_inflation_factor
from sklearn import metrics
from sklearn.metrics import pairwise_distances
from joblib import Parallel, delayed
import time
from datetime import datetime
import plotly.express as px
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
from scipy.spatial.distance import cdist
from yellowbrick.cluster import KElbowVisualizer
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.cm as cm
from sklearn.metrics import davies_bouldin_score
import scipy.cluster.hierarchy as shc
from sklearn.metrics.pairwise import euclidean_distances
from sklearn import metrics
from time import time
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
#from sklearn_extra.cluster import KMedoids
from sklearn.cluster import AgglomerativeClustering
import plotly as py
import plotly.graph_objs as go
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
df_main=pd.read_csv('Sales_Training.csv')
df_main.head(5)
Item_Identifier | Item_Weight | Item_Visibility | Item_MRP | Outlet_Identifier | Item_Outlet_Sales | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | ... | Outlet_0 | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | FDA15 | 9.30 | 0.016047 | 249.8092 | OUT049 | 3735.1380 | 10 | 1 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | DRC01 | 5.92 | 0.019278 | 48.2692 | OUT018 | 443.4228 | 0 | 0 | 1 | 0 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | FDN15 | 17.50 | 0.016760 | 141.6180 | OUT049 | 2097.2700 | 10 | 1 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
3 | FDX07 | 19.20 | 0.017834 | 182.0950 | OUT010 | 732.3800 | 11 | 0 | 1 | 0 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | NCD19 | 8.93 | 0.009780 | 53.8614 | OUT013 | 994.7052 | 22 | 1 | 0 | 0 | ... | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5 rows × 33 columns
df_main.columns
Index(['Item_Identifier', 'Item_Weight', 'Item_Visibility', 'Item_MRP', 'Outlet_Identifier', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9'], dtype='object')
x=df_main[['Outlet_Identifier','Item_Identifier']].groupby(['Item_Identifier'])['Outlet_Identifier'].agg({'nunique'})
x[x['nunique']>1]
nunique | |
---|---|
Item_Identifier | |
DRA12 | 4 |
DRB13 | 2 |
DRB48 | 4 |
DRC27 | 2 |
DRD24 | 3 |
... | ... |
NCY41 | 4 |
NCZ06 | 4 |
NCZ18 | 3 |
NCZ42 | 2 |
NCZ54 | 3 |
585 rows × 1 columns
df_main[['Outlet_Identifier','Item_Identifier']].groupby(['Outlet_Identifier'])['Item_Identifier'].agg({'count','nunique'})
count | nunique | |
---|---|---|
Outlet_Identifier | ||
OUT010 | 295 | 121 |
OUT013 | 555 | 225 |
OUT017 | 557 | 215 |
OUT018 | 524 | 203 |
OUT019 | 317 | 125 |
OUT027 | 530 | 227 |
OUT035 | 560 | 221 |
OUT045 | 580 | 235 |
OUT046 | 548 | 224 |
OUT049 | 539 | 206 |
insights
,[Outlet_9].
df_main[['Outlet_Identifier','Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5',
'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9']].drop_duplicates().reset_index(drop=True)
Outlet_Identifier | Outlet_0 | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | OUT049 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | OUT018 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | OUT010 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | OUT013 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | OUT027 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
5 | OUT045 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
6 | OUT017 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7 | OUT046 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
8 | OUT035 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
9 | OUT019 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
df=df_main.copy()
there are main components of exploring data:
print('list of parameters in the data ')
df.columns
list of parameters in the data
Index(['Item_Identifier', 'Item_Weight', 'Item_Visibility', 'Item_MRP', 'Outlet_Identifier', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9'], dtype='object')
print('number of rows in the data',df.shape[0])
print('number of columns in the data',df.shape[1])
number of rows in the data 5005 number of columns in the data 33
df.describe().T
count | mean | std | min | 25% | 50% | 75% | max | |
---|---|---|---|---|---|---|---|---|
Item_Weight | 5005.0 | 13.012739 | 4.570505 | 4.59000 | 9.000000 | 13.000000 | 16.850000 | 21.350000 |
Item_Visibility | 5005.0 | 0.071238 | 0.049871 | 0.00478 | 0.032284 | 0.061331 | 0.098664 | 0.328391 |
Item_MRP | 5005.0 | 142.253086 | 62.656992 | 31.29000 | 93.912000 | 145.047000 | 187.387200 | 265.222600 |
Item_Outlet_Sales | 5005.0 | 2233.863293 | 1754.290056 | 33.29000 | 866.871600 | 1808.312800 | 3125.931000 | 11445.102000 |
Outlet_Years | 5005.0 | 11.133467 | 8.354372 | 0.00000 | 5.000000 | 10.000000 | 22.000000 | 24.000000 |
Item_Fat_Content_0 | 5005.0 | 0.654745 | 0.475499 | 0.00000 | 0.000000 | 1.000000 | 1.000000 | 1.000000 |
Item_Fat_Content_1 | 5005.0 | 0.345255 | 0.475499 | 0.00000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 |
Outlet_Location_Type_0 | 5005.0 | 0.280519 | 0.449298 | 0.00000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 |
Outlet_Location_Type_1 | 5005.0 | 0.339061 | 0.473438 | 0.00000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 |
Outlet_Location_Type_2 | 5005.0 | 0.380420 | 0.485538 | 0.00000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 |
Outlet_Size_0 | 5005.0 | 0.110889 | 0.314026 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_Size_1 | 5005.0 | 0.318282 | 0.465856 | 0.00000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 |
Outlet_Size_2 | 5005.0 | 0.511888 | 0.499909 | 0.00000 | 0.000000 | 1.000000 | 1.000000 | 1.000000 |
Outlet_Size_3 | 5005.0 | 0.058941 | 0.235538 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_Type_0 | 5005.0 | 0.122278 | 0.327639 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_Type_1 | 5005.0 | 0.667133 | 0.471287 | 0.00000 | 0.000000 | 1.000000 | 1.000000 | 1.000000 |
Outlet_Type_2 | 5005.0 | 0.104695 | 0.306191 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_Type_3 | 5005.0 | 0.105894 | 0.307733 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Item_Type_Combined_0 | 5005.0 | 0.096304 | 0.295037 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Item_Type_Combined_1 | 5005.0 | 0.721079 | 0.448513 | 0.00000 | 0.000000 | 1.000000 | 1.000000 | 1.000000 |
Item_Type_Combined_2 | 5005.0 | 0.182617 | 0.386391 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_0 | 5005.0 | 0.058941 | 0.235538 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_1 | 5005.0 | 0.110889 | 0.314026 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_2 | 5005.0 | 0.111289 | 0.314521 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_3 | 5005.0 | 0.104695 | 0.306191 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_4 | 5005.0 | 0.063337 | 0.243592 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_5 | 5005.0 | 0.105894 | 0.307733 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_6 | 5005.0 | 0.111888 | 0.315260 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_7 | 5005.0 | 0.115884 | 0.320118 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_8 | 5005.0 | 0.109491 | 0.312285 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Outlet_9 | 5005.0 | 0.107692 | 0.310022 | 0.00000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
Insights
df.replace('?', np.NAN, inplace=True)
#double check the null values
print('Null values in the number of columns ?')
df.isnull().any().sum()
Null values in the number of columns ?
0
df.isnull().sum()
Item_Identifier 0 Item_Weight 0 Item_Visibility 0 Item_MRP 0 Outlet_Identifier 0 Item_Outlet_Sales 0 Outlet_Years 0 Item_Fat_Content_0 0 Item_Fat_Content_1 0 Outlet_Location_Type_0 0 Outlet_Location_Type_1 0 Outlet_Location_Type_2 0 Outlet_Size_0 0 Outlet_Size_1 0 Outlet_Size_2 0 Outlet_Size_3 0 Outlet_Type_0 0 Outlet_Type_1 0 Outlet_Type_2 0 Outlet_Type_3 0 Item_Type_Combined_0 0 Item_Type_Combined_1 0 Item_Type_Combined_2 0 Outlet_0 0 Outlet_1 0 Outlet_2 0 Outlet_3 0 Outlet_4 0 Outlet_5 0 Outlet_6 0 Outlet_7 0 Outlet_8 0 Outlet_9 0 dtype: int64
bool_value= False
columns_with_null = []
count_null = df.isnull().sum()
for count_ in count_null:
if count_ > 0:
bool_value= True
if bool_value:
null_df = pd.DataFrame(count_null).reset_index().rename(columns={'index': 'col_name', 0:'no_of_nulls'})
columns_with_null = list(null_df[null_df['no_of_nulls'] > 0]['col_name'].values)
columns_with_null
[]
#checking for data types of the columns
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 5005 entries, 0 to 5004 Data columns (total 33 columns): Item_Identifier 5005 non-null object Item_Weight 5005 non-null float64 Item_Visibility 5005 non-null float64 Item_MRP 5005 non-null float64 Outlet_Identifier 5005 non-null object Item_Outlet_Sales 5005 non-null float64 Outlet_Years 5005 non-null int64 Item_Fat_Content_0 5005 non-null int64 Item_Fat_Content_1 5005 non-null int64 Outlet_Location_Type_0 5005 non-null int64 Outlet_Location_Type_1 5005 non-null int64 Outlet_Location_Type_2 5005 non-null int64 Outlet_Size_0 5005 non-null int64 Outlet_Size_1 5005 non-null int64 Outlet_Size_2 5005 non-null int64 Outlet_Size_3 5005 non-null int64 Outlet_Type_0 5005 non-null int64 Outlet_Type_1 5005 non-null int64 Outlet_Type_2 5005 non-null int64 Outlet_Type_3 5005 non-null int64 Item_Type_Combined_0 5005 non-null int64 Item_Type_Combined_1 5005 non-null int64 Item_Type_Combined_2 5005 non-null int64 Outlet_0 5005 non-null int64 Outlet_1 5005 non-null int64 Outlet_2 5005 non-null int64 Outlet_3 5005 non-null int64 Outlet_4 5005 non-null int64 Outlet_5 5005 non-null int64 Outlet_6 5005 non-null int64 Outlet_7 5005 non-null int64 Outlet_8 5005 non-null int64 Outlet_9 5005 non-null int64 dtypes: float64(4), int64(27), object(2) memory usage: 1.3+ MB
from doccumentation we know , we have the following as categorical features, but its already one hot encoded data.
df.columns
Index(['Item_Identifier', 'Item_Weight', 'Item_Visibility', 'Item_MRP', 'Outlet_Identifier', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9'], dtype='object')
p=df.hist(figsize=(15,10))
df_main.columns
Index(['Item_Identifier', 'Item_Weight', 'Item_Visibility', 'Item_MRP', 'Outlet_Identifier', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9'], dtype='object')
df[['Item_Weight', 'Item_Visibility', 'Item_MRP']].boxplot()
<matplotlib.axes._subplots.AxesSubplot at 0x156d1a28a88>
df[['Item_Outlet_Sales']].boxplot()
<matplotlib.axes._subplots.AxesSubplot at 0x156d4b837c8>
df[['Outlet_Years']].boxplot()
<matplotlib.axes._subplots.AxesSubplot at 0x156d46117c8>
p=sns.scatterplot(df_main["Item_MRP"],df_main["Item_Outlet_Sales"])
C:\Users\affine\AppData\Roaming\Python\Python37\site-packages\seaborn\_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
df_main['Item_Visibility'].unique()
array([0.0160473 , 0.01927822, 0.01676007, ..., 0.03922186, 0.02158192, 0.128206 ])
p=sns.scatterplot(df_main["Item_Visibility"],df_main["Item_Outlet_Sales"])
C:\Users\affine\AppData\Roaming\Python\Python37\site-packages\seaborn\_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
p=sns.barplot(df_main["Outlet_Years"],df_main["Item_Outlet_Sales"])
C:\Users\affine\AppData\Roaming\Python\Python37\site-packages\seaborn\_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
temp=df_main[["Outlet_Identifier",'Item_Outlet_Sales']].groupby(["Outlet_Identifier"]).agg({'Item_Outlet_Sales':'sum'})
temp.plot(kind="bar")
<matplotlib.axes._subplots.AxesSubplot at 0x156d4821a88>
plt.figure(figsize = (14,9))
sns.boxplot(x='Outlet_Identifier', y='Item_Outlet_Sales', data=df_main, palette="Set1")
plt.title("Outlet_Identifier vs Item_Outlet_Sales ")
Text(0.5, 1.0, 'Outlet_Identifier vs Item_Outlet_Sales ')
x,y,z = df_main[df_main["Item_Type_Combined_0"]==1],df_main[df_main["Item_Type_Combined_1"]==1],df_main[df_main["Item_Type_Combined_2"]==1]
df_pie = pd.DataFrame([[x.shape[0],y.shape[0],z.shape[0]]], columns=["Item_Type_Combined_0","Item_Type_Combined_1","Item_Type_Combined_2"])
df_pie
Item_Type_Combined_0 | Item_Type_Combined_1 | Item_Type_Combined_2 | |
---|---|---|---|
0 | 482 | 3609 | 914 |
plt.pie(df_pie, labels=df_pie.columns, autopct='%1.1f%%',
shadow=True, startangle=90)
plt.show()
D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:2: MatplotlibDeprecationWarning: Non-1D inputs to pie() are currently squeeze()d, but this behavior is deprecated since 3.1 and will be removed in 3.3; pass a 1D array instead.
column= ["Item_Type_Combined_0","Item_Type_Combined_1","Item_Type_Combined_2"]
for col in column:
print(col,df_main[df_main[col]==1][col].value_counts()[1])
Item_Type_Combined_0 482 Item_Type_Combined_1 3609 Item_Type_Combined_2 914
plt.figure(figsize=(20,7), facecolor='white')
plotnumber = 1
for column in ["Item_Type_Combined_0","Item_Type_Combined_1","Item_Type_Combined_2"]:
ax = plt.subplot(1,3,plotnumber)
sns.countplot(x = column,data = df_main,ax=ax)
plt.xlabel(column,fontsize=20)
plotnumber+=1
plt.tight_layout()
sns.boxplot(x='Item_Type_Combined_0', y='Item_Outlet_Sales', data=df_main, palette="Set1")
<matplotlib.axes._subplots.AxesSubplot at 0x156d5fabd88>
x,y = df_main[df_main["Item_Fat_Content_0"]==1],df_main[df_main["Item_Fat_Content_1"]==1]
df_pie = pd.DataFrame([[x.shape[0],y.shape[0]]], columns=["Item_Fat_Content_0","Item_Fat_Content_1"])
df_pie
Item_Fat_Content_0 | Item_Fat_Content_1 | |
---|---|---|
0 | 3277 | 1728 |
plt.pie(df_pie, labels=df_pie.columns, autopct='%1.1f%%',
shadow=True, startangle=90)
plt.show()
D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:2: MatplotlibDeprecationWarning: Non-1D inputs to pie() are currently squeeze()d, but this behavior is deprecated since 3.1 and will be removed in 3.3; pass a 1D array instead.
x=df_main[df_main["Outlet_Location_Type_0"]==1]['Item_Outlet_Sales'].sum()
y=df_main[df_main["Outlet_Location_Type_1"]==1]['Item_Outlet_Sales'].sum()
z=df_main[df_main["Outlet_Location_Type_2"]==1]['Item_Outlet_Sales'].sum()
temp=pd.DataFrame([x,y,z],index=["Outlet_Location_Type_0","Outlet_Location_Type_1","Outlet_Location_Type_2"],columns=['sales'])
temp.head()
sales | |
---|---|
Outlet_Location_Type_0 | 2.712625e+06 |
Outlet_Location_Type_1 | 4.027673e+06 |
Outlet_Location_Type_2 | 4.440188e+06 |
temp.plot(kind='bar',rot=10)
<matplotlib.axes._subplots.AxesSubplot at 0x156d609c688>
df_main['Item_Identifier'].unique()
array(['FDA15', 'DRC01', 'FDN15', ..., 'FDZ43', 'FDJ50', 'FDV35'], dtype=object)
temp=df_main[["Item_Identifier",'Item_Outlet_Sales']].groupby(["Item_Identifier"]).agg({'Item_Outlet_Sales':'sum'})
temp['Item_Outlet_Sales']=round(temp['Item_Outlet_Sales'],2)
temp=temp.sort_values(by = 'Item_Outlet_Sales',ascending=False)
temp.head(20).plot(kind='bar')
<matplotlib.axes._subplots.AxesSubplot at 0x156d6115708>
temp.tail(20).plot(kind='bar')
<matplotlib.axes._subplots.AxesSubplot at 0x156d4ab1f88>
df_main.corr()
Item_Weight | Item_Visibility | Item_MRP | Item_Outlet_Sales | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | Outlet_Location_Type_1 | Outlet_Location_Type_2 | ... | Outlet_0 | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Item_Weight | 1.000000 | -0.028674 | -0.000255 | 0.010784 | 0.016975 | 0.024335 | -0.024335 | -0.022108 | 0.012272 | 0.008492 | ... | 0.022577 | 0.010177 | 0.012942 | -0.028762 | -0.002504 | 0.014350 | 0.014923 | -0.009263 | 0.006385 | -0.036504 |
Item_Visibility | -0.028674 | 1.000000 | -0.030495 | -0.141637 | 0.100036 | -0.032534 | 0.032534 | 0.070483 | -0.091197 | 0.023702 | ... | 0.178385 | -0.022856 | -0.042400 | -0.031459 | 0.222598 | -0.044514 | -0.056060 | -0.038007 | -0.024618 | -0.047956 |
Item_MRP | -0.000255 | -0.030495 | 1.000000 | 0.586390 | 0.003133 | -0.026634 | 0.026634 | -0.016943 | 0.025257 | -0.008949 | ... | -0.016716 | 0.005037 | 0.006770 | -0.019139 | -0.019026 | 0.012579 | -0.004686 | 0.035316 | 0.010870 | -0.020555 |
Item_Outlet_Sales | 0.010784 | -0.141637 | 0.586390 | 1.000000 | 0.059710 | -0.032061 | 0.032061 | -0.107430 | 0.056979 | 0.043853 | ... | -0.267919 | 0.009033 | 0.051358 | -0.068616 | -0.282744 | 0.333309 | -0.003498 | 0.037254 | 0.008891 | 0.057511 |
Outlet_Years | 0.016975 | 0.100036 | 0.003133 | 0.059710 | 1.000000 | 0.020204 | -0.020204 | 0.209903 | -0.551707 | 0.343721 | ... | -0.003999 | 0.459396 | -0.386910 | -0.455762 | 0.400523 | 0.530069 | -0.260612 | -0.179144 | 0.036373 | -0.047138 |
Item_Fat_Content_0 | 0.024335 | -0.032534 | -0.026634 | -0.032061 | 0.020204 | 1.000000 | -1.000000 | 0.042783 | -0.038263 | -0.002281 | ... | 0.001517 | -0.036649 | -0.019633 | 0.010862 | 0.040452 | 0.021831 | -0.023539 | -0.014116 | 0.012381 | 0.017748 |
Item_Fat_Content_1 | -0.024335 | 0.032534 | 0.026634 | 0.032061 | -0.020204 | -1.000000 | 1.000000 | -0.042783 | 0.038263 | 0.002281 | ... | -0.001517 | 0.036649 | 0.019633 | -0.010862 | -0.040452 | -0.021831 | 0.023539 | 0.014116 | -0.012381 | -0.017748 |
Outlet_Location_Type_0 | -0.022108 | 0.070483 | -0.016943 | -0.107430 | 0.209903 | 0.042783 | -0.042783 | 1.000000 | -0.447229 | -0.489277 | ... | -0.156269 | -0.220515 | -0.220962 | -0.213526 | 0.416451 | -0.214889 | -0.221631 | -0.226063 | 0.561561 | 0.556369 |
Outlet_Location_Type_1 | 0.012272 | -0.091197 | 0.025257 | 0.056979 | -0.551707 | -0.038263 | 0.038263 | -0.447229 | 1.000000 | -0.561230 | ... | -0.179250 | -0.252944 | 0.494068 | -0.244927 | -0.186249 | -0.246490 | 0.495564 | 0.505474 | -0.251147 | -0.248825 |
Outlet_Location_Type_2 | 0.008492 | 0.023702 | -0.008949 | 0.043853 | 0.343721 | -0.002281 | 0.002281 | -0.489277 | -0.561230 | 1.000000 | ... | 0.319388 | 0.450696 | -0.277286 | 0.436411 | -0.203760 | 0.439196 | -0.278125 | -0.283687 | -0.274759 | -0.272218 |
Outlet_Size_0 | 0.010177 | -0.022856 | 0.005037 | 0.009033 | 0.459396 | -0.036649 | 0.036649 | -0.220515 | -0.252944 | 0.450696 | ... | -0.088383 | 1.000000 | -0.124972 | -0.120766 | -0.091834 | -0.121537 | -0.125350 | -0.127857 | -0.123833 | -0.122688 |
Outlet_Size_1 | -0.033718 | -0.081995 | -0.017949 | 0.213349 | 0.019224 | 0.033371 | -0.033371 | 0.087965 | -0.489397 | 0.395801 | ... | -0.171003 | -0.241307 | -0.241796 | 0.500466 | -0.177680 | 0.503661 | -0.242528 | -0.247378 | -0.239592 | 0.508431 |
Outlet_Size_2 | 0.014391 | 0.006719 | 0.021439 | -0.078258 | -0.304608 | -0.008792 | 0.008792 | 0.130175 | 0.699408 | -0.802436 | ... | -0.256288 | -0.361655 | 0.345555 | -0.350192 | 0.253926 | -0.352427 | 0.346601 | 0.353533 | 0.342406 | -0.355765 |
Outlet_Size_3 | 0.022577 | 0.178385 | -0.016716 | -0.267919 | -0.003999 | 0.001517 | -0.001517 | -0.156269 | -0.179250 | 0.319388 | ... | 1.000000 | -0.088383 | -0.088562 | -0.085581 | -0.065078 | -0.086128 | -0.088830 | -0.090606 | -0.087755 | -0.086943 |
Outlet_Type_0 | 0.014369 | 0.293736 | -0.026162 | -0.402819 | 0.294904 | 0.031165 | -0.031165 | 0.197281 | -0.267333 | 0.078115 | ... | 0.670510 | -0.131814 | -0.132081 | -0.127636 | 0.696692 | -0.128451 | -0.132481 | -0.135130 | -0.130877 | -0.129667 |
Outlet_Type_1 | -0.000673 | -0.154702 | 0.022409 | 0.106981 | -0.255029 | -0.042978 | 0.042978 | 0.141891 | 0.505927 | -0.624618 | ... | -0.354300 | 0.249457 | 0.249962 | -0.484115 | -0.368135 | -0.487205 | 0.250719 | 0.255733 | 0.247684 | 0.245394 |
Outlet_Type_2 | -0.028762 | -0.031459 | -0.019139 | -0.068616 | -0.455762 | 0.010862 | -0.010862 | -0.213526 | -0.244927 | 0.436411 | ... | -0.085581 | -0.120766 | -0.121011 | 1.000000 | -0.088923 | -0.117685 | -0.121377 | -0.123804 | -0.119908 | -0.118799 |
Outlet_Type_3 | 0.014350 | -0.044514 | 0.012579 | 0.333309 | 0.530069 | 0.021831 | -0.021831 | -0.214889 | -0.246490 | 0.439196 | ... | -0.086128 | -0.121537 | -0.121783 | -0.117685 | -0.089491 | 1.000000 | -0.122152 | -0.124594 | -0.120673 | -0.119557 |
Item_Type_Combined_0 | -0.060947 | -0.025330 | -0.062313 | -0.042982 | -0.003756 | 0.170101 | -0.170101 | 0.026819 | 0.045170 | -0.068862 | ... | -0.038562 | -0.026851 | 0.030923 | -0.038631 | 0.040241 | -0.013297 | 0.034526 | 0.002420 | 0.024348 | -0.017277 |
Item_Type_Combined_1 | 0.010059 | 0.048820 | 0.066332 | 0.061257 | 0.027430 | -0.407589 | 0.407589 | 0.000600 | -0.039217 | 0.037685 | ... | -0.020276 | 0.038027 | -0.032074 | 0.019142 | -0.015698 | 0.017126 | -0.009616 | -0.017017 | 0.026893 | -0.013885 |
Item_Type_Combined_2 | 0.034861 | -0.037328 | -0.029417 | -0.038286 | -0.028972 | 0.343235 | -0.343235 | -0.021175 | 0.011032 | 0.008837 | ... | 0.052980 | -0.023639 | 0.013619 | 0.007278 | -0.012505 | -0.009726 | -0.015201 | 0.017904 | -0.049808 | 0.029310 |
Outlet_0 | 0.022577 | 0.178385 | -0.016716 | -0.267919 | -0.003999 | 0.001517 | -0.001517 | -0.156269 | -0.179250 | 0.319388 | ... | 1.000000 | -0.088383 | -0.088562 | -0.085581 | -0.065078 | -0.086128 | -0.088830 | -0.090606 | -0.087755 | -0.086943 |
Outlet_1 | 0.010177 | -0.022856 | 0.005037 | 0.009033 | 0.459396 | -0.036649 | 0.036649 | -0.220515 | -0.252944 | 0.450696 | ... | -0.088383 | 1.000000 | -0.124972 | -0.120766 | -0.091834 | -0.121537 | -0.125350 | -0.127857 | -0.123833 | -0.122688 |
Outlet_2 | 0.012942 | -0.042400 | 0.006770 | 0.051358 | -0.386910 | -0.019633 | 0.019633 | -0.220962 | 0.494068 | -0.277286 | ... | -0.088562 | -0.124972 | 1.000000 | -0.121011 | -0.092020 | -0.121783 | -0.125604 | -0.128116 | -0.124084 | -0.122936 |
Outlet_3 | -0.028762 | -0.031459 | -0.019139 | -0.068616 | -0.455762 | 0.010862 | -0.010862 | -0.213526 | -0.244927 | 0.436411 | ... | -0.085581 | -0.120766 | -0.121011 | 1.000000 | -0.088923 | -0.117685 | -0.121377 | -0.123804 | -0.119908 | -0.118799 |
Outlet_4 | -0.002504 | 0.222598 | -0.019026 | -0.282744 | 0.400523 | 0.040452 | -0.040452 | 0.416451 | -0.186249 | -0.203760 | ... | -0.065078 | -0.091834 | -0.092020 | -0.088923 | 1.000000 | -0.089491 | -0.092298 | -0.094144 | -0.091181 | -0.090338 |
Outlet_5 | 0.014350 | -0.044514 | 0.012579 | 0.333309 | 0.530069 | 0.021831 | -0.021831 | -0.214889 | -0.246490 | 0.439196 | ... | -0.086128 | -0.121537 | -0.121783 | -0.117685 | -0.089491 | 1.000000 | -0.122152 | -0.124594 | -0.120673 | -0.119557 |
Outlet_6 | 0.014923 | -0.056060 | -0.004686 | -0.003498 | -0.260612 | -0.023539 | 0.023539 | -0.221631 | 0.495564 | -0.278125 | ... | -0.088830 | -0.125350 | -0.125604 | -0.121377 | -0.092298 | -0.122152 | 1.000000 | -0.128504 | -0.124459 | -0.123309 |
Outlet_7 | -0.009263 | -0.038007 | 0.035316 | 0.037254 | -0.179144 | -0.014116 | 0.014116 | -0.226063 | 0.505474 | -0.283687 | ... | -0.090606 | -0.127857 | -0.128116 | -0.123804 | -0.094144 | -0.124594 | -0.128504 | 1.000000 | -0.126948 | -0.125774 |
Outlet_8 | 0.006385 | -0.024618 | 0.010870 | 0.008891 | 0.036373 | 0.012381 | -0.012381 | 0.561561 | -0.251147 | -0.274759 | ... | -0.087755 | -0.123833 | -0.124084 | -0.119908 | -0.091181 | -0.120673 | -0.124459 | -0.126948 | 1.000000 | -0.121816 |
Outlet_9 | -0.036504 | -0.047956 | -0.020555 | 0.057511 | -0.047138 | 0.017748 | -0.017748 | 0.556369 | -0.248825 | -0.272218 | ... | -0.086943 | -0.122688 | -0.122936 | -0.118799 | -0.090338 | -0.119557 | -0.123309 | -0.125774 | -0.121816 | 1.000000 |
31 rows × 31 columns
plt.figure(figsize=(20,18))
#matrix = np.triu(df_main.corr())
p=sns.heatmap(df_main.corr(), annot=True,cmap= 'RdYlGn',linewidths=1, linecolor='black')
df.columns
Index(['Item_Identifier', 'Item_Weight', 'Item_Visibility', 'Item_MRP', 'Outlet_Identifier', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9'], dtype='object')
df.drop(columns=["Item_Identifier","Outlet_Identifier"],inplace=True)
X = df_main.drop(["Item_Identifier","Outlet_Identifier","Item_Outlet_Sales"],axis=1)
y = df_main["Item_Outlet_Sales"]
X.head()
Item_Weight | Item_Visibility | Item_MRP | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | Outlet_Location_Type_1 | Outlet_Location_Type_2 | Outlet_Size_0 | ... | Outlet_0 | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 9.30 | 0.016047 | 249.8092 | 10 | 1 | 0 | 1 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | 5.92 | 0.019278 | 48.2692 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 17.50 | 0.016760 | 141.6180 | 10 | 1 | 0 | 1 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
3 | 19.20 | 0.017834 | 182.0950 | 11 | 0 | 1 | 0 | 0 | 1 | 0 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 8.93 | 0.009780 | 53.8614 | 22 | 1 | 0 | 0 | 0 | 1 | 1 | ... | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5 rows × 30 columns
y.head()
0 3735.1380 1 443.4228 2 2097.2700 3 732.3800 4 994.7052 Name: Item_Outlet_Sales, dtype: float64
import sklearn
x_train,x_test,y_train,y_test = sklearn.model_selection.train_test_split(X,y,test_size=1 / 3,random_state=0)
from sklearn.linear_model import LinearRegression
reg = LinearRegression()
reg.fit(x_train,y_train)
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)
reg.score(x_train,y_train)
0.5829014005926508
reg.score(x_test,y_test)
0.5745067008281586
from sklearn.preprocessing import PolynomialFeatures
poly= PolynomialFeatures(2)
x_tr=poly.fit_transform(x_train)
x_te=poly.transform(x_test)
(x_train.shape,x_tr.shape)
((3336, 30), (3336, 496))
from sklearn.linear_model import RidgeCV
reg=RidgeCV(cv=5,scoring='neg_mean_absolute_error')
reg.fit(x_tr,y_train)
RidgeCV(alphas=array([ 0.1, 1. , 10. ]), cv=5, fit_intercept=True, gcv_mode=None, normalize=False, scoring='neg_mean_absolute_error', store_cv_values=False)
reg.score(x_tr,y_train)
0.6339190443896361
reg.score(x_te,y_test)
0.6268405557416854
from sklearn.ensemble import RandomForestRegressor
estimator = RandomForestRegressor()
estimator.fit(x_train,y_train)
RandomForestRegressor(bootstrap=True, ccp_alpha=0.0, criterion='mse', max_depth=None, max_features='auto', max_leaf_nodes=None, max_samples=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=100, n_jobs=None, oob_score=False, random_state=None, verbose=0, warm_start=False)
estimator.score(x_train,y_train)
0.9805070802427924
estimator.score(x_test,y_test)
0.8480563202395021
p=pd.Series(estimator.feature_importances_,X.columns).sort_values(ascending=False).plot(kind='bar',figsize=(20,10))
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import GridSearchCV
from sklearn.ensemble import RandomForestRegressor
from sklearn.ensemble import ExtraTreesRegressor
from catboost import CatBoostRegressor
model_params = {
'Linear_reg': {
'model': LinearRegression(),
'params' : {
'fit_intercept': [True, False], 'normalize': [True, False], 'copy_X': [True, False]
}
},
'random_forest': {
'model': RandomForestRegressor(),
'params' : {"n_estimators": [10, 50, 100, 130],
'criterion':['mse'],
"max_depth": [None,2,3,4],
"max_features": ['auto', 'log2']
}
},
'ExtraTree_reg' : {
'model': ExtraTreesRegressor(),
'params': {"n_estimators": [10, 50, 100, 130],
'criterion':['mse'],
"max_depth": [None,2,3,4],
"max_features": ['auto', 'log2']
}
},
'CatBoost_reg':
{
'model':CatBoostRegressor(),
'params':{"n_estimators": [130,200],
'loss_function':['RMSE','MAE'],
'learning_rate':[0.01,0.5,1]
}
}
}
scores = []
for model_name, mp in model_params.items():
reg = GridSearchCV(mp['model'], mp['params'], cv=5, return_train_score=False)
reg.fit(x_train, y_train)
scores.append({
'model name' :model_name,
'model': reg.best_estimator_,
'best_score': reg.best_score_,
'best_params': reg.best_params_,
'R2_score' : sklearn.metrics.r2_score( y_test,reg.best_estimator_.predict(x_test))
})
df1 = pd.DataFrame(scores,columns=['model name','model','best_score','best_params','R2_score'])
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df1
model name | model | best_score | best_params | R2_score | |
---|---|---|---|---|---|
0 | Linear_reg | LinearRegression(copy_X=True, fit_intercept=Tr... | 0.578577 | {'copy_X': True, 'fit_intercept': True, 'norma... | 0.574507 |
1 | random_forest | (DecisionTreeRegressor(ccp_alpha=0.0, criterio... | 0.835779 | {'criterion': 'mse', 'max_depth': None, 'max_f... | 0.852770 |
2 | ExtraTree_reg | (ExtraTreeRegressor(ccp_alpha=0.0, criterion='... | 0.847186 | {'criterion': 'mse', 'max_depth': None, 'max_f... | 0.873905 |
3 | CatBoost_reg | <catboost.core.CatBoostRegressor object at 0x0... | 0.813387 | {'learning_rate': 0.5, 'loss_function': 'RMSE'... | 0.817854 |
. These methods include direct methods and statistical testing methods:
And from this graph, we determine the number of clusters we’d like to keep. To that effect, we use the Elbow-method. The approach consists of looking for a kink or elbow in the WCSS graph. Usually, the part of the graph before the elbow would be steeply declining, while the part after it – much smoother. In this instance, the kink comes at the 7 clusters mark.
wcss = []
cluster_range = range(1, 11)
for i in cluster_range:
kmeans = KMeans(n_clusters=i, init='k-means++')
kmeans.fit(df)
wcss.append(kmeans.inertia_)
# generate the plot
plt.plot(cluster_range, wcss) # creating the graph between WCSS and the number of clusters
plt.title('The Elbow Method')
plt.xlabel('Number of clusters')
plt.ylabel('WCSS')
Text(0, 0.5, 'WCSS')
Silhouette analysis can be used to study the separation distance between the resulting clusters. The silhouette plot displays a measure of how close each point in one cluster is to points in the neighboring clusters and thus provides a way to assess parameters like number of clusters visually. This measure has a range of [-1, 1]. Where 1 means that points are very close to their own cluster and far from other clusters, whereas -1 indicates that points are close to the neighboring clusters.
The silhouette score of 1 means that the clusters are very dense and nicely separated. The score of 0 means that clusters are overlapping. The score of less than 0 means that data belonging to clusters may be wrong/incorrect. The silhouette plots can be used to select the most optimal value of the K (no. of cluster) in K-means clustering. The aspects to look out for in Silhouette plots are cluster scores below the average silhouette score, wide fluctuations in the size of the clusters, and also the thickness of the silhouette plot.
range_n_clusters = [2, 3, 4, 5, 6,7]
avg_silhouette(df,range_n_clusters)
For n_clusters = 2 The average silhouette_score is : 0.6168169774752235 For n_clusters = 3 The average silhouette_score is : 0.5921198687195769 For n_clusters = 4 The average silhouette_score is : 0.5553436623224265 For n_clusters = 5 The average silhouette_score is : 0.5483397242438969 For n_clusters = 6 The average silhouette_score is : 0.5477836113039588 For n_clusters = 7 The average silhouette_score is : 0.531358975820681
gap_statistics(df)
Optimal clusters: 5
#KMeans++ removes the drawback of K means which is it is dependent on initialization of centroid
kmodel=KMeans(init='k-means++', n_clusters=2, n_init=10,max_iter=500)
kmodel.fit(df)
df['cluster_label']=kmodel.labels_
df.head()
Item_Weight | Item_Visibility | Item_MRP | Item_Outlet_Sales | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | Outlet_Location_Type_1 | Outlet_Location_Type_2 | ... | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | cluster_label | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 9.30 | 0.016047 | 249.8092 | 3735.1380 | 10 | 1 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
1 | 5.92 | 0.019278 | 48.2692 | 443.4228 | 0 | 0 | 1 | 0 | 0 | 1 | ... | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 17.50 | 0.016760 | 141.6180 | 2097.2700 | 10 | 1 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
3 | 19.20 | 0.017834 | 182.0950 | 732.3800 | 11 | 0 | 1 | 0 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 8.93 | 0.009780 | 53.8614 | 994.7052 | 22 | 1 | 0 | 0 | 0 | 1 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5 rows × 32 columns
Vizualising the clusters using PCA
. PCA is an algorithm that is used for dimensionality reduction - meaning, informally, that it can take in a DataFrame with many columns and return a DataFrame with a reduced number of columns that still retains much of the information from the columns of the original DataFrame. The columns of the DataFrame produced from the PCA procedure are called Principal Components. We will use these principal components to help us visualize our clusters in 1-D, 2-D, and 3-D space, since we cannot easily visualize the data we have in higher dimensions.
plot_k_means_2D(df,2)
plot_k_means_3D(df,2)
df.head()
Item_Weight | Item_Visibility | Item_MRP | Item_Outlet_Sales | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | Outlet_Location_Type_1 | Outlet_Location_Type_2 | ... | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | cluster_label | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 9.30 | 0.016047 | 249.8092 | 3735.1380 | 10 | 1 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
1 | 5.92 | 0.019278 | 48.2692 | 443.4228 | 0 | 0 | 1 | 0 | 0 | 1 | ... | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 17.50 | 0.016760 | 141.6180 | 2097.2700 | 10 | 1 | 0 | 1 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
3 | 19.20 | 0.017834 | 182.0950 | 732.3800 | 11 | 0 | 1 | 0 | 0 | 1 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 8.93 | 0.009780 | 53.8614 | 994.7052 | 22 | 1 | 0 | 0 | 0 | 1 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5 rows × 32 columns
list_of_clusters = df['cluster_label'].unique()
from sklearn.ensemble import RandomForestRegressor
dict_={}
for i in list_of_clusters:
# get data for each
cluster_data = df[df['cluster_label'] == i]
# step 4.1 get cluster features & labels
cluster_features =df.drop(['Item_Outlet_Sales', 'cluster_label'], axis=1)
cluster_label = df['Item_Outlet_Sales']
# step 4.2 split data into test & train
x_train, x_test, y_train, y_test = sklearn.model_selection.train_test_split(cluster_features,
cluster_label,
test_size=1 / 3,
random_state=0)
scores = []
estimator = RandomForestRegressor()
estimator.fit(x_train,y_train)
scores.append(
{'train_score': estimator.score(x_train,y_train),
'test_score' :estimator.score(x_test,y_test)
})
dict_[i]=scores
dict_
{1: [{'train_score': 0.9814861935839829, 'test_score': 0.8511212879187413}], 0: [{'train_score': 0.980229323362237, 'test_score': 0.8490949806204267}]}
final_models={}
for i in dict_.keys():
inner_list=dict_[i]
final_models['cluster'+str(i)]=(inner_list[0])
pd.DataFrame(final_models).T
train_score | test_score | |
---|---|---|
cluster1 | 0.981486 | 0.851121 |
cluster0 | 0.980229 | 0.849095 |
df.columns
Index(['Item_Weight', 'Item_Visibility', 'Item_MRP', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9', 'cluster_label'], dtype='object')
df.groupby(['cluster_label']).agg({
'mean'
})
Item_Weight | Item_Visibility | Item_MRP | Item_Outlet_Sales | Outlet_Years | Item_Fat_Content_0 | Item_Fat_Content_1 | Outlet_Location_Type_0 | Outlet_Location_Type_1 | Outlet_Location_Type_2 | ... | Outlet_0 | Outlet_1 | Outlet_2 | Outlet_3 | Outlet_4 | Outlet_5 | Outlet_6 | Outlet_7 | Outlet_8 | Outlet_9 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mean | mean | mean | mean | mean | mean | mean | mean | mean | mean | ... | mean | mean | mean | mean | mean | mean | mean | mean | mean | mean | |
cluster_label | |||||||||||||||||||||
0 | 12.977314 | 0.074199 | 120.980642 | 1282.858552 | 10.677947 | 0.665328 | 0.334672 | 0.297677 | 0.330370 | 0.371953 | ... | 0.0846 | 0.106108 | 0.101233 | 0.124176 | 0.090909 | 0.057069 | 0.112704 | 0.116432 | 0.106395 | 0.100373 |
1 | 13.094114 | 0.064434 | 191.118047 | 4418.417662 | 12.179842 | 0.630435 | 0.369565 | 0.241107 | 0.359025 | 0.399868 | ... | 0.0000 | 0.121871 | 0.134387 | 0.059947 | 0.000000 | 0.218050 | 0.110013 | 0.114625 | 0.116601 | 0.124506 |
2 rows × 31 columns
INSIGHTS
from pycaret.utils import version
version()
'2.2.3'
df.columns
Index(['Item_Weight', 'Item_Visibility', 'Item_MRP', 'Item_Outlet_Sales', 'Outlet_Years', 'Item_Fat_Content_0', 'Item_Fat_Content_1', 'Outlet_Location_Type_0', 'Outlet_Location_Type_1', 'Outlet_Location_Type_2', 'Outlet_Size_0', 'Outlet_Size_1', 'Outlet_Size_2', 'Outlet_Size_3', 'Outlet_Type_0', 'Outlet_Type_1', 'Outlet_Type_2', 'Outlet_Type_3', 'Item_Type_Combined_0', 'Item_Type_Combined_1', 'Item_Type_Combined_2', 'Outlet_0', 'Outlet_1', 'Outlet_2', 'Outlet_3', 'Outlet_4', 'Outlet_5', 'Outlet_6', 'Outlet_7', 'Outlet_8', 'Outlet_9', 'cluster_label'], dtype='object')
features =list(df.drop(columns=['Item_Outlet_Sales']).columns)
import pycaret
from pycaret.regression import *
reg = setup(df, target = 'Item_Outlet_Sales',numeric_features=features, session_id=786)
Description | Value | |
---|---|---|
0 | session_id | 786 |
1 | Target | Item_Outlet_Sales |
2 | Original Data | (5005, 32) |
3 | Missing Values | False |
4 | Numeric Features | 31 |
5 | Categorical Features | 0 |
6 | Ordinal Features | False |
7 | High Cardinality Features | False |
8 | High Cardinality Method | None |
9 | Transformed Train Set | (3503, 26) |
10 | Transformed Test Set | (1502, 26) |
11 | Shuffle Train-Test | True |
12 | Stratify Train-Test | False |
13 | Fold Generator | KFold |
14 | Fold Number | 10 |
15 | CPU Jobs | -1 |
16 | Use GPU | False |
17 | Log Experiment | False |
18 | Experiment Name | reg-default-name |
19 | USI | c1d1 |
20 | Imputation Type | simple |
21 | Iterative Imputation Iteration | None |
22 | Numeric Imputer | mean |
23 | Iterative Imputation Numeric Model | None |
24 | Categorical Imputer | constant |
25 | Iterative Imputation Categorical Model | None |
26 | Unknown Categoricals Handling | least_frequent |
27 | Normalize | False |
28 | Normalize Method | None |
29 | Transformation | False |
30 | Transformation Method | None |
31 | PCA | False |
32 | PCA Method | None |
33 | PCA Components | None |
34 | Ignore Low Variance | False |
35 | Combine Rare Levels | False |
36 | Rare Level Threshold | None |
37 | Numeric Binning | False |
38 | Remove Outliers | False |
39 | Outliers Threshold | None |
40 | Remove Multicollinearity | False |
41 | Multicollinearity Threshold | None |
42 | Clustering | False |
43 | Clustering Iteration | None |
44 | Polynomial Features | False |
45 | Polynomial Degree | None |
46 | Trignometry Features | False |
47 | Polynomial Threshold | None |
48 | Group Features | False |
49 | Feature Selection | False |
50 | Features Selection Threshold | None |
51 | Feature Interaction | False |
52 | Feature Ratio | False |
53 | Interaction Threshold | None |
54 | Transform Target | False |
55 | Transform Target Method | box-cox |
compare_models()
Model | MAE | MSE | RMSE | R2 | RMSLE | MAPE | TT (Sec) | |
---|---|---|---|---|---|---|---|---|
et | Extra Trees Regressor | 145.5 | 1.805e+05 | 418.1 | 0.9423 | 0.235 | 0.1091 | 0.652 |
rf | Random Forest Regressor | 231.7 | 2.081e+05 | 450.4 | 0.9332 | 0.2631 | 0.1719 | 0.811 |
dt | Decision Tree Regressor | 180.3 | 2.771e+05 | 519.7 | 0.9108 | 0.3179 | 0.1304 | 0.023 |
catboost | CatBoost Regressor | 364.1 | 2.889e+05 | 535.2 | 0.9068 | 0.392 | 0.3172 | 5.826 |
lightgbm | Light Gradient Boosting Machine | 380.1 | 3.124e+05 | 556.8 | 0.8993 | 0.3977 | 0.3365 | 0.084 |
gbr | Gradient Boosting Regressor | 506.3 | 4.967e+05 | 703.6 | 0.8398 | 0.4484 | 0.4204 | 0.251 |
lr | Linear Regression | 600.5 | 6.478e+05 | 802.7 | 0.792 | 0.5751 | 0.5725 | 0.565 |
lasso | Lasso Regression | 600.2 | 6.478e+05 | 802.7 | 0.792 | 0.5759 | 0.572 | 0.017 |
ridge | Ridge Regression | 600.4 | 6.477e+05 | 802.7 | 0.792 | 0.5733 | 0.5728 | 0.027 |
br | Bayesian Ridge | 600.3 | 6.477e+05 | 802.7 | 0.792 | 0.5739 | 0.573 | 0.017 |
huber | Huber Regressor | 593.4 | 6.683e+05 | 815 | 0.7857 | 0.5749 | 0.5628 | 0.079 |
ada | AdaBoost Regressor | 649.5 | 6.95e+05 | 832.6 | 0.7754 | 0.5725 | 0.6639 | 0.141 |
omp | Orthogonal Matching Pursuit | 707.3 | 8.675e+05 | 928.8 | 0.7214 | 0.5886 | 0.6524 | 0.063 |
en | Elastic Net | 824.9 | 1.284e+06 | 1132 | 0.5863 | 0.7571 | 0.9942 | 0.018 |
knn | K Neighbors Regressor | 801.4 | 1.406e+06 | 1181 | 0.5479 | 0.7108 | 0.9009 | 0.056 |
par | Passive Aggressive Regressor | 925.1 | 1.532e+06 | 1227 | 0.5067 | 0.7682 | 1.052 | 0.024 |
ExtraTreesRegressor(bootstrap=False, ccp_alpha=0.0, criterion='mse', max_depth=None, max_features='auto', max_leaf_nodes=None, max_samples=None, min_impurity_decrease=0.0, min_impurity_split=None, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=100, n_jobs=-1, oob_score=False, random_state=786, verbose=0, warm_start=False)
create_model('catboost')
MAE | MSE | RMSE | R2 | RMSLE | MAPE | |
---|---|---|---|---|---|---|
0 | 355.8 | 2.886e+05 | 537.2 | 0.916 | 0.3973 | 0.3113 |
1 | 349.9 | 2.756e+05 | 525 | 0.9103 | 0.3803 | 0.3243 |
2 | 362.5 | 2.625e+05 | 512.4 | 0.9106 | 0.4676 | 0.3562 |
3 | 357.3 | 2.873e+05 | 536 | 0.9055 | 0.4251 | 0.3307 |
4 | 340.8 | 2.327e+05 | 482.4 | 0.9188 | 0.3479 | 0.2828 |
5 | 403.2 | 4.53e+05 | 673 | 0.8619 | 0.361 | 0.2922 |
6 | 364.3 | 2.502e+05 | 500.2 | 0.9096 | 0.403 | 0.3264 |
7 | 390.3 | 2.972e+05 | 545.1 | 0.8939 | 0.4444 | 0.3991 |
8 | 349.6 | 2.573e+05 | 507.2 | 0.9287 | 0.3504 | 0.2942 |
9 | 367.8 | 2.844e+05 | 533.3 | 0.9125 | 0.3432 | 0.2551 |
Mean | 364.1 | 2.889e+05 | 535.2 | 0.9068 | 0.392 | 0.3172 |
SD | 18.18 | 5.792e+04 | 49.53 | 0.0172 | 0.0411 | 0.0385 |
<catboost.core.CatBoostRegressor at 0x156e1aa43c8>
dt=create_model('et')
plot_model(estimator = dt, plot = 'learning')
from sklearn import metrics
from sklearn.metrics import pairwise_distances
def normalize_df(df):
#normalizing before VIF
min_max_scaler = preprocessing.MinMaxScaler()
df_scaled = min_max_scaler.fit_transform(df)
Scaled_df_used=pd.DataFrame(df_scaled,columns=df.columns.tolist(),index=df.index)
return df_scaled,Scaled_df_used
#VIF Treatment
from joblib import Parallel, delayed
# Defining the function that you will run later
import time
from joblib import Parallel, delayed
# Defining the function that you will run later
def calculate_vif_(X, thresh=5):
# for thresh in thresh:
# print('running for threshold= ',thresh)
variables = [X.columns[i] for i in range(X.shape[1])]
dropped=True
while dropped:
dropped=False
print(len(variables))
vif = Parallel(n_jobs=-1,verbose=5)(delayed(variance_inflation_factor)(X[variables].values, ix)
for ix in range(len(variables)))
maxloc = vif.index(max(vif))
if max(vif) > thresh:
print(time.ctime() + ' dropping \'' + X[variables].columns[maxloc] + '\' at index: ' + str(maxloc))
variables.pop(maxloc)
dropped=True
print('Remaining variables:')
print([variables])
#return X[[i for i in variables]]
return (variables)
import plotly.express as px
from sklearn.decomposition import PCA
def PCA_components(df):
"""
input to this function is scaled array of dataframe to be used
"""
pca = PCA()
pca.fit(df)
exp_var_cumul = np.cumsum(pca.explained_variance_ratio_)
return (px.area(
x=range(1, exp_var_cumul.shape[0] + 1),
y=exp_var_cumul,
labels={"x": "# Components", "y": "Explained Variance"}
))
#!pip install yellowbrick
from sklearn.cluster import KMeans
from scipy.spatial.distance import cdist
from yellowbrick.cluster import KElbowVisualizer
def elbow_kmeans(Cluster_data_used):
#within cluster sunm of squares=WCSS
WCSS = []
#distortions = []
for i in range(1,31):
kmeans = KMeans(n_clusters=i,init = 'k-means++',max_iter=500, n_init = 10, random_state = 0)
kmeans.fit(Cluster_data_used)
WCSS.append(kmeans.inertia_)
#using scipy
#distortions.append(sum(np.min(cdist(Cluster_data_used, kmeans.cluster_centers_, 'euclidean'), axis=1)) / Cluster_data_used.shape[0])
plt.plot(range(1,31),WCSS,marker='o', color='c')
plt.title('The Elbow Method showing the optimal k')
plt.xlabel('# of clusters')
plt.ylabel('WCSS')
plt.show()
# Elbow Method for K means
# Import ElbowVisualizer
model = KMeans()
# k is range of number of clusters.
visualizer = KElbowVisualizer(model, k=(2,30), timings= True)
visualizer.fit(Cluster_data_used) # Fit data to visualizer
visualizer.show()
return
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.cm as cm
from yellowbrick.cluster import KElbowVisualizer
def avg_silhouette(Cluster_data_used,range_n_clusters):
for n_clusters in range_n_clusters:
# Create a subplot with 1 row and 2 columns
# fig, ax1 = plt.subplots(1, 1)
# fig.set_size_inches(18, 7)
# The 1st subplot is the silhouette plot
# The silhouette coefficient can range from -1, 1 but in this example all
# lie within [-0.1, 1]
# ax1.set_xlim([-0.1, 1])
# # The (n_clusters+1)*10 is for inserting blank space between silhouette
# # plots of individual clusters, to demarcate them clearly.
# ax1.set_ylim([0, Cluster_data_used.shape[0] + (n_clusters + 1) * 10])
# Initialize the clusterer with n_clusters value and a random generator
# seed of 10 for reproducibility.
clusterer = KMeans(n_clusters=n_clusters, random_state=10)
cluster_labels = clusterer.fit_predict(Cluster_data_used)
# The silhouette_score gives the average value for all the samples.
# This gives a perspective into the density and separation of the formed
# clusters
silhouette_avg = silhouette_score(Cluster_data_used, cluster_labels)
print("For n_clusters =", n_clusters,
"The average silhouette_score is :", silhouette_avg)
plt.show()
# Silhouette Score for K means
# Import ElbowVisualizer
model = KMeans()
# k is range of number of clusters.
visualizer = KElbowVisualizer(model, k=(2,30),metric='silhouette', timings= True)
visualizer.fit(Cluster_data_used) # Fit the data to the visualizer
visualizer.show()
return
# !pip install gap-stat==2.0.1
# !pip install gapstat-rs
# !pip install gap-stat==2.0.1
# !pip install gapstat-rs
from gap_statistic import OptimalK
def gap_statistics(Cluster_data_used):
optimalK = OptimalK(parallel_backend='rust')
n_clusters = optimalK(Cluster_data_used, cluster_array=np.arange(1, 8))
print('Optimal clusters: ', n_clusters)
#print(optimalK.gap_df)
plt.plot(optimalK.gap_df.n_clusters, optimalK.gap_df.gap_value, linewidth=3)
plt.scatter(optimalK.gap_df[optimalK.gap_df.n_clusters == n_clusters].n_clusters,
optimalK.gap_df[optimalK.gap_df.n_clusters == n_clusters].gap_value, s=250, c='r')
plt.grid(True)
plt.xlabel('Cluster Count')
plt.ylabel('Gap Value')
plt.title('Gap Values by Cluster Count')
plt.show()
#function for dun index
#couldnot import jqmcvi so copying the relevant three functions to calculating dunn index
import numpy as np
from sklearn.metrics.pairwise import euclidean_distances
def delta(ck, cl):
values = np.ones([len(ck), len(cl)])*10000
for i in range(0, len(ck)):
for j in range(0, len(cl)):
values[i, j] = np.linalg.norm(ck[i]-cl[j])
return np.min(values)
def big_delta(ci):
values = np.zeros([len(ci), len(ci)])
for i in range(0, len(ci)):
for j in range(0, len(ci)):
values[i, j] = np.linalg.norm(ci[i]-ci[j])
return np.max(values)
def dunn(k_list):
""" Dunn index [CVI]
Parameters
----------
k_list : list of np.arrays
A list containing a numpy array for each cluster |c| = number of clusters
c[K] is np.array([N, p]) (N : number of samples in cluster K, p : sample dimension)
"""
deltas = np.ones([len(k_list), len(k_list)])*1000000
big_deltas = np.zeros([len(k_list), 1])
l_range = list(range(0, len(k_list)))
for k in l_range:
for l in (l_range[0:k]+l_range[k+1:]):
deltas[k, l] = delta(k_list[k], k_list[l])
big_deltas[k] = big_delta(k_list[k])
di = np.min(deltas)/np.max(big_deltas)
return di
def get_scores(data,data_with_labels,model,label_column,algorithm_name):
"""
data is array version of data fit into the model,model is clustering model,
label_colun is the column that has labels predicted, name of algorithm
"""
silhouette_score=metrics.silhouette_score(data, model.labels_, metric='euclidean')
calinski_harabasz_score=metrics.calinski_harabasz_score(data, model.labels_)
davies_bouldin_score=metrics.davies_bouldin_score(data, model.labels_)
te=data_with_labels.copy()
klist=[]
clus={}
for i in np.unique(te[label_column]):
clus[i]=te.loc[te[label_column]==i]
for (key,values) in clus.items():
klist.append(clus[key].values)
dun_val=dunn(klist)
metrics_=["silhouette_score","calinski_harabasz_score","davies_bouldin_score","dunn index"]
algorithms_=[algorithm_name]
score=pd.DataFrame([silhouette_score,calinski_harabasz_score,davies_bouldin_score,dun_val],columns=algorithms_,index=metrics_)
return score
from sklearn import metrics
from time import time
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
def K_means(Cluster_data_used,k):
X=np.array(Cluster_data_used)
#KMeans++ removes the drawback of K means which is it is dependent on initialization of centroid
kmodel=KMeans(init='k-means++', n_clusters=k, n_init=10,max_iter=500)
kmodel.fit(X)
clusters = kmodel.predict(Cluster_data_used)
Cluster_data_used_copy=Cluster_data_used.copy()
Cluster_data_used_copy["Cluster_Kmeans"]=clusters
score=get_scores(X,Cluster_data_used_copy,kmodel,"Cluster_Kmeans","K-means")
return score
import plotly as py
import plotly.graph_objs as go
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
def plot_k_means_2D(df,n_clusters):
Cluster_data_used=df
X=np.array(Cluster_data_used)
#KMeans++ removes the drawback of K means which is it is dependent on initialization of centroid
kmodel=KMeans(init='k-means++', n_clusters=n_clusters, n_init=10,max_iter=500)
kmodel.fit(X)
clusters = kmodel.predict(Cluster_data_used)
Cluster_data_used_copy=Cluster_data_used.copy()
Cluster_data_used_copy["Cluster_Kmeans"]=clusters
############################################################
#plotX is a DataFrame containing 5000 values sampled randomly from X
plotX = pd.DataFrame(np.array(Cluster_data_used_copy))
#Rename plotX's columns since it was briefly converted to an np.array above
plotX.columns = Cluster_data_used_copy.columns
#PCA with one principal component
pca_1d = PCA(n_components=1)
#PCA with two principal components
pca_2d = PCA(n_components=2)
#PCA with three principal components
pca_3d = PCA(n_components=3)
#This DataFrame holds that single principal component mentioned above
PCs_1d = pd.DataFrame(pca_1d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
#This DataFrame contains the two principal components that will be used
#for the 2-D visualization mentioned above
PCs_2d = pd.DataFrame(pca_2d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
#And this DataFrame contains three principal components that will aid us
#in visualizing our clusters in 3-D
PCs_3d = pd.DataFrame(pca_3d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
PCs_1d.columns = ["PC1_1d"]
#"PC1_2d" means: 'The first principal component of the components created for 2-D visualization, by PCA.'
#And "PC2_2d" means: 'The second principal component of the components created for 2-D visualization, by PCA.'
PCs_2d.columns = ["PC1_2d", "PC2_2d"]
PCs_3d.columns = ["PC1_3d", "PC2_3d", "PC3_3d"]
#We concatenate these newly created DataFrames to plotX so that they can be used by plotX as columns.
plotX = pd.concat([plotX,PCs_1d,PCs_2d,PCs_3d], axis=1, join='inner')
cluster0 = plotX[plotX["Cluster_Kmeans"] == 0]
cluster1 = plotX[plotX["Cluster_Kmeans"] == 1]
cluster2 = plotX[plotX["Cluster_Kmeans"] == 2]
cluster3 = plotX[plotX["Cluster_Kmeans"] == 3]
#cluster4 = plotX[plotX["Cluster_Kmeans"] == 4]
#####################################################################
trace1 = go.Scatter(
x = cluster0["PC1_2d"],
y = cluster0["PC2_2d"],
mode = "markers",
name = "Cluster 1",
marker = dict(color = 'rgba(255, 128, 255, 0.8)'),
text = None)
#trace2 is for 'Cluster 1'
trace2 = go.Scatter(
x = cluster1["PC1_2d"],
y = cluster1["PC2_2d"],
mode = "markers",
name = "Cluster 2",
marker = dict(color = 'rgba(255, 128, 2, 0.8)'),
text = None)
#trace3 is for 'Cluster 3'
trace3 = go.Scatter(
x = cluster2["PC1_2d"],
y = cluster2["PC2_2d"],
mode = "markers",
name = "Cluster 3",
marker = dict(color = 'rgba(0, 255, 200, 0.8)'),
text = None)
#trace4 is for 'Cluster 4'
trace4 = go.Scatter(
x = cluster3["PC1_2d"],
y = cluster3["PC2_2d"],
mode = "markers",
name = "Cluster 4",
marker = dict(color = 'rgba(255, 255, 100, 0.8)'),
text = None)
# #trace5 is for 'Cluster 5'
# trace5 = go.Scatter(
# x = cluster4["PC1_2d"],
# y = cluster4["PC2_2d"],
# mode = "markers",
# name = "Cluster 5",
# marker = dict(color = 'rgba(255, 255, 2, 0.8)'),
# text = None)
data = [trace1, trace2, trace3,trace4]#,trace5]
title = "Visualizing Clusters in Two Dimensions Using PCA"
layout = dict(title = title,
xaxis= dict(title= 'PC1',ticklen= 5,zeroline= False),
yaxis= dict(title= 'PC2',ticklen= 5,zeroline= False)
)
fig = dict(data = data, layout = layout)
iplot(fig)
import plotly as py
import plotly.graph_objs as go
from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot
def plot_k_means_3D(df,n_clusters):
Cluster_data_used=df
X=np.array(Cluster_data_used)
#KMeans++ removes the drawback of K means which is it is dependent on initialization of centroid
kmodel=KMeans(init='k-means++', n_clusters=n_clusters, n_init=10,max_iter=500)
kmodel.fit(X)
clusters = kmodel.predict(Cluster_data_used)
Cluster_data_used_copy=Cluster_data_used.copy()
Cluster_data_used_copy["Cluster_Kmeans"]=clusters
############################################################
#plotX is a DataFrame containing 5000 values sampled randomly from X
plotX = pd.DataFrame(np.array(Cluster_data_used_copy))
#Rename plotX's columns since it was briefly converted to an np.array above
plotX.columns = Cluster_data_used_copy.columns
#PCA with one principal component
pca_1d = PCA(n_components=1)
#PCA with two principal components
pca_2d = PCA(n_components=2)
#PCA with three principal components
pca_3d = PCA(n_components=3)
#This DataFrame holds that single principal component mentioned above
PCs_1d = pd.DataFrame(pca_1d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
#This DataFrame contains the two principal components that will be used
#for the 2-D visualization mentioned above
PCs_2d = pd.DataFrame(pca_2d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
#And this DataFrame contains three principal components that will aid us
#in visualizing our clusters in 3-D
PCs_3d = pd.DataFrame(pca_3d.fit_transform(plotX.drop(["Cluster_Kmeans"], axis=1)))
PCs_1d.columns = ["PC1_1d"]
#"PC1_2d" means: 'The first principal component of the components created for 2-D visualization, by PCA.'
#And "PC2_2d" means: 'The second principal component of the components created for 2-D visualization, by PCA.'
PCs_2d.columns = ["PC1_2d", "PC2_2d"]
PCs_3d.columns = ["PC1_3d", "PC2_3d", "PC3_3d"]
#We concatenate these newly created DataFrames to plotX so that they can be used by plotX as columns.
plotX = pd.concat([plotX,PCs_1d,PCs_2d,PCs_3d], axis=1, join='inner')
cluster0 = plotX[plotX["Cluster_Kmeans"] == 0]
cluster1 = plotX[plotX["Cluster_Kmeans"] == 1]
cluster2 = plotX[plotX["Cluster_Kmeans"] == 2]
cluster3 = plotX[plotX["Cluster_Kmeans"] == 3]
#cluster4 = plotX[plotX["Cluster_Kmeans"] == 4]
#####################################################################
trace1 = go.Scatter3d(
x = cluster0["PC1_3d"],
y = cluster0["PC2_3d"],
z = cluster0["PC3_3d"],
mode = "markers",
name = "Cluster 1",
marker = dict(color = 'rgba(255, 128, 255, 0.8)'),
text = None)
#trace2 is for 'Cluster 1'
trace2 = go.Scatter3d(
x = cluster1["PC1_3d"],
y = cluster1["PC2_3d"],
z = cluster1["PC3_3d"],
mode = "markers",
name = "Cluster 2",
marker = dict(color = 'rgba(255, 128, 2, 0.8)'),
text = None)
#trace3 is for 'Cluster 3'
trace3 = go.Scatter3d(
x = cluster2["PC1_3d"],
y = cluster2["PC2_3d"],
z = cluster2["PC3_3d"],
mode = "markers",
name = "Cluster 3",
marker = dict(color = 'rgba(0, 255, 200, 0.8)'),
text = None)
#trace4 is for 'Cluster 4'
trace4 = go.Scatter3d(
x = cluster3["PC1_3d"],
y = cluster3["PC2_3d"],
z = cluster3["PC3_3d"],
mode = "markers",
name = "Cluster 4",
marker = dict(color = 'rgba(255, 255, 100, 0.8)'),
text = None)
# #trace5 is for 'Cluster 5'
# trace5 = go.Scatter3d(
# x = cluster4["PC1_3d"],
# y = cluster4["PC2_3d"],
# z = cluster4["PC3_3d"],
# mode = "markers",
# name = "Cluster 5",
# marker = dict(color = 'rgba(255, 255, 2, 0.8)'),
# text = None)
data = [trace1, trace2, trace3,trace4]#,trace5]
title = "Visualizing Clusters in Three Dimensions Using PCA"
layout = dict(title = title,
xaxis= dict(title= 'PC1',ticklen= 5,zeroline= False),
yaxis= dict(title= 'PC2',ticklen= 5,zeroline= False)
)
fig = dict(data = data, layout = layout)
iplot(fig)