Importing Libraries and Exploration of Dataset¶
In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
# To scale the data using z-score
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
# Libraries for Decision Tree
from sklearn import tree
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import GridSearchCV
# Algorithms to use
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
# Metrics to evaluate the model
from sklearn import metrics
from sklearn.metrics import confusion_matrix, classification_report, precision_recall_curve,recall_score, roc_auc_score
from sklearn.preprocessing import label_binarize
from sklearn.metrics import ConfusionMatrixDisplay
from sklearn.pipeline import Pipeline
from sklearn.metrics import accuracy_score, classification_report
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
# Clustering libraries
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
# To ignore warnings
import warnings
warnings.filterwarnings("ignore")
#Monitor the time to run the notebook
import time
start_time = time.time()
Loading the dataset as a dataframe¶
In [2]:
# Loading the dataset in to a Pandas Dataframe
df = pd.read_csv('online_gaming_behavior_dataset.csv')
In [3]:
# printing a section of the dataframe to check everything has loaded in correctly
df.head()
Out[3]:
| PlayerID | Age | Gender | Location | GameGenre | PlayTimeHours | InGamePurchases | GameDifficulty | SessionsPerWeek | AvgSessionDurationMinutes | PlayerLevel | AchievementsUnlocked | EngagementLevel | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9000 | 43 | Male | Other | Strategy | 16.271119 | 0 | Medium | 6 | 108 | 79 | 25 | Medium |
| 1 | 9001 | 29 | Female | USA | Strategy | 5.525961 | 0 | Medium | 5 | 144 | 11 | 10 | Medium |
| 2 | 9002 | 22 | Female | USA | Sports | 8.223755 | 0 | Easy | 16 | 142 | 35 | 41 | High |
| 3 | 9003 | 35 | Male | USA | Action | 5.265351 | 1 | Easy | 9 | 85 | 57 | 47 | Medium |
| 4 | 9004 | 33 | Male | Europe | Action | 15.531945 | 0 | Medium | 2 | 131 | 95 | 37 | Medium |
Checking the dataframe to ensure there are no blanks and what datatypes Python is inferring¶
In [4]:
# display the information about the dataframe
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 40034 entries, 0 to 40033 Data columns (total 13 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 PlayerID 40034 non-null int64 1 Age 40034 non-null int64 2 Gender 40034 non-null object 3 Location 40034 non-null object 4 GameGenre 40034 non-null object 5 PlayTimeHours 40034 non-null float64 6 InGamePurchases 40034 non-null int64 7 GameDifficulty 40034 non-null object 8 SessionsPerWeek 40034 non-null int64 9 AvgSessionDurationMinutes 40034 non-null int64 10 PlayerLevel 40034 non-null int64 11 AchievementsUnlocked 40034 non-null int64 12 EngagementLevel 40034 non-null object dtypes: float64(1), int64(7), object(5) memory usage: 4.0+ MB
There are 40,034 rows and 13 columns of data in the dataset. All the columns are complete with no missing data so no pre-processing is required to handle blank values
We can also check to see how many unique values are present in each column of data
In [5]:
# Check for number of unique values each column has
df.nunique()
Out[5]:
PlayerID 40034 Age 35 Gender 2 Location 4 GameGenre 5 PlayTimeHours 40034 InGamePurchases 2 GameDifficulty 3 SessionsPerWeek 20 AvgSessionDurationMinutes 170 PlayerLevel 99 AchievementsUnlocked 50 EngagementLevel 3 dtype: int64
- PlayerId is a unique identifier and will not add any value to the analysis of the data so it can be dropped
- Based on the numbers of unique values present, we can clearly define continuous (numerical) and categorical columns.
We will now drop the PlayerID column and create lists for numerical and categorical data
In [6]:
# dropping the playerid column
df=df.drop(['PlayerID'],axis=1) # axis 1 for column
To assist in the exploration of the data, we will determine which columns contain categorical data, and those that contain numerical data only.
In [7]:
# Create list of Numerical Columns
numerical_cols = ['Age', 'PlayTimeHours', 'SessionsPerWeek', 'AvgSessionDurationMinutes',
'PlayerLevel', 'AchievementsUnlocked']
categorical_cols = ['Gender', 'Location', 'GameGenre', 'InGamePurchases', 'GameDifficulty', 'EngagementLevel']
In [8]:
# Create a summary table of the dataset
df[numerical_cols].describe().T
Out[8]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| Age | 40034.0 | 31.992531 | 10.043227 | 15.000000 | 23.000000 | 32.000000 | 41.000000 | 49.000000 |
| PlayTimeHours | 40034.0 | 12.024365 | 6.914638 | 0.000115 | 6.067501 | 12.008002 | 17.963831 | 23.999592 |
| SessionsPerWeek | 40034.0 | 9.471774 | 5.763667 | 0.000000 | 4.000000 | 9.000000 | 14.000000 | 19.000000 |
| AvgSessionDurationMinutes | 40034.0 | 94.792252 | 49.011375 | 10.000000 | 52.000000 | 95.000000 | 137.000000 | 179.000000 |
| PlayerLevel | 40034.0 | 49.655568 | 28.588379 | 1.000000 | 25.000000 | 49.000000 | 74.000000 | 99.000000 |
| AchievementsUnlocked | 40034.0 | 24.526477 | 14.430726 | 0.000000 | 12.000000 | 25.000000 | 37.000000 | 49.000000 |
Observations from Univariate Analysis of Numerical Fields
- Average Age is around 32 years old. There is a large range in ages, from 15 to 49 which indicates a good diversity across the players
- The average time a player spends per week is around 12 hours. There is a very large range, with the lowest average per week being just 0.000115 hours and the highest being just under 24 hours
- Average minutes spent per session is almost 95 minutes, with the highest being 179 and the lowest being just 10 minutes.
- Player level and achievements unlocked have wide ranges. Lowest level is 1 and highest is 99 while lowest number of achievements unlocked is 0 and the highest is 49. This could demonstrate a wide demographic of player abilities.
We can explore further by plotting historgrams to display their distribution
In [9]:
# Create Histograms
df[numerical_cols].hist(figsize=(6,6))
plt.show
Out[9]:
<function matplotlib.pyplot.show(close=None, block=None)>
Observation: While the values look fairly evenly distributed, as the dataset is made up of over 40,000 rows of data, random noise could be smoothing them out.
It could also be that the dataset has been synthetically engineered or intentionally evenly sampled, leading to them appearing to be uniformly distributed
Univariate analysis for the categorical variables¶
In [10]:
# Display the % sub categories of each category
for i in categorical_cols:
print(df[i].value_counts (normalize=True))
print('*'*40)
Gender Male 0.598466 Female 0.401534 Name: proportion, dtype: float64 **************************************** Location USA 0.399660 Europe 0.299845 Asia 0.202203 Other 0.098291 Name: proportion, dtype: float64 **************************************** GameGenre Sports 0.201029 Action 0.200804 Strategy 0.200130 Simulation 0.199406 RPG 0.198631 Name: proportion, dtype: float64 **************************************** InGamePurchases 0 0.799146 1 0.200854 Name: proportion, dtype: float64 **************************************** GameDifficulty Easy 0.49995 Medium 0.30002 Hard 0.20003 Name: proportion, dtype: float64 **************************************** EngagementLevel Medium 0.483939 High 0.258181 Low 0.257881 Name: proportion, dtype: float64 ****************************************
Observation:
- The gender makeup of the players is slightly more skewed towards male players, at around 59% being male compared to 41% being female
- Most players are based in the USA (almost 40%) which could make regionality a contributing factor to outcomes.
- The types of game (genre) that people play appears to be fairly evenly split, with all 5 categories being almost evenly split at around 20% each
- Almost 80% of players do not make in-game purchases, which could either be indicative of the type of game they play, or them actively making a choice to play the games a certain way
- The majority of the players reported (almost 50%) play the games on an easy level, this could be either that they have less gaming experience, or prefer to play more casually.
- Engagement levels for players are mostly categorised at medium, with 49% of players sampled falling in to this category
Bivariate/Multivariate Analysis¶
As we are most interested in the engagement level of players, we can see how this is related to other categorical and numerical variables in the data.
First we will look at the categorical variables:
In [11]:
for i in categorical_cols:
if i!='EngagementLevel':
(pd.crosstab(df[i],df['EngagementLevel'],normalize='index')*100).plot(kind='bar',figsize=(6,3),stacked=False)
plt.ylabel('Percentage Engagement %')
Observation
The distribution of engagement level is evenly split across all the categories, meaning there is no relationship between engagement level and these categories.
Next, we will check the relationships between engagement level and the numerical variables
In [12]:
# Average of numerical variables by engagement level
df.groupby(['EngagementLevel'])[numerical_cols].mean()
Out[12]:
| Age | PlayTimeHours | SessionsPerWeek | AvgSessionDurationMinutes | PlayerLevel | AchievementsUnlocked | |
|---|---|---|---|---|---|---|
| EngagementLevel | ||||||
| High | 31.920085 | 12.069238 | 14.254547 | 131.921827 | 50.823723 | 25.095975 |
| Low | 31.896939 | 12.104915 | 4.530511 | 66.882119 | 46.101414 | 22.661565 |
| Medium | 32.082120 | 11.957503 | 9.553267 | 89.856405 | 50.926293 | 25.216424 |
Observation:
- Unsurprisingly, engagement levels are highest in those players with the highest average sessions per week and average session duration.
- Age, Play Time, Player Level and Achievements unlocked are fairly evenly spread across the three engagement levels.
So we ask, is there a relationship between the different numerical variables
In [13]:
# Plot any correlation between numerical values
plt.figure(figsize=(6,6))
sns.heatmap(df[numerical_cols].corr(), annot=True, fmt='0.2f', cmap='YlOrRd')
Out[13]:
<Axes: >
As with some of our other analysis, the lack of correlation between the categories such as age and player level, or Sessions Per Week and Achievements Unlocked show there are no meaningful linear corrleations in the data, and this could be due to the fact that this is simulated data, rather than real-world data.
Data Preparation for Support Machine Vector (SVM) Modelling¶
In [14]:
# Creating categorical variables
get_categories = ['Gender', 'Location', 'GameGenre', 'GameDifficulty']
# Creating variables
df = pd.get_dummies(data = df, columns = get_categories, drop_first = True)
# Mapping engagement
dict_engagement = {'Low': 0, 'Medium': 1, 'High': 2}
df['EngagementLevel'] = df.EngagementLevel.map(dict_engagement)
In [15]:
df.head()
Out[15]:
| Age | PlayTimeHours | InGamePurchases | SessionsPerWeek | AvgSessionDurationMinutes | PlayerLevel | AchievementsUnlocked | EngagementLevel | Gender_Male | Location_Europe | Location_Other | Location_USA | GameGenre_RPG | GameGenre_Simulation | GameGenre_Sports | GameGenre_Strategy | GameDifficulty_Hard | GameDifficulty_Medium | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 43 | 16.271119 | 0 | 6 | 108 | 79 | 25 | 1 | True | False | True | False | False | False | False | True | False | True |
| 1 | 29 | 5.525961 | 0 | 5 | 144 | 11 | 10 | 1 | False | False | False | True | False | False | False | True | False | True |
| 2 | 22 | 8.223755 | 0 | 16 | 142 | 35 | 41 | 2 | False | False | False | True | False | False | True | False | False | False |
| 3 | 35 | 5.265351 | 1 | 9 | 85 | 57 | 47 | 1 | True | False | False | True | False | False | False | False | False | False |
| 4 | 33 | 15.531945 | 0 | 2 | 131 | 95 | 37 | 1 | True | True | False | False | False | False | False | False | False | True |
Model Data Preparation¶
To implement this data in to the SVM Model, we first need to create the training and test data which can be used in the model.
In [16]:
Y= df.EngagementLevel
X= df.drop(columns = ['EngagementLevel'])
In [17]:
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size = 0.3, random_state = 1, stratify = Y)
In [18]:
# Scaling the data
sc=StandardScaler()
# Fit_transform on train data
X_train_scaled=sc.fit_transform(X_train)
X_train_scaled=pd.DataFrame(X_train_scaled, columns=X.columns)
# Transform on test data
X_test_scaled=sc.transform(X_test)
X_test_scaled=pd.DataFrame(X_test_scaled, columns=X.columns)
In [19]:
# Create a metric function
def metrics_score(actual, predicted):
print(classification_report(actual, predicted))
cm = confusion_matrix(actual, predicted)
plt.figure(figsize=(8,5))
sns.heatmap(cm, annot=True, fmt='.2f', xticklabels=['Low', 'Medium', 'High'],
yticklabels=['Low', 'Medium', 'High'])
plt.ylabel('Actual')
plt.xlabel('Predicted')
plt.show()
Linear Kernel¶
In [20]:
# Fitting SVM
svm = SVC(kernel='linear') # Linear kernal or linear decision boundary
model = svm.fit(X= X_train_scaled, y = y_train)
In [21]:
y_pred_train_svm = model.predict(X_train_scaled)
metrics_score(y_train, y_pred_train_svm)
precision recall f1-score support
0 0.79 0.71 0.75 7227
1 0.81 0.87 0.84 13561
2 0.89 0.85 0.87 7235
accuracy 0.82 28023
macro avg 0.83 0.81 0.82 28023
weighted avg 0.83 0.82 0.82 28023
In [22]:
# Checking performance on the test data
y_pred_test_svm = model.predict(X_test_scaled)
metrics_score(y_test, y_pred_test_svm)
precision recall f1-score support
0 0.79 0.71 0.75 3097
1 0.81 0.87 0.84 5813
2 0.89 0.85 0.87 3101
accuracy 0.82 12011
macro avg 0.83 0.81 0.82 12011
weighted avg 0.82 0.82 0.82 12011
Outcome¶
This model performs fairly well, with a weighted average Precision, Recall and F1 of 82%, but we can apply some hyperperameter tuning to it to improve the outcome.
First we create a pipeline to ensure the same preprocessing is applied consistently during training and testing, and that there is no data leakage during cross-validation.
In [23]:
pipeline = Pipeline([
('scaler', StandardScaler()),
('svm', SVC(probability=True))
])
Next we define the hyperparameter combinations we will use
In [24]:
param_grid = [
{
'svm__kernel': ['linear'],
'svm__C': [0.1, 1]
},
{
'svm__kernel': ['rbf'],
'svm__C': [1, 10],
'svm__gamma': [0.01, 0.1]
}
]
This will call the hyperparameter tuning, training the data on 4 folds and then testing against 1, it will then choose the model which performs best
In [25]:
grid = GridSearchCV(
estimator=pipeline,
param_grid=param_grid,
cv=5,
scoring='accuracy',
n_jobs= 12
)
grid.fit(X_train, y_train)
Out[25]:
GridSearchCV(cv=5,
estimator=Pipeline(steps=[('scaler', StandardScaler()),
('svm', SVC(probability=True))]),
n_jobs=12,
param_grid=[{'svm__C': [0.1, 1], 'svm__kernel': ['linear']},
{'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1],
'svm__kernel': ['rbf']}],
scoring='accuracy')In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
Parameters
| estimator | Pipeline(step...ility=True))]) | |
| param_grid | [{'svm__C': [0.1, 1], 'svm__kernel': ['linear']}, {'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1], 'svm__kernel': ['rbf']}] | |
| scoring | 'accuracy' | |
| n_jobs | 12 | |
| refit | True | |
| cv | 5 | |
| verbose | 0 | |
| pre_dispatch | '2*n_jobs' | |
| error_score | nan | |
| return_train_score | False |
Parameters
| copy | True | |
| with_mean | True | |
| with_std | True |
Parameters
| C | 10 | |
| kernel | 'rbf' | |
| degree | 3 | |
| gamma | 0.01 | |
| coef0 | 0.0 | |
| shrinking | True | |
| probability | True | |
| tol | 0.001 | |
| cache_size | 200 | |
| class_weight | None | |
| verbose | False | |
| max_iter | -1 | |
| decision_function_shape | 'ovr' | |
| break_ties | False | |
| random_state | None |
In [26]:
print("Best parameters:", grid.best_params_)
print("Best CV accuracy:", grid.best_score_)
Best parameters: {'svm__C': 10, 'svm__gamma': 0.01, 'svm__kernel': 'rbf'}
Best CV accuracy: 0.888591874925582
In [27]:
y_pred = grid.best_estimator_.predict(X_test)
print("Test accuracy:", accuracy_score(y_test, y_pred))
print("Classification report:\n")
print(classification_report(
y_test,
y_pred,
target_names=['Low', 'Medium', 'High']
))
Test accuracy: 0.8894346848722005
Classification report:
precision recall f1-score support
Low 0.89 0.82 0.86 3097
Medium 0.87 0.94 0.90 5813
High 0.92 0.86 0.89 3101
accuracy 0.89 12011
macro avg 0.90 0.88 0.88 12011
weighted avg 0.89 0.89 0.89 12011
In [28]:
grid = GridSearchCV(
estimator=pipeline,
param_grid=param_grid,
cv=5,
scoring='f1_macro',
n_jobs= 12
)
grid.fit(X_train, y_train)
Out[28]:
GridSearchCV(cv=5,
estimator=Pipeline(steps=[('scaler', StandardScaler()),
('svm', SVC(probability=True))]),
n_jobs=12,
param_grid=[{'svm__C': [0.1, 1], 'svm__kernel': ['linear']},
{'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1],
'svm__kernel': ['rbf']}],
scoring='f1_macro')In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
Parameters
| estimator | Pipeline(step...ility=True))]) | |
| param_grid | [{'svm__C': [0.1, 1], 'svm__kernel': ['linear']}, {'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1], 'svm__kernel': ['rbf']}] | |
| scoring | 'f1_macro' | |
| n_jobs | 12 | |
| refit | True | |
| cv | 5 | |
| verbose | 0 | |
| pre_dispatch | '2*n_jobs' | |
| error_score | nan | |
| return_train_score | False |
Parameters
| copy | True | |
| with_mean | True | |
| with_std | True |
Parameters
| C | 10 | |
| kernel | 'rbf' | |
| degree | 3 | |
| gamma | 0.01 | |
| coef0 | 0.0 | |
| shrinking | True | |
| probability | True | |
| tol | 0.001 | |
| cache_size | 200 | |
| class_weight | None | |
| verbose | False | |
| max_iter | -1 | |
| decision_function_shape | 'ovr' | |
| break_ties | False | |
| random_state | None |
In [29]:
print("Best parameters:", grid.best_params_)
print("Best CV f1:", grid.best_score_)
Best parameters: {'svm__C': 10, 'svm__gamma': 0.01, 'svm__kernel': 'rbf'}
Best CV f1: 0.8833893422011521
In [30]:
y_pred = grid.best_estimator_.predict(X_test)
print("Test accuracy:", accuracy_score(y_test, y_pred))
print("Classification report:\n")
print(classification_report(
y_test,
y_pred,
target_names=['Low', 'Medium', 'High']
))
Test accuracy: 0.8894346848722005
Classification report:
precision recall f1-score support
Low 0.89 0.82 0.86 3097
Medium 0.87 0.94 0.90 5813
High 0.92 0.86 0.89 3101
accuracy 0.89 12011
macro avg 0.90 0.88 0.88 12011
weighted avg 0.89 0.89 0.89 12011
In [31]:
grid = GridSearchCV(
estimator=pipeline,
param_grid=param_grid,
cv=5,
scoring='roc_auc_ovr',
n_jobs= 12
)
grid.fit(X_train, y_train)
Out[31]:
GridSearchCV(cv=5,
estimator=Pipeline(steps=[('scaler', StandardScaler()),
('svm', SVC(probability=True))]),
n_jobs=12,
param_grid=[{'svm__C': [0.1, 1], 'svm__kernel': ['linear']},
{'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1],
'svm__kernel': ['rbf']}],
scoring='roc_auc_ovr')In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
Parameters
| estimator | Pipeline(step...ility=True))]) | |
| param_grid | [{'svm__C': [0.1, 1], 'svm__kernel': ['linear']}, {'svm__C': [1, 10], 'svm__gamma': [0.01, 0.1], 'svm__kernel': ['rbf']}] | |
| scoring | 'roc_auc_ovr' | |
| n_jobs | 12 | |
| refit | True | |
| cv | 5 | |
| verbose | 0 | |
| pre_dispatch | '2*n_jobs' | |
| error_score | nan | |
| return_train_score | False |
Parameters
| copy | True | |
| with_mean | True | |
| with_std | True |
Parameters
| C | 10 | |
| kernel | 'rbf' | |
| degree | 3 | |
| gamma | 0.01 | |
| coef0 | 0.0 | |
| shrinking | True | |
| probability | True | |
| tol | 0.001 | |
| cache_size | 200 | |
| class_weight | None | |
| verbose | False | |
| max_iter | -1 | |
| decision_function_shape | 'ovr' | |
| break_ties | False | |
| random_state | None |
In [32]:
print("Best parameters:", grid.best_params_)
print("Best CV roc_auc:", grid.best_score_)
Best parameters: {'svm__C': 10, 'svm__gamma': 0.01, 'svm__kernel': 'rbf'}
Best CV roc_auc: 0.9412735457066288
In [33]:
y_pred = grid.best_estimator_.predict(X_test)
print("Test accuracy:", accuracy_score(y_test, y_pred))
print("Classification report:\n")
print(classification_report(
y_test,
y_pred,
target_names=['Low', 'Medium', 'High']
))
Test accuracy: 0.8894346848722005
Classification report:
precision recall f1-score support
Low 0.89 0.82 0.86 3097
Medium 0.87 0.94 0.90 5813
High 0.92 0.86 0.89 3101
accuracy 0.89 12011
macro avg 0.90 0.88 0.88 12011
weighted avg 0.89 0.89 0.89 12011
After tuning based on Accuracy, F1 and ROC_AUC, we have consistently achieved an average Precision, Recall and F1 score of 89%.
Data Modelling for Decision Tree¶
In [34]:
dTree = DecisionTreeClassifier()
In [35]:
dTree = dTree.fit(X, Y)
In [36]:
plt.figure(figsize=(10,8))
tree.plot_tree(dTree, feature_names=X.columns,
class_names=['Low', 'Medium', 'High'],
filled=True,
rounded=True)
Out[36]:
[Text(0.31205567222973857, 0.9852941176470589, 'SessionsPerWeek <= 2.5\ngini = 0.633\nsamples = 40034\nvalue = [10324, 19374, 10336]\nclass = Medium'), Text(0.08971977599821036, 0.9558823529411765, 'SessionsPerWeek <= 1.5\ngini = 0.272\nsamples = 5965\nvalue = [5034.0, 728.0, 203.0]\nclass = Low'), Text(0.20088772411397446, 0.9705882352941178, 'True '), Text(0.058275150061856414, 0.9264705882352942, 'AchievementsUnlocked <= 47.5\ngini = 0.142\nsamples = 3947\nvalue = [3649, 166, 132]\nclass = Low'), Text(0.039564889429159394, 0.8970588235294118, 'PlayerLevel <= 78.5\ngini = 0.134\nsamples = 3782\nvalue = [3514, 144, 124]\nclass = Low'), Text(0.01265555436558141, 0.8676470588235294, 'PlayTimeHours <= 0.041\ngini = 0.118\nsamples = 3021\nvalue = [2834, 90, 97]\nclass = Low'), Text(0.003580865749563602, 0.8382352941176471, 'Location_Europe <= 0.5\ngini = 0.5\nsamples = 2\nvalue = [1, 0, 1]\nclass = Low'), Text(0.0033758788014669376, 0.8088235294117647, 'gini = 0.0\nsamples = 1\nvalue = 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<= 27.5\ngini = 0.375\nsamples = 4\nvalue = [3, 0, 1]\nclass = Low'), Text(0.08348093461236648, 0.45588235294117646, 'gini = 0.0\nsamples = 3\nvalue = [3, 0, 0]\nclass = Low'), Text(0.0838909085085598, 0.45588235294117646, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.0838909085085598, 0.5147058823529411, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]\nclass = Medium'), Text(0.08409589545665647, 0.5441176470588235, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]\nclass = Medium'), Text(0.0845058693528498, 0.6029411764705882, 'PlayerLevel <= 9.5\ngini = 0.357\nsamples = 14\nvalue = [11, 2, 1]\nclass = Low'), Text(0.08430088240475314, 0.5735294117647058, 'gini = 0.0\nsamples = 2\nvalue = [0, 2, 0]\nclass = Medium'), Text(0.08471085630094646, 0.5735294117647058, 'AchievementsUnlocked <= 4.5\ngini = 0.153\nsamples = 12\nvalue = [11, 0, 1]\nclass = Low'), Text(0.0845058693528498, 0.5441176470588235, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.08491584324904312, 0.5441176470588235, 'gini = 0.0\nsamples = 11\nvalue = [11, 0, 0]\nclass = Low'), Text(0.08635075188571978, 0.6911764705882353, 'AvgSessionDurationMinutes <= 31.5\ngini = 0.338\nsamples = 48\nvalue = [38, 1, 9]\nclass = Low'), Text(0.08614576493762312, 0.6617647058823529, 'gini = 0.0\nsamples = 3\nvalue = [0, 0, 3]\nclass = High'), Text(0.08655573883381644, 0.6617647058823529, 'Age <= 38.5\ngini = 0.269\nsamples = 45\nvalue = [38, 1, 6]\nclass = Low'), Text(0.08635075188571978, 0.6323529411764706, 'AvgSessionDurationMinutes <= 46.5\ngini = 0.38\nsamples = 29\nvalue = [22, 1, 6]\nclass = Low'), Text(0.08594077798952644, 0.6029411764705882, 'Location_Other <= 0.5\ngini = 0.302\nsamples = 27\nvalue = [22, 0, 5]\nclass = Low'), Text(0.08573579104142978, 0.5735294117647058, 'PlayTimeHours <= 15.605\ngini = 0.26\nsamples = 26\nvalue = [22, 0, 4]\nclass = Low'), Text(0.08532581714523646, 0.5441176470588235, 'PlayerLevel <= 46.5\ngini = 0.111\nsamples = 17\nvalue = [16, 0, 1]\nclass = Low'), Text(0.08512083019713979, 0.5147058823529411, 'Age <= 18.5\ngini = 0.5\nsamples = 2\nvalue = [1, 0, 1]\nclass = Low'), Text(0.08491584324904312, 0.4852941176470588, 'gini = 0.0\nsamples = 1\nvalue = [1, 0, 0]\nclass = Low'), Text(0.08532581714523646, 0.4852941176470588, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.08553080409333312, 0.5147058823529411, 'gini = 0.0\nsamples = 15\nvalue = [15, 0, 0]\nclass = Low'), Text(0.08614576493762312, 0.5441176470588235, 'PlayTimeHours <= 19.725\ngini = 0.444\nsamples = 9\nvalue = [6, 0, 3]\nclass = Low'), Text(0.08594077798952644, 0.5147058823529411, 'AvgSessionDurationMinutes <= 45.5\ngini = 0.375\nsamples = 4\nvalue = [1, 0, 3]\nclass = High'), Text(0.08573579104142978, 0.4852941176470588, 'gini = 0.0\nsamples = 3\nvalue = [0, 0, 3]\nclass = High'), Text(0.08614576493762312, 0.4852941176470588, 'gini = 0.0\nsamples = 1\nvalue = [1, 0, 0]\nclass = Low'), Text(0.08635075188571978, 0.5147058823529411, 'gini = 0.0\nsamples = 5\nvalue = [5, 0, 0]\nclass = Low'), Text(0.08614576493762312, 0.5735294117647058, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.0867607257819131, 0.6029411764705882, 'GameDifficulty_Hard <= 0.5\ngini = 0.5\nsamples = 2\nvalue = [0, 1, 1]\nclass = Medium'), Text(0.08655573883381644, 0.5735294117647058, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]\nclass = Medium'), Text(0.08696571273000978, 0.5735294117647058, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.0867607257819131, 0.6323529411764706, 'gini = 0.0\nsamples = 16\nvalue = [16, 0, 0]\nclass = Low'), Text(0.09291674006694105, 0.75, 'Location_Other <= 0.5\ngini = 0.086\nsamples = 428\nvalue = [409, 9, 10]\nclass = Low'), Text(0.09097576990215075, 0.7205882352941176, 'PlayTimeHours <= 19.235\ngini = 0.071\nsamples = 385\nvalue = [371, 9, 5]\nclass = Low'), Text(0.08965616642377848, 0.6911764705882353, 'Gender_Male <= 0.5\ngini = 0.051\nsamples = 306\nvalue = [298, 4, 4]\nclass = Low'), Text(0.0888618419999039, 0.6617647058823529, 'AvgSessionDurationMinutes <= 93.5\ngini = 0.088\nsamples = 131\nvalue = [125, 4, 2]\nclass = Low'), Text(0.08865685505180725, 0.6323529411764706, 'AvgSessionDurationMinutes <= 91.5\ngini = 0.136\nsamples = 83\nvalue = [77, 4, 2]\nclass = Low'), Text(0.08788815399644476, 0.6029411764705882, 'InGamePurchases <= 0.5\ngini = 0.106\nsamples = 72\nvalue = [68, 2, 2]\nclass = Low'), Text(0.0873756866262031, 0.5735294117647058, 'GameGenre_Strategy <= 0.5\ngini = 0.063\nsamples = 62\nvalue = [60, 1, 1]\nclass = Low'), Text(0.08696571273000978, 0.5441176470588235, 'GameGenre_Sports <= 0.5\ngini = 0.035\nsamples = 56\nvalue = [55, 0, 1]\nclass = Low'), Text(0.0867607257819131, 0.5147058823529411, 'gini = 0.0\nsamples = 46\nvalue = [46, 0, 0]\nclass = Low'), Text(0.08717069967810644, 0.5147058823529411, 'AchievementsUnlocked <= 8.5\ngini = 0.18\nsamples = 10\nvalue = [9, 0, 1]\nclass = Low'), Text(0.08696571273000978, 0.4852941176470588, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.0873756866262031, 0.4852941176470588, 'gini = 0.0\nsamples = 9\nvalue = [9, 0, 0]\nclass = Low'), Text(0.08778566052239642, 0.5441176470588235, 'Location_Europe <= 0.5\ngini = 0.278\nsamples = 6\nvalue = [5, 1, 0]\nclass = Low'), Text(0.08758067357429976, 0.5147058823529411, 'gini = 0.0\nsamples = 5\nvalue = [5, 0, 0]\nclass = Low'), Text(0.0879906474704931, 0.5147058823529411, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]\nclass = Medium'), Text(0.08840062136668642, 0.5735294117647058, 'PlayerLevel <= 17.5\ngini = 0.34\nsamples = 10\nvalue = [8, 1, 1]\nclass = Low'), Text(0.08819563441858976, 0.5441176470588235, 'gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]\nclass = High'), Text(0.08860560831478308, 0.5441176470588235, 'AchievementsUnlocked <= 32.0\ngini = 0.198\nsamples = 9\nvalue = [8, 1, 0]\nclass = Low'), Text(0.08840062136668642, 0.5147058823529411, 'gini = 0.0\nsamples = 8\nvalue = [8, 0, 0]\nclass = Low'), Text(0.08881059526287975, 0.5147058823529411, 'gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]\nclass = Medium'), Text(0.08942555610716973, 0.6029411764705882, 'AchievementsUnlocked <= 7.5\ngini = 0.298\nsamples = 11\nvalue = [9, 2, 0]\nclass = Low'), Text(0.08922056915907307, 0.5735294117647058, 'InGamePurchases <= 0.5\ngini = 0.444\nsamples = 3\nvalue = [1, 2, 0]\nclass = Medium'), Text(0.08901558221097641, 0.5441176470588235, 'gini = 0.0\nsamples = 2\nvalue = [0, 2, 0]\nclass = Medium'), Text(0.08942555610716973, 0.5441176470588235, 'gini = 0.0\nsamples = 1\nvalue = [1, 0, 0]\nclass = Low'), Text(0.08963054305526641, 0.5735294117647058, 'gini = 0.0\nsamples = 8\nvalue = [8, 0, 0]\nclass = Low'), Text(0.08906682894800058, 0.6323529411764706, 'gini = 0.0\nsamples = 48\nvalue = [48, 0, 0]\nclass = Low'), Text(0.09045049084765305, 0.6617647058823529, 'AvgSessionDurationMinutes <= 115.5\ngini = 0.023\nsamples = 175\nvalue = [173, 0, 2]\nclass = Low'), Text(0.09004051695145973, 0.6323529411764706, 'GameGenre_Simulation <= 0.5\ngini = 0.012\nsamples = 164\nvalue = [163, 0, 1]\nclass = Low'), Text(0.08983553000336307, 0.6029411764705882, 'gini = 0.0\nsamples = 136\nvalue = [136, 0, 0]\nclass = Low'), Text(0.09024550389955639, 0.6029411764705882, 'Age <= 21.5\ngini = 0.069\nsamples = 28\nvalue = [27, 0, 1]\nclass = Low'), Text(0.09004051695145973, 0.5735294117647058, 'Age <= 20.0\ngini = 0.32\nsamples = 5\nvalue = [4, 0, 1]\nclass = Low'), Text(0.08983553000336307, 0.5441176470588235, 'gini = 0.0\nsamples = 4\nvalue = [4, 0, 0]\nclass = Low'), ...]
In [37]:
print("Train accuracy:", accuracy_score(y_train, dTree.predict(X_train)))
print("Test accuracy:", accuracy_score(y_test, dTree.predict(X_test)))
Train accuracy: 1.0 Test accuracy: 1.0
As we see, this unrestricted tree classifier has made the model overfit too much, and there are too many leaves and branches with very small samples.
If we add some regularisation parameters, this will stop the tree getting too tall, prevent tiny groups, ensure meaningful leaf sizes and will make it reproduceable
In [38]:
dTree = DecisionTreeClassifier(
max_depth=4,
min_samples_leaf=10,
random_state=42
)
In [39]:
dTree = dTree.fit(X, Y)
In [40]:
plt.figure(figsize=(24,12))
tree.plot_tree(dTree, feature_names=X.columns,
class_names=['Low', 'Medium', 'High'],
filled=True,
rounded=True)
Out[40]:
[Text(0.5, 0.9, 'SessionsPerWeek <= 2.5\ngini = 0.633\nsamples = 40034\nvalue = [10324, 19374, 10336]\nclass = Medium'), Text(0.25, 0.7, 'SessionsPerWeek <= 1.5\ngini = 0.272\nsamples = 5965\nvalue = [5034.0, 728.0, 203.0]\nclass = Low'), Text(0.375, 0.8, 'True '), Text(0.125, 0.5, 'AchievementsUnlocked <= 47.5\ngini = 0.142\nsamples = 3947\nvalue = [3649, 166, 132]\nclass = Low'), Text(0.0625, 0.3, 'PlayerLevel <= 78.5\ngini = 0.134\nsamples = 3782\nvalue = [3514, 144, 124]\nclass = Low'), Text(0.03125, 0.1, 'gini = 0.118\nsamples = 3021\nvalue = [2834, 90, 97]\nclass = Low'), Text(0.09375, 0.1, 'gini = 0.195\nsamples = 761\nvalue = [680, 54, 27]\nclass = Low'), Text(0.1875, 0.3, 'PlayerLevel <= 75.0\ngini = 0.31\nsamples = 165\nvalue = [135, 22, 8]\nclass = Low'), Text(0.15625, 0.1, 'gini = 0.209\nsamples = 131\nvalue = [116, 10, 5]\nclass = Low'), Text(0.21875, 0.1, 'gini = 0.555\nsamples = 34\nvalue = [19, 12, 3]\nclass = Low'), Text(0.375, 0.5, 'AvgSessionDurationMinutes <= 150.5\ngini = 0.45\nsamples = 2018\nvalue = [1385, 562, 71]\nclass = Low'), Text(0.3125, 0.3, 'AvgSessionDurationMinutes <= 118.5\ngini = 0.338\nsamples = 1653\nvalue = [1314, 281, 58]\nclass = Low'), Text(0.28125, 0.1, 'gini = 0.242\nsamples = 1259\nvalue = [1088, 127, 44]\nclass = Low'), Text(0.34375, 0.1, 'gini = 0.517\nsamples = 394\nvalue = [226.0, 154.0, 14.0]\nclass = Low'), Text(0.4375, 0.3, 'AchievementsUnlocked <= 5.5\ngini = 0.368\nsamples = 365\nvalue = [71, 281, 13]\nclass = Medium'), Text(0.40625, 0.1, 'gini = 0.405\nsamples = 41\nvalue = [30, 10, 1]\nclass = Low'), Text(0.46875, 0.1, 'gini = 0.283\nsamples = 324\nvalue = [41, 271, 12]\nclass = Medium'), Text(0.75, 0.7, 'AvgSessionDurationMinutes <= 93.5\ngini = 0.588\nsamples = 34069\nvalue = [5290, 18646, 10133]\nclass = Medium'), Text(0.625, 0.8, ' False'), Text(0.625, 0.5, 'AvgSessionDurationMinutes <= 25.5\ngini = 0.497\nsamples = 16747\nvalue = [4694, 10850, 1203]\nclass = Medium'), Text(0.5625, 0.3, 'SessionsPerWeek <= 13.5\ngini = 0.431\nsamples = 3155\nvalue = [2229, 825, 101]\nclass = Low'), Text(0.53125, 0.1, 'gini = 0.263\nsamples = 2047\nvalue = [1739, 246, 62]\nclass = Low'), Text(0.59375, 0.1, 'gini = 0.53\nsamples = 1108\nvalue = [490, 579, 39]\nclass = Medium'), Text(0.6875, 0.3, 'SessionsPerWeek <= 5.5\ngini = 0.417\nsamples = 13592\nvalue = [2465, 10025, 1102]\nclass = Medium'), Text(0.65625, 0.1, 'gini = 0.501\nsamples = 2505\nvalue = [1514, 914, 77]\nclass = Low'), Text(0.71875, 0.1, 'gini = 0.309\nsamples = 11087\nvalue = [951, 9111, 1025]\nclass = Medium'), Text(0.875, 0.5, 'SessionsPerWeek <= 9.5\ngini = 0.53\nsamples = 17322\nvalue = [596.0, 7796.0, 8930.0]\nclass = High'), Text(0.8125, 0.3, 'SessionsPerWeek <= 8.5\ngini = 0.225\nsamples = 7212\nvalue = [283, 6312, 617]\nclass = Medium'), Text(0.78125, 0.1, 'gini = 0.165\nsamples = 6211\nvalue = [249, 5662, 300]\nclass = Medium'), Text(0.84375, 0.1, 'gini = 0.477\nsamples = 1001\nvalue = [34, 650, 317]\nclass = Medium'), Text(0.9375, 0.3, 'SessionsPerWeek <= 12.5\ngini = 0.301\nsamples = 10110\nvalue = [313, 1484, 8313]\nclass = High'), Text(0.90625, 0.1, 'gini = 0.497\nsamples = 3053\nvalue = [97, 1086, 1870]\nclass = High'), Text(0.96875, 0.1, 'gini = 0.162\nsamples = 7057\nvalue = [216, 398, 6443]\nclass = High')]
In [41]:
print("Train accuracy:", accuracy_score(y_train, dTree.predict(X_train)))
print("Test accuracy:", accuracy_score(y_test, dTree.predict(X_test)))
Train accuracy: 0.8189701316775506 Test accuracy: 0.8227458163350262
This output is more realistic, with an improved test score coming out at 82% Accuracy.
Hyperperameter Tuning¶
In [42]:
param_grid = {
'max_depth': [2, 3, 4, 5, 6],
'min_samples_leaf': [5, 10, 20, 50],
'min_samples_split': [10, 20, 50],
'criterion': ['gini', 'entropy']
}
dt = DecisionTreeClassifier(random_state=42)
grid = GridSearchCV(
estimator=dt,
param_grid=param_grid,
cv=5,
scoring='accuracy',
n_jobs= 12
)
grid.fit(X_train, y_train)
print("Best parameters:", grid.best_params_)
print("Best CV accuracy:", grid.best_score_)
Best parameters: {'criterion': 'entropy', 'max_depth': 6, 'min_samples_leaf': 5, 'min_samples_split': 10}
Best CV accuracy: 0.874674639816978
In [43]:
best_tree = grid.best_estimator_
best_tree.fit(X_train, y_train)
Out[43]:
DecisionTreeClassifier(criterion='entropy', max_depth=6, min_samples_leaf=5,
min_samples_split=10, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
Parameters
| criterion | 'entropy' | |
| splitter | 'best' | |
| max_depth | 6 | |
| min_samples_split | 10 | |
| min_samples_leaf | 5 | |
| min_weight_fraction_leaf | 0.0 | |
| max_features | None | |
| random_state | 42 | |
| max_leaf_nodes | None | |
| min_impurity_decrease | 0.0 | |
| class_weight | None | |
| ccp_alpha | 0.0 | |
| monotonic_cst | None |
In [44]:
y_pred = best_tree.predict(X_test)
print("Accuracy:", accuracy_score(y_test, y_pred))
print("\nClassification report:\n")
print(classification_report(y_test, y_pred,
target_names=['Low', 'Medium', 'High']))
ConfusionMatrixDisplay.from_estimator(
best_tree,
X_test,
y_test,
display_labels=['Low', 'Medium', 'High'],
cmap='Blues'
);
Accuracy: 0.8770293897260845
Classification report:
precision recall f1-score support
Low 0.86 0.84 0.85 3097
Medium 0.87 0.91 0.89 5813
High 0.90 0.85 0.88 3101
accuracy 0.88 12011
macro avg 0.88 0.87 0.87 12011
weighted avg 0.88 0.88 0.88 12011
Observations¶
After hyperparameter tuning, test set scores come out at 88% which is a good improvement on the pre-tuned results
In [45]:
classes = y_test.unique()
# Binarise y_test for multiclass ROC
y_test_bin = label_binarize(y_test, classes=classes)
In [46]:
y_prob_tree = best_tree.predict_proba(X_test)
auc_roc_tree = roc_auc_score(
y_test_bin,
y_prob_tree,
average="macro",
multi_class="ovr"
)
print("Decision Tree AUC-ROC (OvR, macro average):", auc_roc_tree)
Decision Tree AUC-ROC (OvR, macro average): 0.29113166318714756
Final Observation¶
The AUC_ROC tuning on the Decision tree drastically reduced the accuracy, bringing it down to just 29%. This is an isue with using a Decision Tree model on this data. It just doesn't perform as well as the SVM model. What it tells us is that no configuration of a single decision tree will generalise well on this dataset.
Clustering¶
From our previous analysis, the best features to cluster on are Sessions Played Per Week and the Average Session Duration
In [47]:
features = [
'SessionsPerWeek',
'AvgSessionDurationMinutes'
]
In [48]:
X = df[['SessionsPerWeek', 'AvgSessionDurationMinutes']]
X_scaled = StandardScaler().fit_transform(X)
In [49]:
inertia = []
K = range(2, 11)
for k in K:
km = KMeans(n_clusters=k, random_state=42)
km.fit(X_scaled)
inertia.append(km.inertia_)
plt.plot(K, inertia, marker='o')
plt.xlabel('Number of clusters')
plt.ylabel('Inertia')
plt.title('Elbow Method for Optimal K')
plt.show()
Observations¶
The elbow is showing us that anywhere between 2 and 5 clusters should give us the best results
In [50]:
for k in [2, 3, 4, 5]:
labels = KMeans(n_clusters=k, random_state=42).fit_predict(X_scaled)
print(k, silhouette_score(X_scaled, labels))
2 0.35347207319244445 3 0.37591677846954025 4 0.4093028147348912 5 0.3798706976290071
The result of the clustering shows that 4 clusters will provide the best possible outcome for clustering of the data based on these features.
In [51]:
kmeans = KMeans(n_clusters=4, random_state=42)
labels = kmeans.fit_predict(X_scaled)
sil_score = silhouette_score(X_scaled, labels)
print(sil_score)
0.4093028147348912
In [52]:
df['Cluster'] = labels
df.groupby('Cluster')[features].mean()
Out[52]:
| SessionsPerWeek | AvgSessionDurationMinutes | |
|---|---|---|
| Cluster | ||
| 0 | 4.499600 | 137.501699 |
| 1 | 14.516325 | 51.977489 |
| 2 | 4.520307 | 52.769496 |
| 3 | 14.510655 | 137.026613 |
In [53]:
end_time = time.time()
elapsed_time = end_time - start_time
minutes = int(elapsed_time // 60)
seconds = elapsed_time % 60
print(f"Total notebook execution time: {minutes} minutes {seconds:.2f} seconds")
Total notebook execution time: 29 minutes 20.22 seconds