Neural Networks Assignment: Heart Disease Classification¶
Source: The dataset was obtained from the Heart Disease Classification - Neural Network Kaggle Notebook data page.
Introduction and Task Details¶
The goal is to create a classification model that can accurately predict whether a patient will or won't have heart disease based on their recorded health metrics.
Contents
Importing Python Packages and the Dataset¶
In [ ]:
import numpy as np
import numpy.matlib
import pandas as pd
import matplotlib.pyplot as plt
from scipy.spatial import distance_matrix
from scipy.cluster.hierarchy import dendrogram, linkage
from sklearn.cluster import AgglomerativeClustering
import seaborn as sns
from sklearn.preprocessing import RobustScaler
from sklearn.ensemble import RandomForestClassifier
from sklearn import tree
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import average_precision_score
from sklearn.model_selection import cross_val_score
from sklearn.metrics import precision_recall_curve
from sklearn.neighbors import KNeighborsClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix
from sklearn.metrics import accuracy_score
from sklearn.naive_bayes import GaussianNB
from sklearn.metrics import roc_curve
from sklearn.metrics import roc_auc_score
from sklearn.metrics import f1_score
from sklearn.metrics import auc
from sklearn.svm import SVC
%matplotlib inline
In [ ]:
heart = pd.read_csv('heart.csv')
heart.head(10)
Out[ ]:
| age | sex | cp | trestbps | chol | fbs | restecg | thalach | exang | oldpeak | slope | ca | thal | target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 63 | 1 | 3 | 145 | 233 | 1 | 0 | 150 | 0 | 2.3 | 0 | 0 | 1 | 1 |
| 1 | 37 | 1 | 2 | 130 | 250 | 0 | 1 | 187 | 0 | 3.5 | 0 | 0 | 2 | 1 |
| 2 | 41 | 0 | 1 | 130 | 204 | 0 | 0 | 172 | 0 | 1.4 | 2 | 0 | 2 | 1 |
| 3 | 56 | 1 | 1 | 120 | 236 | 0 | 1 | 178 | 0 | 0.8 | 2 | 0 | 2 | 1 |
| 4 | 57 | 0 | 0 | 120 | 354 | 0 | 1 | 163 | 1 | 0.6 | 2 | 0 | 2 | 1 |
| 5 | 57 | 1 | 0 | 140 | 192 | 0 | 1 | 148 | 0 | 0.4 | 1 | 0 | 1 | 1 |
| 6 | 56 | 0 | 1 | 140 | 294 | 0 | 0 | 153 | 0 | 1.3 | 1 | 0 | 2 | 1 |
| 7 | 44 | 1 | 1 | 120 | 263 | 0 | 1 | 173 | 0 | 0.0 | 2 | 0 | 3 | 1 |
| 8 | 52 | 1 | 2 | 172 | 199 | 1 | 1 | 162 | 0 | 0.5 | 2 | 0 | 3 | 1 |
| 9 | 57 | 1 | 2 | 150 | 168 | 0 | 1 | 174 | 0 | 1.6 | 2 | 0 | 2 | 1 |
Column Names Explained¶
- age = age in years
- sex = male or female (1 = male; 0 = female)
- cp = chest pain type
- trestbps = resting blood pressure (in mm Hg on admission to the hospital)
- chol = serum cholesterol (in mg/dl)
- fbs = fasting blood sugar (> 120 mg/dl, 1 = true; 0 = false)
- restecg = resting electrocardiographic results
- thalach = maximum heart rate achieved
- exang = exercise induced angina (1 = yes; 0 = no)
- oldpeak = ST depression induced by exercise relative to rest ('ST' relates to positions on the ECG plot.)
- slope = the slope of the peak exercise ST segment (Value 1: upsloping, Value 2: flat, Value 3: downsloping)
- ca = The number of major vessels (0-3)
- thal = A blood disorder called thalassemia (3 = normal; 6 = fixed defect; 7 = reversable defect)
- target = Heart disease (0 = no, 1 = yes)
Data Quality Assessment¶
In [ ]:
heart.describe()
Out[ ]:
| age | sex | cp | trestbps | chol | fbs | restecg | thalach | exang | oldpeak | slope | ca | thal | target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 |
| mean | 54.366337 | 0.683168 | 0.966997 | 131.623762 | 246.264026 | 0.148515 | 0.528053 | 149.646865 | 0.326733 | 1.039604 | 1.399340 | 0.729373 | 2.313531 | 0.544554 |
| std | 9.082101 | 0.466011 | 1.032052 | 17.538143 | 51.830751 | 0.356198 | 0.525860 | 22.905161 | 0.469794 | 1.161075 | 0.616226 | 1.022606 | 0.612277 | 0.498835 |
| min | 29.000000 | 0.000000 | 0.000000 | 94.000000 | 126.000000 | 0.000000 | 0.000000 | 71.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 47.500000 | 0.000000 | 0.000000 | 120.000000 | 211.000000 | 0.000000 | 0.000000 | 133.500000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 | 2.000000 | 0.000000 |
| 50% | 55.000000 | 1.000000 | 1.000000 | 130.000000 | 240.000000 | 0.000000 | 1.000000 | 153.000000 | 0.000000 | 0.800000 | 1.000000 | 0.000000 | 2.000000 | 1.000000 |
| 75% | 61.000000 | 1.000000 | 2.000000 | 140.000000 | 274.500000 | 0.000000 | 1.000000 | 166.000000 | 1.000000 | 1.600000 | 2.000000 | 1.000000 | 3.000000 | 1.000000 |
| max | 77.000000 | 1.000000 | 3.000000 | 200.000000 | 564.000000 | 1.000000 | 2.000000 | 202.000000 | 1.000000 | 6.200000 | 2.000000 | 4.000000 | 3.000000 | 1.000000 |
In [ ]:
heart.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 303 entries, 0 to 302 Data columns (total 14 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 age 303 non-null int64 1 sex 303 non-null int64 2 cp 303 non-null int64 3 trestbps 303 non-null int64 4 chol 303 non-null int64 5 fbs 303 non-null int64 6 restecg 303 non-null int64 7 thalach 303 non-null int64 8 exang 303 non-null int64 9 oldpeak 303 non-null float64 10 slope 303 non-null int64 11 ca 303 non-null int64 12 thal 303 non-null int64 13 target 303 non-null int64 dtypes: float64(1), int64(13) memory usage: 33.3 KB
In [ ]:
heart.isnull().sum()
Out[ ]:
age 0 sex 0 cp 0 trestbps 0 chol 0 fbs 0 restecg 0 thalach 0 exang 0 oldpeak 0 slope 0 ca 0 thal 0 target 0 dtype: int64
In [ ]:
heart.shape
Out[ ]:
(303, 14)
Overview of the Data
- There are no missing/null values
- All data is numerical (everything int except oldpeak which is float)
- There are 303 rows/samples and 14 columns/features
- Age range is from 29 to 77 years with mean age of 54 years (to 2 s.f.).
- Some feature values range between 0 and 1 whilst others between 0 and 100s.
Considerations
- As the distributions for each feature are not all gaussian bell curves and the dataset contains features with different ranges/varying scales, the dataset requires normalistion.
- The normalisation will change the values of numeric columns in the dataset to a common scale, without distorting differences in the ranges of values.
- Normalisation is being performed so that features with larger ranges won't intrinsicaly have more influence on the results (i.e. what the main predictors are for heart disease) than features with smaller ranges. In other words, we don't want to conflate feature size with feature importance as a predictor.
- The algorithms to be used on this data (artificial neural networks, k-nearest neighbours) do not make assumptions about the data distribution. As such, standardisation is not being used to transform the data (standardisation assumes normally distributed data and requires that the selected algorithms assume normal distribution too e.g. logistic regression).
- One way to normalise the data is to use MinMaxScaler which rescales the data set such that all feature values are in the range [0, 1].
- It must be noted however, MinMaxScalar is sensitive to outliers (compared to StandardScaler) because it does not use a bounded range with smaller standard deviations, which would have suppressed the effects of outliers.
- There are many normalisation techniques to choose from on scikit-learn so it will be important to select the right one for this dataset. See here for scikit-learn's article "Compare the effect of different scalers on data with outliers".
- To decide which is the best, visual data quality assessments now need to be performed.
Source: For more information on normalisation and how to know when to use standardisation vs normalisation click here and here.
Visual Data Quality Assessment¶
At this stage, we are checking data distributions and for the presence of outliers to help decide which normalisation technique will be best to use.
Source: See this medium article for a guide on detecting and removing outliers from datasets in Python.
In [ ]:
# Create some smaller data frames (each df contains columns of similar ranges) so we can have multiple boxplots in each figure
heartbox1 = pd.DataFrame(heart, columns=["age", "trestbps", "chol", "thalach"])
# Check to see above worked and that ranges are in similar range (e.g. tens and hundreds)
heartbox1.describe()
Out[ ]:
| age | trestbps | chol | thalach | |
|---|---|---|---|---|
| count | 303.000000 | 303.000000 | 303.000000 | 303.000000 |
| mean | 54.366337 | 131.623762 | 246.264026 | 149.646865 |
| std | 9.082101 | 17.538143 | 51.830751 | 22.905161 |
| min | 29.000000 | 94.000000 | 126.000000 | 71.000000 |
| 25% | 47.500000 | 120.000000 | 211.000000 | 133.500000 |
| 50% | 55.000000 | 130.000000 | 240.000000 | 153.000000 |
| 75% | 61.000000 | 140.000000 | 274.500000 | 166.000000 |
| max | 77.000000 | 200.000000 | 564.000000 | 202.000000 |
In [ ]:
heartbox2 = pd.DataFrame(heart, columns=["cp", "restecg", "oldpeak", "slope", "ca", "thal"])
heartbox2.describe()
Out[ ]:
| cp | restecg | oldpeak | slope | ca | thal | |
|---|---|---|---|---|---|---|
| count | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 |
| mean | 0.966997 | 0.528053 | 1.039604 | 1.399340 | 0.729373 | 2.313531 |
| std | 1.032052 | 0.525860 | 1.161075 | 0.616226 | 1.022606 | 0.612277 |
| min | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 | 2.000000 |
| 50% | 1.000000 | 1.000000 | 0.800000 | 1.000000 | 0.000000 | 2.000000 |
| 75% | 2.000000 | 1.000000 | 1.600000 | 2.000000 | 1.000000 | 3.000000 |
| max | 3.000000 | 2.000000 | 6.200000 | 2.000000 | 4.000000 | 3.000000 |
In [ ]:
heartbox3 = pd.DataFrame(heart, columns=["sex", "fbs", "exang", "target"])
heartbox3.describe()
Out[ ]:
| sex | fbs | exang | target | |
|---|---|---|---|---|
| count | 303.000000 | 303.000000 | 303.000000 | 303.000000 |
| mean | 0.683168 | 0.148515 | 0.326733 | 0.544554 |
| std | 0.466011 | 0.356198 | 0.469794 | 0.498835 |
| min | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 50% | 1.000000 | 0.000000 | 0.000000 | 1.000000 |
| 75% | 1.000000 | 0.000000 | 1.000000 | 1.000000 |
| max | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
In [ ]:
# Create boxplot for each feature with range between 10s and 100s
plt.figure(figsize=(20,10))
ax1 = sns.boxplot(data=heartbox1, orient="h", palette="Set1")
In [ ]:
# Get closer look at age
ax1a = sns.boxplot(x=heart["age"])
In [ ]:
# Create boxplot for each feature with range between 0 and less than 10
plt.figure(figsize=(20,10))
ax2 = sns.boxplot(data=heartbox2, orient="h", palette="Set2")
In [ ]:
# Create boxplot for each feature with range between 0 and 1
plt.figure(figsize=(20,10))
ax3 = sns.boxplot(data=heartbox3, orient="h", palette="Set3")
Features with Outliers
- trestbps (high values)
- chol (high values)
- thalach (low value)
- oldpeak (high values)
- ca (high values)
- thal (low value)
- fbs (high value)
Features with skews
- cp (left-skew)
- restecg (left-skew)
- oldpeak (left-skew)
- slope (right-skew)
- ca (left-skew)
- thal (right-skew)
Given the high presence of outliers, MinMaxScaler will not be an appropriate normalisation technique to adopt for this dataset. RobustScaler will be implemented initially as it appears to be the most robust to outliers (compared to MinMaxScaler, Normalization, and StandardScaler). Below is information on the Robust Scaler technique [see scikit-learn's][https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.RobustScaler.html#sklearn.preprocessing.RobustScaler] guide on RobustScaler for more information.
- Scale features using statistics that are robust to outliers.
- This Scaler removes the median and scales the data according to the quantile range (defaults to IQR: Interquartile Range). The IQR is the range between the 1st quartile (25th quantile) and the 3rd quartile (75th quantile).
- Centering and scaling happen independently on each feature by computing the relevant statistics on the samples in the training set. Median and interquartile range are then stored to be used on later data using the transform method.
- Standardization of a dataset is a common requirement for many machine learning estimators. Typically this is done by removing the mean and scaling to unit variance. However, outliers can often influence the sample mean / variance in a negative way. In such cases, the median and the interquartile range often give better results.
Data Preprocessing¶
In [ ]:
# Apply the RobustScaler
Rscaler = RobustScaler(quantile_range=(25,75))
Rscaled_heart = Rscaler.fit_transform(heart)
In [ ]:
print('The means after using RobustScaler for heart is: ', Rscaled_heart.mean(axis=0))
print('The standard deviations after using RobustScaler for heart is: ', Rscaled_heart.std(axis=0))
The means after using RobustScaler for heart is: [-0.04693803 -0.31683168 -0.01650165 0.08118812 0.09864609 0.14851485 -0.47194719 -0.10317339 0.32673267 0.14975248 0.39933993 0.72937294 0.31353135 -0.45544554] The standard deviations after using RobustScaler for heart is: [0.67163716 0.46524119 0.51517401 0.8754589 0.81488427 0.3556096 0.52499112 0.70361023 0.46901859 0.72447342 0.61520843 1.0209175 0.61126531 0.49801094]
In [ ]:
print('The means before using RobustScaler for heart is: \n', heart.mean(axis=0))
print('The standard deviations before using RobustScaler for heart is: \n', heart.std(axis=0))
The means before using RobustScaler for heart is: age 54.366337 sex 0.683168 cp 0.966997 trestbps 131.623762 chol 246.264026 fbs 0.148515 restecg 0.528053 thalach 149.646865 exang 0.326733 oldpeak 1.039604 slope 1.399340 ca 0.729373 thal 2.313531 target 0.544554 dtype: float64 The standard deviations before using RobustScaler for heart is: age 9.082101 sex 0.466011 cp 1.032052 trestbps 17.538143 chol 51.830751 fbs 0.356198 restecg 0.525860 thalach 22.905161 exang 0.469794 oldpeak 1.161075 slope 0.616226 ca 1.022606 thal 0.612277 target 0.498835 dtype: float64
In [ ]:
compare = {'Old Mean':[54.366337, 0.683168, 0.966997, 131.623762, 246.264026, 0.148515, 0.528053, 149.646865, 0.326733, 1.039604, 1.399340, 0.729373, 2.313531, 0.544554],
'New Mean':[-0.04693803, -0.31683168, -0.01650165, 0.08118812, 0.09864609, 0.14851485, -0.47194719, -0.10317339, 0.32673267, 0.14975248, 0.39933993, 0.72937294, 0.31353135, -0.45544554],
'Old Std Dev':[9.082101, 0.466011, 1.032052, 17.538143, 51.830751, 0.356198, 0.525860, 22.905161, 0.469794, 1.161075, 0.616226, 1.022606, 0.612277, 0.498835],
'New Std Dev':[0.67163716, 0.46524119, 0.51517401, 0.8754589, 0.81488427, 0.3556096, 0.52499112, 0.70361023, 0.46901859, 0.72447342, 0.61520843, 1.0209175, 0.61126531, 0.49801094]}
compare_df = pd.DataFrame(data=compare)
compare_df
Out[ ]:
| Old Mean | New Mean | Old Std Dev | New Std Dev | |
|---|---|---|---|---|
| 0 | 54.366337 | -0.046938 | 9.082101 | 0.671637 |
| 1 | 0.683168 | -0.316832 | 0.466011 | 0.465241 |
| 2 | 0.966997 | -0.016502 | 1.032052 | 0.515174 |
| 3 | 131.623762 | 0.081188 | 17.538143 | 0.875459 |
| 4 | 246.264026 | 0.098646 | 51.830751 | 0.814884 |
| 5 | 0.148515 | 0.148515 | 0.356198 | 0.355610 |
| 6 | 0.528053 | -0.471947 | 0.525860 | 0.524991 |
| 7 | 149.646865 | -0.103173 | 22.905161 | 0.703610 |
| 8 | 0.326733 | 0.326733 | 0.469794 | 0.469019 |
| 9 | 1.039604 | 0.149752 | 1.161075 | 0.724473 |
| 10 | 1.399340 | 0.399340 | 0.616226 | 0.615208 |
| 11 | 0.729373 | 0.729373 | 1.022606 | 1.020917 |
| 12 | 2.313531 | 0.313531 | 0.612277 | 0.611265 |
| 13 | 0.544554 | -0.455446 | 0.498835 | 0.498011 |
In [ ]:
# Plot boxplot for RobustScaler version of heart data to demonstrate that all data is within similar ranges of each other and have maintained individual range integrity.
plt.figure(figsize=(20,10))
ax4 = sns.boxplot(data=Rscaled_heart, orient="h", palette="Set3")
Did it Work? Overview of RobustScaler Impact The table below demonstrates that the existence of outliers and skews for each feature have not changed at all since using RobustScaler.
Before vs After: Features with Outliers, Features with skew
| Outliers Before | Outliers After | Skew Before | Skew After | |
|---|---|---|---|---|
| age | NO | NO | NO | NO |
| sex | NO | NO | NO | NO |
| cp | NO | NO | LEFT | LEFT |
| trestbps | YES | YES | NO | NO |
| chol | YES | YES | NO | NO |
| fbs | YES | YES | NO | NO |
| restecg | NO | NO | LEFT | LEFT |
| thalach | YES | YES | NO | NO |
| exang | NO | NO | NO | NO |
| oldpeak | YES | YES | LEFT | LEFT |
| slope | NO | NO | RIGHT | RIGHT |
| ca | YES | YES | LEFT | LEFT |
| thal | YES | YES | RIGHT | RIGHT |
| target | NO | NO | NO | NO |
- All unique feature data now falls within a range of -2 and 5.
- Outliers will not be removed from this data as the high presence of them in certain features implies a need for further exploration. More importantly as the data is for predicting heart disease, it is not recommended to simply drop inconvenient data when it could be providing valuable insight.
In [ ]:
rscaled_heart_df = pd.DataFrame(data=Rscaled_heart, columns=(['age', 'sex','cp', 'trestbps', 'chol', 'fbs', 'restecg', 'thalach', 'exang', 'oldpeak', 'slope', 'ca', 'thal', 'target']))
rscaled_heart_df.describe() # Note below that all features now have a median value of 0
Out[ ]:
| age | sex | cp | trestbps | chol | fbs | restecg | thalach | exang | oldpeak | slope | ca | thal | target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 | 303.000000 |
| mean | -0.046938 | -0.316832 | -0.016502 | 0.081188 | 0.098646 | 0.148515 | -0.471947 | -0.103173 | 0.326733 | 0.149752 | 0.399340 | 0.729373 | 0.313531 | -0.455446 |
| std | 0.672748 | 0.466011 | 0.516026 | 0.876907 | 0.816232 | 0.356198 | 0.525860 | 0.704774 | 0.469794 | 0.725672 | 0.616226 | 1.022606 | 0.612277 | 0.498835 |
| min | -1.925926 | -1.000000 | -0.500000 | -1.800000 | -1.795276 | 0.000000 | -1.000000 | -2.523077 | 0.000000 | -0.500000 | -1.000000 | 0.000000 | -2.000000 | -1.000000 |
| 25% | -0.555556 | -1.000000 | -0.500000 | -0.500000 | -0.456693 | 0.000000 | -1.000000 | -0.600000 | 0.000000 | -0.500000 | 0.000000 | 0.000000 | 0.000000 | -1.000000 |
| 50% | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 75% | 0.444444 | 0.000000 | 0.500000 | 0.500000 | 0.543307 | 0.000000 | 0.000000 | 0.400000 | 1.000000 | 0.500000 | 1.000000 | 1.000000 | 1.000000 | 0.000000 |
| max | 1.629630 | 0.000000 | 1.000000 | 3.500000 | 5.102362 | 1.000000 | 1.000000 | 1.507692 | 1.000000 | 3.375000 | 1.000000 | 4.000000 | 1.000000 | 0.000000 |
See below for a summarised comparison of the two dataframes (RobustScaler is presented first).
In [ ]:
rscaled_heart_df.head()
Out[ ]:
| age | sex | cp | trestbps | chol | fbs | restecg | thalach | exang | oldpeak | slope | ca | thal | target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.592593 | 0.0 | 1.0 | 0.75 | -0.110236 | 1.0 | -1.0 | -0.092308 | 0.0 | 0.9375 | -1.0 | 0.0 | -1.0 | 0.0 |
| 1 | -1.333333 | 0.0 | 0.5 | 0.00 | 0.157480 | 0.0 | 0.0 | 1.046154 | 0.0 | 1.6875 | -1.0 | 0.0 | 0.0 | 0.0 |
| 2 | -1.037037 | -1.0 | 0.0 | 0.00 | -0.566929 | 0.0 | -1.0 | 0.584615 | 0.0 | 0.3750 | 1.0 | 0.0 | 0.0 | 0.0 |
| 3 | 0.074074 | 0.0 | 0.0 | -0.50 | -0.062992 | 0.0 | 0.0 | 0.769231 | 0.0 | 0.0000 | 1.0 | 0.0 | 0.0 | 0.0 |
| 4 | 0.148148 | -1.0 | -0.5 | -0.50 | 1.795276 | 0.0 | 0.0 | 0.307692 | 1.0 | -0.1250 | 1.0 | 0.0 | 0.0 | 0.0 |
In [ ]:
heart.head()
Out[ ]:
| age | sex | cp | trestbps | chol | fbs | restecg | thalach | exang | oldpeak | slope | ca | thal | target | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 63 | 1 | 3 | 145 | 233 | 1 | 0 | 150 | 0 | 2.3 | 0 | 0 | 1 | 1 |
| 1 | 37 | 1 | 2 | 130 | 250 | 0 | 1 | 187 | 0 | 3.5 | 0 | 0 | 2 | 1 |
| 2 | 41 | 0 | 1 | 130 | 204 | 0 | 0 | 172 | 0 | 1.4 | 2 | 0 | 2 | 1 |
| 3 | 56 | 1 | 1 | 120 | 236 | 0 | 1 | 178 | 0 | 0.8 | 2 | 0 | 2 | 1 |
| 4 | 57 | 0 | 0 | 120 | 354 | 0 | 1 | 163 | 1 | 0.6 | 2 | 0 | 2 | 1 |
Correlations¶
In [ ]:
# Pairwise plot to show every feature plotted against every feature (each feature gets to be both y-axis and x-axis at least once). Hue is set to 'target' with blue plots representing individuals with heart disease (-1.0) and red plots representing those without heart disease (0.0). This plot shows the individual relationships between each pair of features; could be considered a more visual representaion of a correlation matrix.
sns.pairplot(rscaled_heart_df, hue='target', palette='Set1')
Out[ ]:
<seaborn.axisgrid.PairGrid at 0x13f683e1490>
Numerical categories key:
- sex = (0 = male; -1 = female)
- fbs = (fbs > 120 mg/dl, 1 = true; 0 = false)
- exang = (1 = yes; 0 = no)
- slope = (Value -1: upsloping, Value 0: flat, Value 1: downsloping)
- ca = (0 to 4)
- thal = (-1 = normal; 0 = fixed defect; 1 = reversable defect)
Pairplot Explained (this will be a lot, skim read for summaries) NB: duplicate pairs and pairs with inverted axis (e.g. thal against thal, age against thal, thal against age) have not been included, only one version of each pair is discussed.
- thalassemia (thal) against age: no correlations seen
- thalassemia against sex: no correlations seen
- thalassemia against chest pain (cp): no correlations seen
- thalassemia against resting blood pressure (trestbps): no correlations seen
- thalassemia against cholesterol (chol): no correlations seen
- thalassemia against fasting blood sugar (fbs): no correlations seen
- thalassemia against resting electrocardiographic results (restecg): no correlations seen
- thalassemia against maximum heart rate (thalach): no correlations seen
- thalassemia against exercise induced angina (exang): no correlations seen
- thalassemia against ST depression induced by exercise relative to rest (oldpeak): no correlations seen
- thalassemia against the slope of the peak exercise ST segment (slope): no correlations seen
- thalassemia against number of major vessels (ca): no correlations seen
</br>
- number of major vessels (ca) against age: no correlations seen
- number of major vessels (ca) against sex: no correlations seen
- number of major vessels (ca) against chest pain (cp): no correlations seen
- number of major vessels (ca) against resting blood pressure (trestbps): no correlations seen
- number of major vessels (ca) against cholesterol (chol): no correlations seen
- number of major vessels (ca) against fasting blood sugar (fbs): no correlations seen
- number of major vessels (ca) against resting electrocardiographic results (restecg): no correlations seen
- number of major vessels (ca) against maximum heart rate (thalach): no correlations seen
- number of major vessels (ca) against exercise induced angina (exang): no correlations seen
- number of major vessels (ca) against ST depression induced by exercise relative to rest (oldpeak): no correlations seen
- number of major vessels (ca) against the slope of the peak exercise ST segment (slope): no correlations seen
</br>
- the slope of the peak exercise ST segment (slope) against age: no correlations seen
- the slope of the peak exercise ST segment (slope) against sex: no correlations seen
- the slope of the peak exercise ST segment (slope) against chest pain (cp): no correlations seen
- the slope of the peak exercise ST segment (slope) against resting blood pressure (trestbps): no correlations seen
- the slope of the peak exercise ST segment (slope) against cholesterol (chol): no correlations seen
- the slope of the peak exercise ST segment (slope) against fasting blood sugar (fbs): no correlations seen
- the slope of the peak exercise ST segment (slope) against resting electrocardiographic results (restecg): no correlations seen
- the slope of the peak exercise ST segment (slope) against maximum heart rate (thalach): no correlations seen
- the slope of the peak exercise ST segment (slope) against exercise induced angina (exang): no correlations seen
- the slope of the peak exercise ST segment (slope) against ST depression induced by exercise relative to rest (oldpeak): no correlations seen
</br>
- ST depression induced by exercise relative to rest (oldpeak) against age: no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against sex: no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against chest pain (cp): no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against resting blood pressure (trestbps): slightly clustered around lower trestbps
- ST depression induced by exercise relative to rest (oldpeak) against cholesterol (chol): slightly clusetered around lower cholesterol
- ST depression induced by exercise relative to rest (oldpeak) against fasting blood sugar (fbs): no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against resting electrocardiographic results (restecg): no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against maximum heart rate (thalach): no correlations seen
- ST depression induced by exercise relative to rest (oldpeak) against exercise induced angina (exang): no correlations seen
</br>
- exercise induced angina (exang) against age: no correlations seen
- exercise induced angina (exang) against sex: no correlations seen
- exercise induced angina (exang) against chest pain (cp): no correlations seen
- exercise induced angina (exang) against resting blood pressure (trestbps): no correlations seen
- exercise induced angina (exang) against cholesterol (chol): no correlations seen
- exercise induced angina (exang) against fasting blood sugar (fbs): no correlations seen
- exercise induced angina (exang) against resting electrocardiographic results (restecg): no correlations seen
- exercise induced angina (exang) against maximum heart rate (thalach): no correlations seen
</br>
- maximum heart rate (thalach) against age: no correlations seen
- maximum heart rate (thalach) against sex: no correlations seen
- maximum heart rate (thalach) against chest pain (cp): no correlations seen
- maximum heart rate (thalach) against resting blood pressure (trestbps): slightly clustered around lower trestbps
- maximum heart rate (thalach) against cholesterol (chol): slightly clustered around lower cholesterol
- maximum heart rate (thalach) against fasting blood sugar (fbs): no correlations seen
- maximum heart rate (thalach) against resting electrocardiographic results (restecg): no correlations seen
</br>
- resting electrocardiographic results (restecg) against age: no correlations seen
- resting electrocardiographic results (restecg) against sex: no correlations seen
- resting electrocardiographic results (restecg) against chest pain (cp): no correlations seen
- resting electrocardiographic results (restecg) against resting blood pressure (trestbps): no correlations seen
- resting electrocardiographic results (restecg) against cholesterol (chol): no correlations seen
- resting electrocardiographic results (restecg) against fasting blood sugar (fbs): no correlations seen
</br>
- fasting blood sugar (fbs) against age: no correlations seen
- fasting blood sugar (fbs) against sex: no correlations seen
- fasting blood sugar (fbs) against chest pain (cp): no correlations seen
- fasting blood sugar (fbs) against resting blood pressure (trestbps): no correlations seen
- fasting blood sugar (fbs) against cholesterol (chol): no correlations seen
</br>
- cholesterol (chol) against age: no correlations seen
- cholesterol (chol) against sex: no correlations seen
- cholesterol (chol) against chest pain (cp): no correlations seen
- cholesterol (chol) against resting blood pressure (trestbps): slightly clustered around lower trestbps
</br>
- resting blood pressure (trestbps) against age: no correlations seen
- resting blood pressure (trestbps) against sex: no correlations seen
- resting blood pressure (trestbps) against chest pain (cp): no correlations seen
</br>
- chest pain (cp) against age: no correlations seen
- chest pain (cp) against sex: no correlations seen
</br>
- sex against age: no correlations seen
It is very difficult to see any strong pairwise relationships or correlations between the features. The pairplot did not highlight any significant correlations. Next step is to create heatmaps to see this better.
In [ ]:
plt.subplots(figsize=(20, 10))
sns.heatmap(rscaled_heart_df.corr(), annot=True, cmap="rainbow")
plt.show()
In [ ]:
# See if individual features correlate to target using vertical heatmap (heart disease: -1 = no, 0 = yes).
heart_corr = rscaled_heart_df.corr().loc[:,['target']]
plt.figure(figsize = (3,10))
sns.heatmap(heart_corr,annot = True, cmap='seismic')
Out[ ]:
<AxesSubplot:>
Individual correlations to target summarised
- age = negative correlation (As age value goes up, heart disease value goes down. Increased age trends to no heart disease.)
- sex = negative correlation (as sex value goes up, heart disease value goes down. Male trends to no heart disease.)
- cp = positive correlation (as cp value goes up, heart disease value goes up. Increased chest pain trends to heart disease.)
- trestbps = slight negative correlation (as trestbps value goes up, heart disease value goes down. Increased resting blood pressure trends to no heart disease.)
- chol = slight negative correlation (as chol value goes up, heart disease value goes down. Increased cholesterol trends to no heart disease.)
- fbs = slight negative correlation (as fbs value goes up, heart disease value goes down. Increased fasting blood sugar trends to no heart disease.)
- restecg = slight positive correlation (as restecg value goes up, heart disease value goes up. Increased resting ECG results value trends to heart disease.)
- thalach = positive correlation (as thalach value goes up, heart disease value goes up. Increased maximum heart rate trends to heart disease.)
- exang = negative correlation (as exang value goes up, heart disease value goes down. Exercise angina (yes) trends to no heart disease.)
- oldpeak = negative correlation (as oldpeak value goes up, heart disease value goes down. Increased ST depression induced by exercise relative to rest trends to no heart disease.)
- slope = positive correlation (as slope value goes up, heart disease value goes up. Downsloping slope trends to heart disease.)
- ca = negative correlation (as ca value goes up, heart disease value goes down. Increased number of major vessels trends to no heart disease.)
- thal = negative correlation (as thal value goes up, heart disease value goes down. Reversable defect trends to no heart disease.)
Split dataset for models¶
In [ ]:
# Define X and y for train test split
X = rscaled_heart_df.drop(columns=['target'], axis=1)
y = heart.target.values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=56) # creates training and test sets
Models (currently unfinished)¶
In [ ]:
# Make a decision tree
tree_mod = DecisionTreeClassifier(max_leaf_nodes=13)
tree_mod.fit(X_train, y_train)
# Make predictions
pred = tree_mod.predict(X_test)
# Show tree plot (clipped version for readability)
score1 = accuracy_score(y_test, pred)
# print(pred)
print(score1)
tree.plot_tree(tree_mod, filled=True)
plt.show()
0.7868852459016393
See this tutorial of a beginner's guide to deeep learning in python.
In [ ]:
from keras.models import Sequential
from keras.layers import Dense, Dropout, Activation, Flatten
from keras.layers import Convolution2D, MaxPooling2D
from keras.utils import np_utils
In [ ]:
classifier = Sequential()
# classifier.add(Dense(6, activation='relu', kernel_initializer='glorot_uniform',input_dim=11))
# Adding the input layer and the first hidden layer
classifier.add(Dense(11, kernel_initializer = 'uniform', activation = 'relu', input_dim = 13))
# Adding the second hidden layer
classifier.add(Dense(11, kernel_initializer = 'uniform', activation = 'relu'))
# Adding the output layer
classifier.add(Dense(1, kernel_initializer = 'uniform', activation = 'sigmoid'))
# Compiling the ANN
classifier.compile(optimizer = 'adam', loss = 'binary_crossentropy', metrics = ['accuracy'])
In [ ]:
classifier.fit(X_train, y_train, batch_size = 10, epochs = 100)
Epoch 1/100 25/25 [==============================] - 1s 1ms/step - loss: 0.6928 - accuracy: 0.5248 Epoch 2/100 25/25 [==============================] - 0s 1ms/step - loss: 0.6912 - accuracy: 0.6529 Epoch 3/100 25/25 [==============================] - 0s 1ms/step - loss: 0.6849 - accuracy: 0.8099 Epoch 4/100 25/25 [==============================] - 0s 1ms/step - loss: 0.6670 - accuracy: 0.7934 Epoch 5/100 25/25 [==============================] - 0s 1ms/step - loss: 0.6329 - accuracy: 0.8099 Epoch 6/100 25/25 [==============================] - 0s 1ms/step - loss: 0.5858 - accuracy: 0.7934 Epoch 7/100 25/25 [==============================] - 0s 1ms/step - loss: 0.5398 - accuracy: 0.8017 Epoch 8/100 25/25 [==============================] - 0s 1ms/step - loss: 0.4953 - accuracy: 0.8306 Epoch 9/100 25/25 [==============================] - 0s 1ms/step - loss: 0.4579 - accuracy: 0.8430 Epoch 10/100 25/25 [==============================] - 0s 1ms/step - loss: 0.4273 - accuracy: 0.8512 Epoch 11/100 25/25 [==============================] - 0s 1ms/step - loss: 0.4061 - accuracy: 0.8430 Epoch 12/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3907 - accuracy: 0.8595 Epoch 13/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3803 - accuracy: 0.8678 Epoch 14/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3716 - accuracy: 0.8719 Epoch 15/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3678 - accuracy: 0.8678 Epoch 16/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3636 - accuracy: 0.8678 Epoch 17/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3633 - accuracy: 0.8636 Epoch 18/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3603 - accuracy: 0.8678 Epoch 19/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3592 - accuracy: 0.8678 Epoch 20/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3573 - accuracy: 0.8595 Epoch 21/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3573 - accuracy: 0.8636 Epoch 22/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3551 - accuracy: 0.8595 Epoch 23/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3538 - accuracy: 0.8554 Epoch 24/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3531 - accuracy: 0.8595 Epoch 25/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3516 - accuracy: 0.8595 Epoch 26/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3513 - accuracy: 0.8678 Epoch 27/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3507 - accuracy: 0.8678 Epoch 28/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3489 - accuracy: 0.8636 Epoch 29/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3479 - accuracy: 0.8554 Epoch 30/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3484 - accuracy: 0.8595 Epoch 31/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3517 - accuracy: 0.8678 Epoch 32/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3468 - accuracy: 0.8636 Epoch 33/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3458 - accuracy: 0.8636 Epoch 34/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3455 - accuracy: 0.8636 Epoch 35/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3439 - accuracy: 0.8678 Epoch 36/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3436 - accuracy: 0.8595 Epoch 37/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3426 - accuracy: 0.8636 Epoch 38/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3427 - accuracy: 0.8595 Epoch 39/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3432 - accuracy: 0.8512 Epoch 40/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3411 - accuracy: 0.8636 Epoch 41/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3415 - accuracy: 0.8636 Epoch 42/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3413 - accuracy: 0.8719 Epoch 43/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3415 - accuracy: 0.8678 Epoch 44/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3395 - accuracy: 0.8719 Epoch 45/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3386 - accuracy: 0.8636 Epoch 46/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3395 - accuracy: 0.8595 Epoch 47/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3385 - accuracy: 0.8678 Epoch 48/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3381 - accuracy: 0.8719 Epoch 49/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3367 - accuracy: 0.8595 Epoch 50/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3366 - accuracy: 0.8595 Epoch 51/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3370 - accuracy: 0.8595 Epoch 52/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3362 - accuracy: 0.8595 Epoch 53/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3353 - accuracy: 0.8719 Epoch 54/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3350 - accuracy: 0.8719 Epoch 55/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3351 - accuracy: 0.8678 Epoch 56/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3336 - accuracy: 0.8636 Epoch 57/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3327 - accuracy: 0.8719 Epoch 58/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3311 - accuracy: 0.8719 Epoch 59/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3329 - accuracy: 0.8636 Epoch 60/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3329 - accuracy: 0.8719 Epoch 61/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3313 - accuracy: 0.8760 Epoch 62/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3305 - accuracy: 0.8760 Epoch 63/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3301 - accuracy: 0.8719 Epoch 64/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3296 - accuracy: 0.8843 Epoch 65/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3286 - accuracy: 0.8719 Epoch 66/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3314 - accuracy: 0.8595 Epoch 67/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3291 - accuracy: 0.8636 Epoch 68/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3275 - accuracy: 0.8719 Epoch 69/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3268 - accuracy: 0.8719 Epoch 70/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3265 - accuracy: 0.8719 Epoch 71/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3261 - accuracy: 0.8719 Epoch 72/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3256 - accuracy: 0.8595 Epoch 73/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3270 - accuracy: 0.8719 Epoch 74/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3245 - accuracy: 0.8719 Epoch 75/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3253 - accuracy: 0.8636 Epoch 76/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3238 - accuracy: 0.8719 Epoch 77/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3233 - accuracy: 0.8760 Epoch 78/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3237 - accuracy: 0.8760 Epoch 79/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3240 - accuracy: 0.8678 Epoch 80/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3224 - accuracy: 0.8719 Epoch 81/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3226 - accuracy: 0.8719 Epoch 82/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3223 - accuracy: 0.8760 Epoch 83/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3220 - accuracy: 0.8760 Epoch 84/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3215 - accuracy: 0.8636 Epoch 85/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3196 - accuracy: 0.8760 Epoch 86/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3198 - accuracy: 0.8760 Epoch 87/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3197 - accuracy: 0.8802 Epoch 88/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3182 - accuracy: 0.8802 Epoch 89/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3178 - accuracy: 0.8802 Epoch 90/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3182 - accuracy: 0.8802 Epoch 91/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3172 - accuracy: 0.8802 Epoch 92/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3168 - accuracy: 0.8802 Epoch 93/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3164 - accuracy: 0.8802 Epoch 94/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3163 - accuracy: 0.8802 Epoch 95/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3159 - accuracy: 0.8802 Epoch 96/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3154 - accuracy: 0.8802 Epoch 97/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3149 - accuracy: 0.8802 Epoch 98/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3152 - accuracy: 0.8760 Epoch 99/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3152 - accuracy: 0.8719 Epoch 100/100 25/25 [==============================] - 0s 1ms/step - loss: 0.3137 - accuracy: 0.8760
Out[ ]:
<keras.callbacks.History at 0x13f7a581a60>
In [ ]:
# Predicting the Test set results
y_pred = classifier.predict(X_test)
In [ ]:
cm1 = confusion_matrix(y_test, y_pred.round())
sns.heatmap(cm1,annot=True,cmap="Reds",fmt="d",cbar=False)
#accuracy score
ac1 = accuracy_score(y_test, y_pred.round())
print('accuracy of the model: ',ac1)
accuracy of the model: 0.8032786885245902
In [ ]:
pd.crosstab(rscaled_heart_df.sex, rscaled_heart_df.target).plot(kind="bar",figsize=(10,5),color=['purple','orange' ])
plt.xlabel('Sex (-1 = Female, 0 = Male)')
plt.xticks(rotation=0)
plt.legend(["No Heart Disease", "Heart Disease"])
plt.ylabel('Frequency')
plt.show()
