Model Data to Diagnose Heart Disease

Clean, transform and visualize data to predict diagnoses

The dataset used here comes from the UCI Machine Learning Repository, which consists of data from 1,541 patients including age, cholesterol level, resting blood pressure and heart disease diagnosis. A smaller version of the dataset is available from the Wolfram Data Repository.

Import heart disease diagnosis data:

In[1]:=

original=Import["https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/new.data","Table"];

Parse the data so the rows correspond to different patients, and the columns correspond to different attributes:

In[2]:=

data=Tabular[Flatten/@Most/@Partition[original,12]]

Out[2]=

Extract the relevant attributes into "features":

In[3]:=

features=data〚All,{3,4,9,10,12,16,19,32,38,40,41,44,51}〛

Out[3]=

Define labels for the columns:

In[4]:=

schema=TabularSchema[features,"ColumnKeys"{"age","sex","cp","trestbps","chol","fbs","restecg","thalach","exang","oldpeak","slope","ca","thal"}]

Out[4]=

TabularSchema

Column count: 13

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Add the labels:

In[5]:=

features=Tabular[features,schema]

Out[5]=

For each patient, the feature vector is a list of numerical values. However, the data is not complete and has missing fields stored as

-9

. Flag the -9 values as missing:

In[6]:=

features=TransformAnomalies[features,#-9&"Flag"]

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Replace missing values by the average of the available data in the corresponding attribute:

In[7]:=

features=TransformMissing[features,"Mean"]

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Visualize the correlation between different attributes:

In[8]:=

MatrixPlot[Correlation[Values@Normal[features]],ImageSizeMedium,PlotTheme"Detailed"]

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To visualize the distribution of the data, extract the first two leading components:

In[9]:=

pcs2=Take[PrincipalComponents[Values@Normal[features],Method"Correlation"],All,2];

Column 58 of the data corresponds to presence and absence of heart disease:

In[10]:=

classLabels=Unitize[data〚All,58〛]//Normal;

Present the projected data on a scatter plot:

In[11]:=

splot=With{ind=Pick[Range[Length[pcs2]],classLabels,0]},ListPlot{pcs2〚ind〛,Delete[pcs2,Transpose[{ind}]]},

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Out[11]=

	Absence
	Presence

To distinguish the two classes, fit the projected data to a two-component Gaussian mixture model:

In[12]:=

edist=EstimatedDistribution[pcs2,MixtureDistribution[{p1,p2},{BinormalDistribution[{m11,m12},{s11,s12},r1],BinormalDistribution[{m21,m22},{s21,s22},r2]}]];

Based on the mixture model, plot the decision boundary (black curve) and probability density contours (red curve) of the mixture model and show them together with the scatter plot:

In[13]:=

Module{p=edist〚1,1〛,dist1=edist〚2,1〛,dist2=edist〚2,2〛,prob},prob[x_,y_]:=pPDF[dist1,{x,y}](pPDF[dist1,{x,y}]+(1-p)PDF[dist2,{x,y}]);Showsplot,

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Out[13]=

	Absence
	Presence

Probability Density

Decision Boundary

The first component of the Gaussian mixture has higher probability inside the decision boundary.

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Contributed by: Wolfram Staff

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Model Data to Diagnose Heart Disease

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Model Data to Diagnose Heart Disease

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