Let's look at a real-life example of the application of the PCA method. Import the libraries with which we will work:

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# Linear algebra and data processing
import numpy as np 
import pandas as pd 
from sklearn.preprocessing import StandardScaler

# PCA model
from sklearn.decomposition import PCA

# Data visualization
import seaborn as sns
import matplotlib.pyplot as plt

Next, we read the train.csv file (from web), which contains data on house sales with the characteristics of houses and their prices:

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data = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/7b22c447-77ad-48ae-a2d2-4e6714f7a4a6/train_S1.csv')

Let's process our data. This process includes dropping many characteristics from the dataset (we will leave only 10 variables - this way it will be easier for us to work with the results obtained so that there are not too many characteristics), as well as data scaling:

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# Columns that will remain 
columns_ndrop = ['YearBuilt', 'LotArea', 'MSSubClass', 'OverallQual',  'SalePrice', 'PoolArea', 'GarageArea', 'BedroomAbvGr', 'KitchenAbvGr', 'Fireplaces']
data = data.drop(data.columns.difference(columns_ndrop), 1)

data_sc = StandardScaler().fit_transform(data)

Let's create a PCA model:

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pca = PCA(n_components = 3, whiten = True)
pca = pca.fit(data_sc)

Now, to explain the results obtained, we will create a heat map of the factor loading. In the next section, we will learn why we need it.

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factor_analysis = pca.components_.T * np.sqrt(pca.explained_variance_)
fig, ax = plt.subplots(figsize=(3, 20))

sns.heatmap(factor_analysis, xticklabels = ["C1", "C2", "C3"], 
      yticklabels = data_sc.columns, annot = True, 
      cmap = "YlGnBu")
plt.show()

In just a couple of steps, we reduced the dimension of the dataset from 10 characteristics to 3! In the next chapter, we will try to interpret the results of PCA.