[Maki TANAKA] - Fab Futures - Data Science

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7. Transforms

Preprocessing

What I've learnt;

• Preprocessing -> we need to do before analysing.
• Standardization -> All units are changed to same scale

PCA

My "classmate" Rico introduced us one YouTube video about PCA, and I learnt. As sample code is shown in that YouTube, I copied that code and modify it for using my dataset.
I also asked chatGPT to change dataset from sample data to my dataset(Wine).

import pandas as pd
import numpy as np
df = pd.read_csv('./datasets/Wine_dataset.csv')

Display main factors

Five main components were extracted from all items.(with Tsuchiya-san's advice)

import sklearn
X = df.to_numpy() #make array of winedata

# Align the size of the numbers
# mean:0 variance:1
scaler = sklearn.preprocessing.StandardScaler()
Xscale = scaler.fit_transform(X)
pca = sklearn.decomposition.PCA(n_components=5)
pca.fit(Xscale)
print(f"explained variance: {pca.explained_variance_}")

explained variance: [5.56722458 2.51118402 1.45424413 0.9331603  0.88246016]

Next, I see that each main componet explains what percentage of the overall information.

contribution_ratios = pd.DataFrame(pca.explained_variance_ratio_)
contribution_ratios

	0
0	0.395425
1	0.178363
2	0.103291
3	0.066280
4	0.062679

It is shown cumulative sum, which indicates the percentage of the whole by adding the principal components.

cumulative_contribution_ratios = contribution_ratios.cumsum()
cumulative_contribution_ratios

	0
0	0.395425
1	0.573787
2	0.677078
3	0.743358
4	0.806037

Then the major items are indicated.

loadings = pd.DataFrame(pca.components_.T, index=df.columns)
loadings.round(3)

	0	1	2	3	4
class	0.394	0.006	0.001	0.122	0.158
Alcohol	-0.136	0.484	-0.207	-0.082	-0.251
Malic acid	0.223	0.224	0.089	0.470	-0.189
Ash	-0.002	0.316	0.626	-0.250	-0.094
Alcalinity of ash	0.224	-0.012	0.612	0.072	0.047
Magnesium	-0.125	0.301	0.131	-0.163	0.778
Total phenols	-0.359	0.067	0.147	0.191	-0.145
Flavanoids	-0.391	-0.001	0.151	0.145	-0.112
Nonflavanoid phenols	0.267	0.027	0.170	-0.328	-0.433
Proanthocyanins	-0.279	0.041	0.150	0.463	0.092
Color intensity	0.089	0.530	-0.137	0.072	-0.046
Hue	-0.277	-0.278	0.085	-0.435	-0.030
OD280/OD315 of diluted wines	-0.351	-0.163	0.166	0.157	-0.144
Proline	-0.270	0.366	-0.127	-0.256	-0.084

PCA plotting

I make a graph of percentage that each factor effects　and scatter plot of CP1 and CP2.

import pandas as pd
import numpy as np
from sklearn.decomposition import PCA
from sklearn import preprocessing
import matplotlib.pyplot as plt

# ① CSV を読み込む（ここだけ変更）
df = pd.read_csv('./datasets/Wine_dataset.csv')

# ② 特徴量だけ取り出す（ここだけ変更）
# ※ 最初の列が "Class" なので除外、残り13列が特徴量
data = df.drop(columns=[df.columns[0]])

# ③ サンプル名を行インデックスにする（ここだけ変更）
# Wine の場合、サンプル名は無いので番号でOK
sample_names = [f"sample{i}" for i in range(len(data))]

# ④ PCA の前処理（元コードの通り）
scaled_data = preprocessing.scale(data.values)

pca = PCA()
pca.fit(scaled_data)
pca_data = pca.transform(scaled_data)

per_var = np.round(pca.explained_variance_ratio_ * 100, 1)
labels = ['PC' + str(x) for x in range(1, len(per_var)+1)]

# スクリープロット
plt.bar(x=range(1, len(per_var)+1), height=per_var, tick_label=labels)
plt.ylabel('Percentage of Explained Variance')
plt.xlabel('Principal Component')
plt.title('Scree Plot (Wine Data)')
plt.show()

# PCA 結果をデータフレーム化
pca_df = pd.DataFrame(pca_data, index=sample_names, columns=labels)

# 散布図（PC1 vs PC2）
plt.scatter(pca_df.PC1, pca_df.PC2, alpha=0.6)
plt.title('PCA of Wine Dataset')
plt.xlabel(f'PC1 - {per_var[0]}%')
plt.ylabel(f'PC2 - {per_var[1]}%')

# サンプル名を表示
#for sample in pca_df.index:
#    plt.annotate(sample, (pca_df.PC1.loc[sample], pca_df.PC2.loc[sample]))

plt.show()

Then I learn Neil's sample code using my dataset.

import numpy as np
import matplotlib.pyplot as plt
import sklearn

np.set_printoptions(precision=1)
#
# load wine dataset data
#
# class をラベル、それ以外を特徴量にする
y = df['class'].to_numpy()
X = df.drop(columns=['class']).to_numpy()
print(f"Wine data shape (records,features): {X.shape}")

#
# plot vs two pixel values
#
plt.scatter(X[:,0], X[:,1], c=y)
plt.xlabel(df.columns[1])
plt.ylabel(df.columns[2])
plt.title("Wine vs two original features")
plt.colorbar(label="digit")
plt.show()

#
# standardize (zero mean, unit variance) to eliminate dependence on data scaling
#
print(f"data mean: {np.mean(X):.2f}, variance: {np.var(X):.2f}")
X = X-np.mean(X,axis=0)
std = np.std(X,axis=0)
Xscale = X/np.where(std > 0,std,1)
print(f"standardized data mean: {np.mean(Xscale):.2f}, variance: {np.var(Xscale):.2f}")
#
# do 50 component PCA
#
pca = sklearn.decomposition.PCA(n_components=5)
pca.fit(Xscale)
Xpca = pca.transform(Xscale)
plt.plot(pca.explained_variance_,'o')
plt.plot()
plt.xlabel('PCA component')
plt.ylabel('explained variance')
plt.title('MNIST PCA')
plt.show()
#
# plot vs first two PCA components
#
plt.scatter(Xpca[:,0],Xpca[:,1],c=y,s=3)
plt.xlabel("principal component 1")
plt.ylabel("principal component 2")
plt.title("MNIST vs two principal components")
plt.colorbar(label="digit")
plt.show()

Wine data shape (records,features): (178, 13)

data mean: 69.13, variance: 46546.42
standardized data mean: -0.00, variance: 1.00