何らかの測定データの異常値を検出する方法をサンプルデータを用いて３つ示す．

移動平均法

MovingAve_detect_outlier.py

# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# サンプルデータ: 30日間の測定データ
production_data = [
    520, 510, 515, 530, 525, 535, 540, 515, 525, 530,
    520, 510, 515, 525, 530, 535, 540, 545, 550, 555,
    530, 525, 520, 515, 510, 505, 500, 495, 490, 700  # 最後のデータが異常に高い
]

def detect_outliers_moving_average(data, window=5, n_sigmas=2):
    df = pd.DataFrame(data, columns=['value'])
    df['moving_avg'] = df['value'].rolling(window=window, center=True).mean()
    df['moving_std'] = df['value'].rolling(window=window, center=True).std()
    
    df['lower_bound'] = df['moving_avg'] - n_sigmas * df['moving_std']
    df['upper_bound'] = df['moving_avg'] + n_sigmas * df['moving_std']
    
    df['is_outlier'] = (df['value'] < df['lower_bound']) | (df['value'] > df['upper_bound'])
    
    outliers = df[df['is_outlier']].index.tolist()
    return df, outliers

# 異常値の検出
df, outliers = detect_outliers_moving_average(production_data)

print("Detected Outliers:")
for day in outliers:
    print(f"Date: {day+1}, Volume: {production_data[day]}")

# データのプロット
plt.figure(figsize=(12, 6))
plt.plot(range(1, 31), production_data, marker='o', label='Volume')
plt.plot(range(1, 31), df['moving_avg'], label='Moving Average')
plt.fill_between(range(1, 31), df['lower_bound'], df['upper_bound'], alpha=0.2, label='Normal range')

for day in outliers:
    plt.plot(day+1, production_data[day], 'ro', markersize=10)

plt.title('Outlier Detection by Moving Average')
plt.xlabel('Day')
plt.ylabel('Volume')
plt.legend()
plt.grid(True)
plt.show()

IQR

IQR_detect_outlier.py

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt

production_data = [
    520, 510, 515, 530, 525, 535, 540, 515, 525, 530,
    520, 510, 515, 525, 530, 535, 540, 545, 550, 555,
    530, 525, 520, 515, 510, 505, 500, 495, 490, 700  # 最後のデータが異常に高い
]

def detect_outliers_iqr(data):
    q1 = np.percentile(data, 25)
    q3 = np.percentile(data, 75)
    iqr = q3 - q1
    lower_bound = q1 - (1.5 * iqr)
    upper_bound = q3 + (1.5 * iqr)
    return [(i, x) for i, x in enumerate(data) if x < lower_bound or x > upper_bound]

# 異常値の検出
outliers = detect_outliers_iqr(production_data)

print("Detected Outliers : ")
for day, value in outliers:
    print(f"Date: {day+1}, Volume: {value}")

# データのプロット
plt.figure(figsize=(12, 6))
plt.plot(range(1, 31), production_data, marker='o', label='Production Volume')
for day, value in outliers:
    plt.plot(day+1, value, 'ro', markersize=10, label='Outlier' if day == outliers[0][0] else "")

# IQRの範囲を表示
q1 = np.percentile(production_data, 25)
q3 = np.percentile(production_data, 75)
iqr = q3 - q1
lower_bound = q1 - (1.5 * iqr)
upper_bound = q3 + (1.5 * iqr)
plt.axhline(y=lower_bound, color='r', linestyle='--', label='IQR')
plt.axhline(y=upper_bound, color='r', linestyle='--')

plt.title('Production Volume and Outlier Detection by IQR')
plt.xlabel('Date')
plt.ylabel('Production Volume')
plt.legend()
plt.grid(True)
plt.show()

Ｚ Score

zscore_detect_outlier.py

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt

# サンプルデータ: 30日間の測定データ
production_data = [
    520, 510, 515, 530, 525, 535, 540, 515, 525, 530,
    520, 510, 515, 525, 530, 535, 540, 545, 550, 555,
    530, 525, 520, 515, 510, 505, 500, 495, 490, 700  # 最後のデータが異常に高い
]

# Zスコアを計算する関数
def calculate_zscore(data):
    mean = np.mean(data)
    std = np.std(data)
    return [(x - mean) / std for x in data]

# Zスコアの計算
zscore = calculate_zscore(production_data)

# 異常値の検出（閾値は2.5とする）
threshold = 2.5
outliers = [(i, production_data[i]) for i, zscore in enumerate(zscore) if abs(zscore) > threshold]

print("Detected Outliers : ")
for day, value in outliers:
    print(f"Date: {day+1}, Volume: {value}, Zscore: {zscore[day]:.2f}")

# データのプロット
plt.figure(figsize=(12, 6))
plt.plot(range(1, 31), production_data, marker='o')
for day, value in outliers:
    plt.plot(day+1, value, 'ro', markersize=10)  # 異常値を赤で表示

plt.title('Measured data')
plt.xlabel('Day')
plt.ylabel('Value')
plt.grid(True)
plt.show()