一文带您了解伪对数(Pseudo-Log)：可视化倾斜数据的黄金方法

import numpy as np
import matplotlib.pyplot as plt


# 伪对数10变换函数
def pseudo_log10(x):
    return np.log(x/2+np.sqrt(x*x/4+1))/np.log(10)


# 定义数据
x = np.linspace(-15, 15, 400)
y_pseudo_log10 = pseudo_log10(x)
y_log10 = np.log10(x[200:])  


# 创建图形
plt.figure(figsize=(10, 6))


# 绘制伪对数10变换的曲线，绘制经典对数10变换的曲线
plt.plot(x, y_pseudo_log10, label='Pseudo-log10 Transformation', color='blue')
plt.plot(x[200:], y_log10, label='Classic log10 Transformation', color='black')


# 添加图例
plt.legend()


# 添加标题和标签
plt.title('Comparison of Pseudo-log10 and Classic log10 Transformations')
plt.xlabel('x')
plt.ylabel('Transformed value')


# 显示图形
plt.grid(True)
plt.show()

import numpy as np
import matplotlib.pyplot as plt


# 生成1000个来自右偏分布的样本
data = np.random.exponential(scale=2, size=1000)


# 定义伪对数变换函数
def pseudo_log(x):
    return np.log(x/2+np.sqrt(x*x/4+1))/np.log(10)


# 对数据应用变换
log_data = np.log(data)
pseudo_log_data = pseudo_log(data)


# 绘制原始数据、对数变换数据和伪对数变换数据
plt.figure(figsize=(12, 8))


# 绘制原始数据
plt.subplot(3, 1, 1)
plt.hist(data, bins=50, color='blue', alpha=0.7, label='Original Data')
plt.legend()
plt.title('Original Data')


# 绘制对数变换数据
plt.subplot(3, 1, 2)
plt.hist(log_data, bins=50, color='green', alpha=0.7, label='Log-Transformed Data')
plt.legend()
plt.title('Log-Transformed Data')


# 绘制伪对数变换数据
plt.subplot(3, 1, 3)
plt.hist(pseudo_log_data, bins=50, color='red', alpha=0.7, label='Pseudo-Log-Transformed Data')
plt.legend()
plt.title('Pseudo-Log-Transformed Data')


plt.tight_layout()
plt.show()

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns


# Simulate some population density data with a wider range
np.random.seed(42)
data = np.concatenate([np.random.lognormal(mean=0, sigma=2.0, size=(10, 20)), 
                       0-np.random.lognormal(mean=0, sigma=2.0, size=(10, 20))])


# Function to plot the heatmaps
def plot_heatmaps(data):
    fig, axes = plt.subplots(1, 3, figsize=(18, 6))
    
    # Linear color scale
    sns.heatmap(data, ax=axes[0], cmap='viridis', cbar_kws={'label': 'population density / km²'})
    axes[0].set_title('Linear color scale')


    # Log10 transformation
    log_data = np.log10(data + 1)
    sns.heatmap(log_data, ax=axes[1], cmap='viridis', cbar_kws={'label': 'log10(population density / km²)'})
    axes[1].set_title('log10 transformation')
    
    # Pseudo-log transformation (log + sqrt)
    pseudo_log_data = np.log(data + np.sqrt(data**2 + 1))
    sns.heatmap(pseudo_log_data, ax=axes[2], cmap='viridis', cbar_kws={'label': 'pseudo-log(population density / km²)'})
    axes[2].set_title('pseudo-log transformation')
    
    plt.tight_layout()
    plt.show()


plot_heatmaps(data)