3DPCA

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 更新后的数据点
points = {
    'blue': np.array([
        [-12, 6, 0],
        [-13, 3, 0],
        [-15, 1, 0]
    ]),
    'green': np.array([
        [2, 0, 0],
        [3, 0, 0],
        [4, -2, 0]
    ]),
    'orange': np.array([
        [-2, 8, 8],
        [-4, 3, 2]
    ]),
    'pink': np.array([
        [-3, 6, 5],
        [-5, 2, 3],
    ])
}

def draw_ellipsoid(ax, center, radii, rotation, color, alpha=0.2):
    u = np.linspace(0, 2 * np.pi, 100)
    v = np.linspace(0, np.pi, 100)
    x = radii[0] * np.outer(np.cos(u), np.sin(v))
    y = radii[1] * np.outer(np.sin(u), np.sin(v))
    z = radii[2] * np.outer(np.ones_like(u), np.cos(v))
    
    for i in range(len(x)):
        for j in range(len(x)):
            [x[i,j],y[i,j],z[i,j]] = np.dot([x[i,j],y[i,j],z[i,j]], rotation) + center

    ax.plot_surface(x, y, z, color=color, alpha=alpha)

# 创建图形
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')

# 设置白色背景
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
ax.xaxis.pane.set_edgecolor('white')
ax.yaxis.pane.set_edgecolor('white')
ax.zaxis.pane.set_edgecolor('white')
ax.set_facecolor('white')

# 绘制散点图和椭圆
for color, coords in points.items():
    # 绘制散点
    ax.scatter(coords[:, 0], coords[:, 1], coords[:, 2], 
              c=color, s=100, alpha=1.0)
    
    # 添加椭圆
    center = np.mean(coords, axis=0)
    if color == 'blue':
        radii = [2, 3, 1]
        rotation = np.array([[0.8, -0.2, 0], [0.2, 0.8, 0], [0, 0, 1]])
    elif color == 'green':
        radii = [2, 2, 1]
        rotation = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
    elif color in ['orange', 'pink']:
        # 为橙色和粉色点共用一个更大的椭圆
        if color == 'orange':
            radii = [3, 4, 4]
            rotation = np.array([[0.9, -0.1, 0], [0.1, 0.9, 0], [0, 0, 1]])
    
    draw_ellipsoid(ax, center, radii, rotation, color, alpha=0.1)

# 设置坐标轴标签
ax.set_xlabel('PC1')
ax.set_ylabel('PC2')
ax.set_zlabel('PC3')

# 设置坐标轴范围
ax.set_xlim([-15, 5])
ax.set_ylim([-5, 10])
ax.set_zlim([-5, 10])

# 设置网格线
ax.grid(True, linestyle='--', alpha=0.3)

# 调整视角
ax.view_init(elev=20, azim=-45)

plt.show()

image.png

import plotly.graph_objects as go
import plotly.express as px
import numpy as np
from sklearn.manifold import TSNE

def generate_ellipsoid_mesh(center, radii, rotation, n_points=50):
    u = np.linspace(0, 2 * np.pi, n_points)
    v = np.linspace(0, np.pi, n_points)
    
    x = radii[0] * np.outer(np.cos(u), np.sin(v))
    y = radii[1] * np.outer(np.sin(u), np.sin(v))
    z = radii[2] * np.outer(np.ones_like(u), np.cos(v))
    
    # 应用旋转和平移
    points = np.stack([x.flatten(), y.flatten(), z.flatten()])
    transformed_points = np.dot(rotation, points) + center.reshape(-1, 1)
    
    x = transformed_points[0].reshape(n_points, n_points)
    y = transformed_points[1].reshape(n_points, n_points)
    z = transformed_points[2].reshape(n_points, n_points)
    
    return x, y, z

# 年龄分组函数
def age_to_group(age):
    if age == 0:
        return 0
    elif 0  0:  # 如果该组有数据点
        group_points = features_3d[mask]
        
        # 添加散点
        fig.add_trace(go.Scatter3d(
            x=group_points[:, 0],
            y=group_points[:, 1],
            z=group_points[:, 2],
            mode='markers',
            name=label,
            marker=dict(
                size=5,
                color=colors[i % len(colors)],
                opacity=0.6
            ),
            showlegend=True
        ))
        
        # 计算并添加椭圆
        if len(group_points) > 1:
            center = np.mean(group_points, axis=0)
            cov = np.cov(group_points.T)
            eigenvals, eigenvecs = np.linalg.eigh(cov)
            radii = 2 * np.sqrt(eigenvals)
            radii = np.maximum(radii, 0.1)
            
            x, y, z = generate_ellipsoid_mesh(center, radii, eigenvecs)
            
            fig.add_trace(go.Surface(
                x=x, y=y, z=z,
                colorscale=[[0, colors[i % len(colors)]], [1, colors[i % len(colors)]]],
                showscale=False,
                opacity=0.2,
                name=f'{label}_surface',
                showlegend=False
            ))

# 更新布局
fig.update_layout(
    title='t-SNE 3D Visualization with Age Groups',
    scene=dict(
        xaxis_title='t-SNE 1',
        yaxis_title='t-SNE 2',
        zaxis_title='t-SNE 3',
        bgcolor='white'
    ),
    showlegend=True,
    legend=dict(
        yanchor="top",
        y=0.99,
        xanchor="left",
        x=1.05
    ),
    margin=dict(l=0, r=0, t=30, b=0)
)

# 更新场景配置
fig.update_scenes(
    camera=dict(
        up=dict(x=0, y=0, z=1),
        center=dict(x=0, y=0, z=0),
        eye=dict(x=1.5, y=1.5, z=1.5)
    )
)

# 显示图形
fig.show()

image.png

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