import streamlit as st import numpy as np from pathlib import Path from experiments.gmm_dataset import GeneralizedGaussianMixture import plotly.graph_objects as go from plotly.subplots import make_subplots from typing import List, Tuple def init_session_state(): """初始化session state""" if 'prev_K' not in st.session_state: st.session_state.prev_K = 3 if 'p' not in st.session_state: st.session_state.p = 2.0 if 'centers' not in st.session_state: st.session_state.centers = np.array([[-2, -2], [0, 0], [2, 2]], dtype=np.float64) if 'scales' not in st.session_state: st.session_state.scales = np.array([[0.3, 0.3], [0.2, 0.2], [0.4, 0.4]], dtype=np.float64) if 'weights' not in st.session_state: st.session_state.weights = np.ones(3, dtype=np.float64) / 3 if 'sample_points' not in st.session_state: st.session_state.sample_points = None def create_default_parameters(K: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: """创建默认参数""" # 在[-3, 3]范围内均匀生成K个中心点 x = np.linspace(-3, 3, K) y = np.linspace(-3, 3, K) centers = np.column_stack((x, y)) # 默认尺度和权重 scales = np.ones((K, 2), dtype=np.float64) * 3 weights = np.random.random(size=K).astype(np.float64) weights /= weights.sum() # 归一化权重 return centers, scales, weights def generate_latex_formula(p: float, K: int, centers: np.ndarray, scales: np.ndarray, weights: np.ndarray) -> str: """生成LaTeX公式""" formula = r"P(x) = \sum_{k=1}^{" + str(K) + r"} \pi_k P_{\theta_k}(x) \\" formula += r"P_{\theta_k}(x) = \eta_k \exp(-s_k d_k(x)) = \frac{p}{2\alpha_k \Gamma(1/p) }\exp(-\frac{|x-c_k|^p}{\alpha_k^p})= \frac{p}{2\alpha_k \Gamma(1/p) }\exp(-|\frac{x-c_k}{\alpha_k}|^p) \\" formula += r"\text{where: }" for k in range(K): c = centers[k] s = scales[k] w = weights[k] component = f"P_{k+1}(x) = \\frac{{{p:.1f}}}{{2\\alpha_{k+1} \\Gamma(1/{p:.1f})}}\\exp(-|\\frac{{x-({c[0]:.1f}, {c[1]:.1f})}}{{{s[0]:.1f}, {s[1]:.1f}}}|^{{{p:.1f}}}) \\\\" formula += component formula += f"\\pi_{k+1} = {w:.2f} \\\\" return formula st.set_page_config(page_title="GMM Distribution Visualization", layout="wide") st.title("广义高斯混合分布可视化") # 初始化session state init_session_state() # 侧边栏参数设置 with st.sidebar: st.header("分布参数") # 分布基本参数 st.session_state.p = st.slider("形状参数 (p)", 0.1, 5.0, st.session_state.p, 0.1, help="p=1: 拉普拉斯分布, p=2: 高斯分布, p→∞: 均匀分布") K = st.slider("分量数 (K)", 1, 5, st.session_state.prev_K) # 如果K发生变化，重新初始化参数 if K != st.session_state.prev_K: centers, scales, weights = create_default_parameters(K) st.session_state.centers = centers st.session_state.scales = scales st.session_state.weights = weights st.session_state.prev_K = K # 高级参数设置 st.subheader("高级设置") show_advanced = st.checkbox("显示分量参数", value=False) if show_advanced: # 为每个分量设置参数 centers_list: List[List[float]] = [] scales_list: List[List[float]] = [] weights_list: List[float] = [] for k in range(K): st.write(f"分量 {k+1}") col1, col2 = st.columns(2) with col1: cx = st.number_input(f"中心X_{k+1}", -5.0, 5.0, float(st.session_state.centers[k][0]), 0.1) cy = st.number_input(f"中心Y_{k+1}", -5.0, 5.0, float(st.session_state.centers[k][1]), 0.1) with col2: sx = st.number_input(f"尺度X_{k+1}", 0.1, 3.0, float(st.session_state.scales[k][0]), 0.1) sy = st.number_input(f"尺度Y_{k+1}", 0.1, 3.0, float(st.session_state.scales[k][1]), 0.1) w = st.slider(f"权重_{k+1}", 0.0, 1.0, float(st.session_state.weights[k]), 0.1) centers_list.append([cx, cy]) scales_list.append([sx, sy]) weights_list.append(w) centers = np.array(centers_list, dtype=np.float64) scales = np.array(scales_list, dtype=np.float64) weights = np.array(weights_list, dtype=np.float64) weights = weights / weights.sum() st.session_state.centers = centers st.session_state.scales = scales st.session_state.weights = weights else: centers = st.session_state.centers scales = st.session_state.scales weights = st.session_state.weights # 采样设置 st.subheader("采样设置") n_samples = st.slider("采样点数", 5, 20, 10) if st.button("重新采样"): # 生成随机样本 samples = [] for _ in range(n_samples): # 选择分量 k = np.random.choice(K, p=weights) # 从选定的分量生成样本 sample = np.random.normal(centers[k], scales[k], size=2) samples.append(sample) st.session_state.sample_points = np.array(samples) # 创建GMM数据集 dataset = GeneralizedGaussianMixture( D=2, K=K, p=st.session_state.p, centers=centers[:K], scales=scales[:K], weights=weights[:K] ) # 生成网格数据 x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) xy = np.column_stack((X.ravel(), Y.ravel())) # 计算概率密度 Z = dataset.pdf(xy).reshape(X.shape) # 创建2D和3D可视化 fig = make_subplots( rows=1, cols=2, specs=[[{'type': 'surface'}, {'type': 'contour'}]], subplot_titles=('3D概率密度曲面', '等高线图与分量中心') ) # 3D Surface surface = go.Surface( x=X, y=Y, z=Z, colorscale='viridis', showscale=True, colorbar=dict(x=0.45) ) fig.add_trace(surface, row=1, col=1) # Contour Plot with component centers contour = go.Contour( x=x, y=y, z=Z, colorscale='viridis', showscale=True, colorbar=dict(x=1.0), contours=dict( showlabels=True, labelfont=dict(size=12) ) ) fig.add_trace(contour, row=1, col=2) # 添加分量中心点 fig.add_trace( go.Scatter( x=centers[:K, 0], y=centers[:K, 1], mode='markers+text', marker=dict(size=10, color='red'), text=[f'C{i+1}' for i in range(K)], textposition="top center", name='分量中心' ), row=1, col=2 ) # 添加采样点（如果有） if st.session_state.sample_points is not None: samples = st.session_state.sample_points # 计算每个样本点的概率密度 probs = dataset.pdf(samples) # 计算每个样本点属于每个分量的后验概率 posteriors = [] for sample in samples: component_probs = [ weights[k] * np.exp(-np.sum(((sample - centers[k]) / scales[k])**st.session_state.p)) for k in range(K) ] total = sum(component_probs) posteriors.append([p/total for p in component_probs]) # 添加样本点到图表 fig.add_trace( go.Scatter( x=samples[:, 0], y=samples[:, 1], mode='markers+text', marker=dict( size=8, color='yellow', line=dict(color='black', width=1) ), text=[f'S{i+1}' for i in range(len(samples))], textposition="bottom center", name='采样点' ), row=1, col=2 ) # 显示样本点的概率信息 st.subheader("采样点信息") for i, (sample, prob, post) in enumerate(zip(samples, probs, posteriors)): st.write(f"样本点 S{i+1} ({sample[0]:.2f}, {sample[1]:.2f}):") st.write(f"- 概率密度: {prob:.4f}") st.write("- 后验概率:") for k in range(K): st.write(f" - 分量 {k+1}: {post[k]:.4f}") st.write("---") # 更新布局 fig.update_layout( title='广义高斯混合分布', showlegend=True, width=1200, height=600, scene=dict( xaxis_title='X', yaxis_title='Y', zaxis_title='密度' ) ) # 更新2D图的坐标轴 fig.update_xaxes(title_text='X', row=1, col=2) fig.update_yaxes(title_text='Y', row=1, col=2) # 显示图形 st.plotly_chart(fig, use_container_width=True) # 添加参数说明 with st.expander("分布参数说明"): st.markdown(""" - **形状参数 (p)**：控制分布的形状 - p = 1: 拉普拉斯分布 - p = 2: 高斯分布 - p → ∞: 均匀分布 - **分量参数**：每个分量由以下参数确定 - 中心 (μ): 峰值位置，通过X和Y坐标确定 - 尺度 (α): 分布的展宽程度，X和Y方向可不同 - 权重 (π): 混合系数，所有分量权重和为1 """) # 显示当前参数的数学公式 st.latex(generate_latex_formula(st.session_state.p, K, centers[:K], scales[:K], weights[:K]))