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Book4_Ch03_Python_Codes/Streamlit_Bk4_Ch3_03.py

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+
+###############
+# Authored by Weisheng Jiang
+# Book 4  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+import plotly.graph_objects as go
+import streamlit as st
+import numpy as np
+import plotly.express as px
+import pandas as pd
+import sympy
+from scipy.spatial import distance
+
+#%% define a function for distances
+
+def fcn_Minkowski(xx, yy, mu, p = 2, Chebychev = False):
+    
+    if Chebychev:
+        
+        zz = np.maximum(np.abs(xx - mu[0]),np.abs(yy - mu[1]))
+        
+    else:
+        zz = ((np.abs((xx - mu[0]))**p) + (np.abs((yy - mu[1]))**p))**(1./p)
+    
+    return zz
+
+def fcn_mahal(xx, yy, mu, Sigma, standardized = False):
+    
+    if standardized:
+        
+        D = np.diag(np.diag(Sigma))
+        Sigma_inv = np.linalg.inv(D)
+        
+    else:
+        Sigma_inv = np.linalg.inv(Sigma)
+    
+    xy_ = np.stack((xx.flatten(), yy.flatten())).T
+
+    zz = np.diag(np.sqrt(np.dot(np.dot((xy_-mu),Sigma_inv),(xy_-mu).T)))
+    
+    zz = np.reshape(zz,xx.shape)
+    
+    return zz
+
+
+#%%
+df = px.data.iris()
+
+with st.sidebar:
+    
+    dist_type = st.radio('Choose a type of distance: ',
+             options = ['Euclidean',
+                        'City block',
+                        'Minkowski',
+                        'Chebychev',
+                        'Mahalanobis',
+                        'Standardized Euclidean'])
+    
+    if dist_type == 'Minkowski':
+        
+        with st.sidebar:
+            p = st.slider('Specify a p value:',1.0, 20.0, step = 0.5)
+            
+            
+#%% compute distance
+
+X = df[['sepal_length', 'petal_length']]
+
+mu = X.mean().to_numpy()
+Sigma = X.cov().to_numpy()
+
+# st.write(mu)
+# st.write(Sigma)
+
+x_array = np.linspace(0,10,101)
+y_array = np.linspace(0,10,101)
+
+xx,yy = np.meshgrid(x_array,y_array)
+
+
+if dist_type == 'Minkowski':
+    
+    zz = fcn_Minkowski(xx, yy, mu, p)
+
+elif dist_type == 'Euclidean':
+    
+    zz = fcn_Minkowski(xx, yy, mu, 2)
+
+elif dist_type == 'Chebychev':
+    
+    zz = fcn_Minkowski(xx, yy, mu, Chebychev = True)
+    
+elif dist_type == 'Mahalanobis':
+    
+    zz = fcn_mahal(xx, yy, mu, Sigma)
+    
+elif dist_type == 'City block':
+    zz = fcn_Minkowski(xx, yy, mu, 1)
+    
+elif dist_type == 'Standardized Euclidean':
+    
+    zz = fcn_mahal(xx, yy, mu, Sigma, True)
+    # st.write(zz)
+
+#%% Visualization
+
+st.title(dist_type + ' distance')
+
+# Scatter plot
+fig_2 = px.scatter(df, x='sepal_length', y='petal_length')
+
+# plot distance contour
+fig_2.add_trace(go.Contour(
+    x = x_array,
+    y = y_array,
+    z = zz,
+    contours_coloring='lines',
+    showscale=False)
+    )
+
+# st.write(X.mean().to_frame().T)
+
+# plot centroid
+# fig_2.add_traces(
+#     px.scatter(X.mean().to_frame().T, 
+#                 x='sepal_length', 
+#                 y='petal_length').update_traces(
+#         marker_size=20, 
+#         marker_color="yellow").data)
+
+fig_2.add_traces(
+    px.scatter(X.mean().to_frame().T, 
+               x='sepal_length', 
+               y='petal_length').update_traces(
+        marker_size=20, 
+        marker_color="red",
+        marker_symbol= 'x').data)
+
+fig_2.update_layout(yaxis_range=[0,10])
+fig_2.update_layout(xaxis_range=[0,10])
+fig_2.add_hline(y=mu[1])
+fig_2.add_vline(x=mu[0])
+fig_2.update_yaxes(
+    scaleratio = 1,
+  )
+
+
+fig_2.update_layout(width=600, height=600)
+
+st.plotly_chart(fig_2)
+
+
+