Update app.py

incoporated the review comments

app.py

@@ -54,7 +54,7 @@ def visualize_input_data():
 
 
 title = " An example using IsolationForest for anomaly detection."
-description1 = "The isolation forest is an Ensemble of Isolation trees and it isolates the datapoints using recursive random partitioning."
+description1 = "The isolation forest is an Ensemble of Isolation trees and it isolates the data points using recursive random partitioning."
 description2 = "In case of outliers the number of splits required is greater than those required for inliers."
 description3 = "We will use the toy dataset as given in the scikit-learn page for Isolation Forest."
 
@@ -64,7 +64,7 @@ with gr.Blocks(title=title) as demo:
     gr.Markdown(
     """
     The isolation forest is an ensemble of isolation trees and it isolates the data points using recursive random partitioning.
-    In case of outliers the number of splits required is greater than those required for inliers.
+    In case of outliers, the number of splits required is greater than those required for inliers.
     We will use the toy dataset for our educational demo as given in the scikit-learn page for Isolation Forest.
     
     """)
@@ -75,13 +75,55 @@ with gr.Blocks(title=title) as demo:
 
     with gr.Tab("Visualize Input dataset"):
         btn = gr.Button(value="Visualize input dataset")
-        btn.click(visualize_input_data, outputs= gr.Plot(label='Visualizing input dataset') )
-
-    with gr.Tab("Plot Decision Boundary"):
+        with gr.Row():
+        
+            btn.click(visualize_input_data, outputs= gr.Plot(label='Visualizing input dataset') )
+            # out = gr.Textbox(label="explaination of the loss function")
+            gr.Markdown(
+            """
+            # Data Generation
+            We generate 2 clusters one spherical and the other slightly deformed, from Standard Normal distribution
+            For the sake of consistency inliers are assigned a ground label of 1 and outliers are assigned a label -1.
+            The plot is a visualization of the clusters of the input dataset.
+
+            """)
+
+    with gr.Tab("**Plot Decision Boundary**"):
+      # btn_decision = gr.Button(value="Plot decision boundary")
+      # btn_decision.click(plot_decision_boundary, outputs= gr.Plot(label='Plot decision boundary') )
+      with gr.Row():
         image_decision = gr.Image('./downloaded-model/decision_boundary.png')
+        gr.Markdown(
+        """
+        # Plot the Discrete Decision Boundary
+        We plot the discrete decision boundary. 
+        The background colour represents whether a sample in that given area is predicted to be an outlier or not. 
+        The scatter plot displays the true labels
+
+        """)
     
     with gr.Tab("Plot Path"):
+      with gr.Row():
         image_path = gr.Image('./downloaded-model/plot_path.png')
+        gr.Markdown(
+        """
+        # Plot the path length of the decision boundary
+        By setting the response_method="decision_function", the background of the DecisionBoundaryDisplay represents 
+        the measure of the normality of an observation. 
+
+        Normality of Observation = path length/(Number_of_forests_of_random trees) - Eqn.1 
+
+        
+        The RHS of the above equation Eqn.1 is given by the number of splits required to isolate a given sample
+        Such score is given by the path length averaged over a forest of random trees, which itself is given by the depth of 
+        the leaf (or equivalently the number of splits) 
+        required to isolate a given sample.
+
+        When a forest of random trees collectively produces short path lengths for isolating some particular samples, 
+        they are highly likely to be anomalies and the measure of normality is close to 0. 
+        Similarly, large paths correspond to values close to 1 and are more likely to be inliers.
+
+        """)
 
     
     gr.Markdown( f"## Success")