Update app.py

app.py

@@ -17,7 +17,16 @@ theme = gr.themes.Monochrome(
 
 description = f"""
 ## Description
-This demo can be used to evaluate the ability of k-means initializations strategies to make the algorithm convergence robust
+This demo can be used to evaluate the ability of k-means initializations strategies to make the algorithm convergence robust as measured by the 
+relative standard deviation of the inertia of the clustering (i.e. the sum of squared distances to the nearest cluster center).
+
+The dataset used for evaluation is a 2D grid of isotropic Gaussian clusters widely spaced.
+
+The Inertia plot shows the best inertia reached for each combination of the model (KMeans or MiniBatchKMeans), and either random initialization or k-means++ initialization.
+
+The Cluster Allocation plot demonstrates one single run of the MiniBatchKMeans estimator using a single random initialization. 
+
+The demo is based on the [scikit-learn docs](https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_stability_low_dim_dense.html#sphx-glr-auto-examples-cluster-plot-kmeans-stability-low-dim-dense-py)
 """
 
 # k-means models can do several random inits so as to be able to trade
@@ -116,6 +125,8 @@ with gr.Blocks(theme=theme) as demo:
     with gr.Row():
         n_runs = gr.Slider(minimum=1, maximum=10, step=1, value=5, label="Number of Evaluation Runs")
         random_state = gr.Slider(minimum=0, maximum=2000, step=5, value=0, label="Random state")
+    
+    with gr.Row():    
         n_samples_per_center = gr.Slider(minimum=50, maximum=200, step=10, value=100, label="Number of Samples per Center")
         grid_size = gr.Slider(minimum=1, maximum=8, step=1, value=3, label="Grid Size")