Separate Clearly Defined clusters with DBSCAN

I have a dataset with 4 features,with features (1,4) and (2,4) clearly separable.

I am trying to use DBSCAN to come up with the Clusters, however I am unable to create satisfatocty clusters.

Here is the code snippet where I:

• iterate over all combinations of eps and min_sample values.
• Run DBSCAN
• save the results if Clustes are more than 1, and less than 7

#### STEP 4: DBSCAN ####
# Define the parameter combinations to evaluate
eps_values = [0.01, 0.03, 0.05, 0.07, 0.1, 0.15]
min_samples_values = [2, 3, 5, 7, 10, 15]

# Iterate over parameter combinations
names = []
for eps, min_samples in itertools.product(eps_values, min_samples_values):
    # Create a DBSCAN object with the current parameter values
    dbscan = DBSCAN(eps=eps, min_samples=min_samples)

    # Fit the DBSCAN model to the data and obtain the cluster labels
    cluster_labels = dbscan.fit_predict(df_t[new_features])
    if len(pd.Series(cluster_labels).unique()) > 1: 
        if len(pd.Series(cluster_labels).unique()) < 7: 
            name = f"eps_{eps}_mins_{min_samples}"
            df_t[name] = cluster_labels
            names.append(name)
    # Filter out the outliers (-1 label) from the cluster labels
    filtered_labels = cluster_labels[cluster_labels != -1]
    print("Eps:", eps, "Min Samples:", min_samples, "clusters:", len(pd.Series(filtered_labels).unique()))

Here I am plotting the reuslts for clusters that have more than 1, less than 7 clusters. As you can see none of the param gave satisfactory clusters that look like the origianl data.

Q: is it the code/setup that is making it unable to cluster properely?

Here is the complete code that reproduces the example, for completeness. the steps are:

• import the data
• scale using minmax
• create new features using kernel PCA
• run DBSCAN the first 3 steps are just to setup the dataframe DATA to have hte correct features.

import pandas as pd
import requests
import zipfile
import seaborn as sns,  matplotlib.pyplot as plt


from sklearn.preprocessing import MinMaxScaler
from sklearn.manifold import MDS
from sklearn.cluster import DBSCAN


from itertools import combinations
import itertools 
%matplotlib inline

#### SETUP TO MAKE THE DATA ####


#### STEP1: IMPORT THE DATA ####

# Specify the URL of the ZIP file
zip_url = 'https://archive.ics.uci.edu/static/public/267/banknote+authentication.zip'

# Download the ZIP file
response = requests.get(zip_url)

# Save the ZIP file locally
zip_path = 'banknote_authentication.zip'
with open(zip_path, 'wb') as f:
    f.write(response.content)

# Extract the contents of the ZIP file
with zipfile.ZipFile(zip_path, 'r') as zip_ref:
    zip_ref.extractall()

# Specify the path to the extracted CSV file
csv_path = 'data_banknote_authentication.txt'
column_names = ['variance', 'skewness', 'curtosis', 'entropy', 'original']
features  = ['variance', 'skewness', 'curtosis', 'entropy']
df = pd.read_csv(csv_path, names=column_names)



##### STEP2: SCALE THE DATA ####
mms = MinMaxScaler()
data = df.copy()
for col in features:
    data[col] = mms.fit_transform(data[[col]]).squeeze()


### STEP 3: TRANFORM KERNEL PCA ####

embedding =  MDS(n_components=4,max_iter=300, random_state=10)

X_transformed = embedding.fit_transform(data[features])
new_features = ["1","2", "3", "4"]
df_t=pd.DataFrame(X_transformed , columns=new_features)
df_t['original'] = data["original"]



### SHOW THE DATA 
sns.set_context('notebook')
sns.set_style('white')
sns.pairplot(df_t, hue="original")


### CODE FOR MAKING DBSCAN AND PLOTS 

#### STEP 4: DBSCAN ####
# Define the parameter combinations to evaluate
eps_values = [0.01, 0.03, 0.05, 0.07, 0.1, 0.15]
min_samples_values = [2, 3, 5, 7, 10, 15]

# Iterate over parameter combinations
names = []
for eps, min_samples in itertools.product(eps_values, min_samples_values):
    # Create a DBSCAN object with the current parameter values
    dbscan = DBSCAN(eps=eps, min_samples=min_samples)

    # Fit the DBSCAN model to the data and obtain the cluster labels
    cluster_labels = dbscan.fit_predict(df_t[new_features])
    if len(pd.Series(cluster_labels).unique()) > 1: 
        if len(pd.Series(cluster_labels).unique()) < 7: 
            name = f"eps_{eps}_mins_{min_samples}"
            df_t[name] = cluster_labels
            names.append(name)


    # Filter out the outliers (-1 label) from the cluster labels
    filtered_labels = cluster_labels[cluster_labels != -1]
    print("Eps:", eps, "Min Samples:", min_samples, "clusters:", len(pd.Series(filtered_labels).unique()))





###### PLOT THE DBSCAN RESULS #### 
df_plot = df_t.melt(id_vars =new_features, value_vars =['original'] + names , var_name = "cluster")
df_plot['value']= df_plot['value'].astype(str)


# Create a 3 by 3 subplot grid
fig, axes = plt.subplots(nrows=3, ncols=4, figsize=(12, 12))

# Flatten the axes for easy iteration
axes = axes.flatten()

# Iterate over each cluster and create scatter plots
for i, cluster in enumerate(df_plot['cluster'].unique()):
    print (i)
    ax = axes[i]  # Select the current subplot

    # Filter data for the current cluster
    subset = df_plot[df_plot['cluster'] == cluster]

    # Create scatter plot
    sns.scatterplot(data=subset, x="2", y="4", hue='value', legend='full', ax=ax)

    # Set subplot title
    ax.set_title(f"Cluster {cluster}", fontsize=12)

    # Set axis labels
    ax.set_xlabel("x")
    ax.set_ylabel("y")

    # Remove x and y ticks
    ax.set_xticks([])
    ax.set_yticks([])

# Adjust spacing between subplots
plt.tight_layout()

plt.show()

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