Gnostics Cluster Analysis

The ClusterAnalysis class provides an end-to-end, automated workflow for estimating the main cluster bounds of a dataset using Gnostic Distribution Functions (GDFs) and advanced clustering analysis. This approach is robust, interpretable, and reproducible, making it ideal for scientific, engineering, and data science applications where reliable interval estimation is needed.

Key Features:

• Fully automated pipeline for cluster-based bound estimation
• Integrates GDF fitting, homogeneity testing, and cluster analysis
• Supports both local (ELDF) and global (EGDF) GDFs
• Handles weighted data, bounded/unbounded domains, and advanced parameterization
• Detailed error/warning logging and reproducible parameter tracking
• Optional memory-efficient operation via flushing intermediate results
• Visualization support for both GDF and cluster analysis results

---

1. Basic Usage: Automated Cluster Bound Estimation

Let’s see how to estimate the main cluster bounds for a dataset with an outlier.

Basic Cluster Analysis

import numpy as np
from machinegnostics.magcal import ClusterAnalysis

# Example data with an outlier
data = np.array([-13.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
print("Data: ", data)

# Create a ClusterAnalysis object
ca = ClusterAnalysis(verbose=False, flush=False)

# Fit the data and get cluster bounds
clb, cub = ca.fit(data=data)

# Plot the clusters and data
ca.plot()

# Check results
ca.results()

# Print the cluster bounds
print("Cluster Lower Bound: ", clb)
print("Cluster Upper Bound: ", cub)
print("CLB and CUB present the bounds of the main cluster in the data.")

Output:

---

2. Advanced Usage: Manual GDF and Cluster Analysis

For advanced users, you can manually fit a GDF and perform cluster analysis for more control and customization.

Advanced Cluster Analysis

import numpy as np
from machinegnostics.magcal import QLDF, ELDF, DataCluster

data = np.array([-13.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

# Step 1: Fit a GDF (local DFs are a good choice for cluster analysis)
qldf = QLDF()
qldf.fit(data=data)

eldf = ELDF()
eldf.fit(data=data)

# Step 2: Manual Cluster Analysis using DataCluster
dc = DataCluster(gdf=eldf, verbose=False)
clb, cub = dc.fit(plot=True)
dc.results()

# OR, if interested in inliers, use QLDF
dc = DataCluster(gdf=qldf, verbose=False)
clb, cub = dc.fit(plot=True)
dc.results()

Typical Output:

{
 'gdf_type': 'qldf',
 'derivative_threshold': 0.01,
 'slope_percentile': 70,
 'LCB': -2.24,
 'UCB': 6.33,
 'Z0': 2.04,
 'S_opt': 1.0,
 'cluster_width': 8.57,
 'clustering_successful': True,
 'method_used': 'qldf_w-shape_valley_detection',
 'normalization_method': 'min_max_normalization',
 'pdf_shape': 'W-shape',
 'errors': [],
 'warnings': []
}

ELDF

QLDF

API Reference

---

Tips

• Use ClusterAnalysis for a fully automated workflow, or DataCluster for manual, fine-grained control.
• Both local (ELDF/QLDF) and global (EGDF/QGDF) GDFs can be used depending on your analysis needs.
• For more advanced usage and parameter tuning, see the API Reference.

---

Next:
Explore more tutorials and real-world examples in the Examples section!