MathIAs+® Clustering Decision Dashboard

Decision-grade dashboard for selecting the optimal number of clusters (K). The recommendation is based exclusively on deterministic structural signal extracted from the data. Standard clustering metrics are shown for comparison only.

Run status: Completed successfully
Recommended Decision

Recommended number of clusters

K = 10
Deterministic Decision Optimum

K = 10 is selected as the optimal segmentation level based on deterministic structural evidence.

This level maximizes the structural signal gain extracted from the data structure, with a 2.37× gain compared to baseline segmentation (K=2).

The exploration is bounded at K = 16.

Structural Signal Gain
2.37×
Normalized to baseline segmentation (K=2)
Maximum K Evaluated
16
Upper bound of segmentation exploration

Core Decision View

Structural signal gain across K. The recommended K is highlighted by a vertical marker.

Execution Context

Reproducibility, traceability and execution metadata.

Run ID
3fe57f8c-e0e9-47b3-ba29-33ecd50dc804
Timestamp (UTC)
2026-06-12T15:58:30.854017Z
Samples
1797
Features
64
Maximum K Evaluated
16
Scaling Applied
Yes
Engine
Mathias Plus / MathIAs+ MRC / Deterministic Clustering
Engine Version
1.1.0 (2026-06-08)
Dataset Friendly Name
handwritten digits (ten classes)
Dataset Fingerprint (SHA256)
b9debecea080b6a34da6e2a0c55ec4e0fb83608be866209f73d89e4f339870a8
Data Persistence Policy
Only derived artifacts are stored; no raw data is retained.
Artifacts Residency
US
Status
Completed successfully
This decision is reproducible and based on deterministic computation. All results are traceable through the engine version and the dataset fingerprint.
Audit remarks: No execution warnings were reported in the audit log for this run.

Key Metric Definitions

Structural metrics drive the decision. Other metrics provide contextual information.

Structural Signal (MathIAs+® Partition Score)
Primary decision metric derived from deterministic structural analysis. Measures how strongly the data supports a given segmentation.
Structural Signal Gain
Structural signal normalized to its value at K=2. Values indicate the multiplicative gain relative to the baseline segmentation.
Multi-Segment Structure Across K
Captures how data points can belong to multiple consistent segments across different resolutions. This enables richer, multi-dimensional segmentation beyond single-label clustering, supporting use cases such as hybrid profiles, overlapping behaviors, and flexible targeting strategies.

Key Indicators by K

The recommended K is visually emphasized. Structural metrics are the decision layer; standard metrics remain informative.

K Recommended Acceptable Structural Signal Gain Inertia Ratio Calinski–Harabasz Davies–Bouldin Multi-Segment Structure
2 No No 1.0000 0.9162 164.104 3.0077 2
3 No No 1.2446 0.8562 150.670 2.7906 5
4 No Yes 1.5655 0.8130 137.511 2.5117 15
5 No Yes 1.5668 0.7764 129.044 2.2621 32
6 No Yes 1.7403 0.7425 124.231 2.1870 59
7 No Yes 1.7913 0.7086 122.687 2.0642 75
8 No Yes 1.8815 0.6802 120.137 1.9888 86
9 No Yes 1.9805 0.6568 116.811 1.8997 98
11 No Yes 1.6596 0.6107 113.847 1.8268 119
12 No Yes 1.8760 0.5913 112.169 1.7415 151
13 No Yes 1.6677 0.5716 111.442 1.7055 159
14 No No 1.4009 0.5530 110.854 1.6276 159
15 No No 1.2527 0.5366 109.909 1.4968 159
16 No No 1.2354 0.5217 108.875 1.4544 162

Standard Clustering Metrics

Displayed for compatibility with standard clustering practices. These metrics typically do not identify a clear optimal K and are not used in the decision mechanism.

Informational only — Not used in the decision mechanism

Multi-Segment Structure Across K

Shows the richness of segmentation across K, enabling multi-dimensional analysis beyond single-label clustering.

Informational only — Not used in the decision mechanism

Responsible AI Statement

This analysis is based on deterministic algorithms designed for reproducibility, transparency, and auditability. The results reflect structural patterns in the data and do not imply causality or prediction. Human expertise and domain knowledge remain essential for interpretation, validation, and decision-making. No personal data is retained beyond derived analytical artifacts.

Scope and Limitations

This analysis is based solely on the input dataset and its structural properties. Results may vary depending on data quality, feature selection, preprocessing choices, and business context. The recommended segmentation should be interpreted alongside domain-specific knowledge and operational constraints.

Decision Framework

The recommended number of clusters (K) is derived exclusively from deterministic structural signal. Standard clustering metrics are displayed for compatibility with industry practices, but they are not used in the decision mechanism.

Expert Analysis

This dashboard provides an executive-level decision output. A full expert-level analysis is also available, covering the complete evaluation of segmentation across K, including structural metrics, topology insights, and detailed cluster-level statistics.

The analysis also provides explainability through surrogate models, full auditability of the decision process, and optional predictive capabilities for operational deployment. This expert analysis bridges deterministic data structure understanding with real-world decision-making.

Operational Deployment

The selected model is delivered in a production-ready format, enabling immediate integration into downstream systems and workflows.

This includes a structured representation of the model as well as detailed scoring outputs, allowing consistent assignment of new data points and flexible multi-dimensional evaluation of populations.

These outputs support both automated deployment and advanced analytical use cases, ensuring continuity from decision-making to operational execution. Segmentation decisions can therefore be reliably operationalized across business processes and systems.

Auditability and Reproducibility

All results are reproducible based on deterministic computation. The analysis can be audited through the execution metadata, engine version, and dataset fingerprint. No stochastic processes are involved in the decision mechanism.