Gaussian Mixture Models in ML Python - Model Pipeline Trace

Model Pipeline - Gaussian Mixture Models

This pipeline uses Gaussian Mixture Models (GMM) to find groups in data by assuming each group looks like a bell curve. It learns the shape and position of these bell curves to best explain the data.

Data Flow - 6 Stages

1Data in

300 rows x 2 columns→Raw data points with two features→300 rows x 2 columns

[[5.1, 3.5], [4.9, 3.0], [6.7, 3.1]]

↓

2Preprocessing

300 rows x 2 columns→Standardize features to zero mean and unit variance→300 rows x 2 columns

[[0.12, -0.45], [-0.34, -1.02], [1.23, 0.15]]

↓

3Feature Engineering

300 rows x 2 columns→No additional features added; use standardized features→300 rows x 2 columns

[[0.12, -0.45], [-0.34, -1.02], [1.23, 0.15]]

↓

4Model Trains

300 rows x 2 columns→Fit GMM with 3 components using Expectation-Maximization→Model with 3 Gaussian components parameters

Means: [[-0.8, 0.5], [0.1, -0.2], [1.5, 1.0]]; Covariances: [[[0.5,0],[0,0.3]], ...]

↓

5Metrics Improve

Model parameters→Log-likelihood increases, convergence reached→Final log-likelihood: -420.5

Log-likelihood per iteration: [-500, -460, -430, -420.5]

↓

6Prediction

1 row x 2 columns→Calculate probabilities of belonging to each Gaussian component→1 row x 3 columns (probabilities sum to 1)

[0.05, 0.90, 0.05]

Training Trace - Epoch by Epoch

Log-likelihood
-500 |************
-460 |*********
-430 |******
-420 |*****
      1  2  3  4  Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1		N/A	Initial log-likelihood before EM steps
2		N/A	Log-likelihood improved after first EM iteration
3		N/A	Model parameters better fit data clusters
4		N/A	Convergence reached; log-likelihood stabilizes

Prediction Trace - 4 Layers

Layer 1: Input sample

Layer 2: Calculate Gaussian probabilities

Layer 3: Normalize probabilities

Layer 4: Assign cluster

Model Quiz - 3 Questions

What does the Gaussian Mixture Model assume about the data?

A Data is made of several bell-shaped groups

B Data is perfectly linear

C Data has no structure

D Data is only one cluster

Key Insight

Gaussian Mixture Models find hidden groups by fitting bell-shaped curves to data. They use probabilities to softly assign points to clusters, allowing flexible and realistic grouping.