Project 14: Multivariate & Specialized Topics Lab

Build a unified lab for PCA, clustering, time-series forecasting, survival analysis, and non-parametric testing.

Quick Reference

Attribute Value
Difficulty Level 4: Expert
Time Estimate 3 weeks
Main Programming Language Python
Alternative Programming Languages R
Coolness Level Level 5: Pure Magic
Business Potential 2. The “Micro-SaaS / Pro Tool”
Prerequisites Projects 10-13
Key Topics PCA, clustering, ARIMA intro, survival intro, non-parametrics

1. Learning Objectives

  1. Select specialized methods based on data structure.
  2. Interpret PCA loadings and clustering stability.
  3. Build introductory ARIMA forecasts with diagnostics.
  4. Analyze censored outcomes with survival intuition.

2. All Theory Needed (Per-Concept Breakdown)

2.1 High-Dimensional and Unsupervised Methods

  • Fundamentals: PCA and clustering summarize structure when labels are absent.
  • Deep Dive into the concept: Scaling, distance metric choice, and stability checks are essential to avoid false patterns.

2.2 Temporal and Event-Time Analysis

  • Fundamentals: Time-series and survival methods model dependency over time.
  • Deep Dive into the concept: ARIMA needs stationarity diagnostics; survival needs censoring-aware interpretation.

3. Project Specification

3.1 What You Will Build

A multi-track analysis pipeline across dimensionality reduction, segmentation, forecasting, and retention-time modeling.

3.2 Functional Requirements

  1. PCA decomposition and explained-variance reporting.
  2. Clustering with stability and silhouette diagnostics.
  3. Intro ARIMA forecasting with residual diagnostics.
  4. Survival summary and non-parametric group comparison.

3.3 Non-Functional Requirements

  • Modular track outputs with unified final report.
  • Reproducible seeds and split windows.

3.4 Example Usage / Output

$ python multivariate_lab.py --dataset data/subscription_platform.parquet
PCA explained variance (6 comps): 82.4%
Best cluster count: 4
ARIMA MAPE: 6.8%
Median survival (segment_2): 11.4 months
Kruskal-Wallis p-value: 0.012

3.5 Real World Outcome

You produce a coherent multi-method analysis that fits each target type instead of forcing one model.

4. Solution Architecture

Data prep -> PCA/cluster track + time-series track + survival track -> integrated report

5. Implementation Guide

5.1 Development Environment Setup

pip install numpy pandas scikit-learn statsmodels lifelines

5.2 Project Structure

P14/
  multivariate_lab.py
  tracks/
  outputs/

5.3 The Core Question You Are Answering

“Which specialized method matches this data-generating structure, and how do I verify it?”

5.4 Concepts You Must Understand First

  1. Eigen decomposition intuition
  2. Distance metrics and scaling
  3. Stationarity and autocorrelation basics
  4. Censoring concepts

5.5 Questions to Guide Your Design

  1. How will you validate cluster robustness?
  2. How will you check ARIMA residuals?
  3. Which non-parametric test fits your comparison question?

5.6 Thinking Exercise

Create a decision table mapping data type (high-dimensional, temporal, censored) to method family.

5.7 The Interview Questions They’ll Ask

  1. Why can PCA reduce interpretability?
  2. Why are clusters not ground truth classes?
  3. What does stationarity imply in ARIMA?
  4. What is right-censoring?
  5. When is Kruskal-Wallis preferred?

5.8 Hints in Layers

  • Hint 1: Build independent tracks first.
  • Hint 2: Add per-track diagnostics.
  • Hint 3: Add cross-track summary table.
  • Hint 4: Add stability checks across seeds/windows.

5.9 Books That Will Help

Topic Book Chapter
Unsupervised learning ISLR unsupervised chapter
Forecasting Forecasting: Principles and Practice ARIMA chapters
Survival intro biostatistics references survival chapters

6. Testing Strategy

  • Synthetic cluster recovery tests.
  • Forecast backtesting windows.
  • Survival curve sanity tests on simulated censoring.

7. Common Pitfalls & Debugging

Pitfall Symptom Solution
Missing scaling unstable PCA/cluster output mandatory standardization
Overfit ARIMA poor future performance rolling-origin validation
Ignoring censoring biased survival claims censoring-aware summaries

8. Extensions & Challenges

  • Add seasonal and exogenous forecasting variants.
  • Add cluster explainability profiles.

9. Real-World Connections

  • Customer segmentation and retention analysis.
  • Demand forecasting for operations planning.

10. Resources

  • ISLR
  • Forecasting: Principles and Practice

11. Self-Assessment Checklist

  • I can justify each specialized method by data structure.
  • I can diagnose at least one failure per track.
  • I can integrate findings into one coherent narrative.

12. Submission / Completion Criteria

Minimum: functional outputs for PCA, clustering, and one temporal/event-time track.

Full: all tracks with diagnostics and integrated recommendation report.