TDA Point Cloud Pipeline

A comprehensive Python pipeline designed to load 3D point cloud time-series data (e.g., biological embryos), compute topological descriptors via GUDHI, and perform dimensionality reduction and trajectory analysis using Principal Component Analysis (PCA).

Features

• Data Management: Parses and aggregates spatial time-series datasets from directory structures using a unified CloudDataManager.
• Topological Data Analysis: Computes persistence diagrams (Rips complexes) and extracts multi-layer persistence landscapes using gudhi.
• Dimensionality Reduction: Formulates landscape-ready feature matrices for scaling and PCA analysis across multiple dimensions and experimental groups.
• Rich Visualization Engine: Built-in tools for tracking and rendering experimental trajectories over time-steps, vector fields in PCA space, and an interactive ipywidgets slider tracking step-by-step structural changes.
• Distance Profiling: Tools for assessing Euclidean deviations from control-group mean shapes over developmental windows.

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Architecture Overview

The system is organized into a modular structure where specific tasks are decoupled yet accessible through a central manager API:

                  ┌─────────────────────────────────┐
                  │        CloudDataManager         │◄───────── Main public API & entrypoint
                  └────────────────┬────────────────┘
                                   │
      ┌────────────────────────────┼────────────────────────────┐
      ▼                            ▼                            ▼
┌──────────────┐             ┌────────────┐               ┌────────────┐
│ CloudGroup   │             │CloudGroup─ │               │Landscape─  │
│ (Data Model) │             │TDA (Gudhi) │               │Matrix─     │
└──────────────┘             └────────────┘               │Builder     │
                                                          └────────────┘
      ┌────────────────────────────┼────────────────────────────┘
      ▼                            ▼
┌──────────────┐             ┌────────────┐
│ CloudGroup─  │             │TDAPlotter  │
│ PCA          │             │(Matplotlib)│
└──────────────┘             └────────────┘

• CloudGroup: A lightweight data class holding single point-cloud instances, metadata fields, calculated diagrams, and landscapes.
• CloudDataManager: The orchestrator pipeline handling data splitting, I/O operations (CSV & Pickle formats), and delegating execution tasks to submodules.
• CloudGroupTDA: The pipeline compute manager engine utilizing GUDHI wrappers for diagrams and landscape feature mapping.
• LandscapeMatrixBuilder: Filters and formats matrices for downstream statistical learning applications.
• CloudGroupPCA: Handles vector calculations, variance scoring, and structural spatial mappings.
• TDAPlotter: Manages underlying 3D renderings, persistence diagrams, landscape charts, and trajectory-vector visualizations.

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Prerequisites & Installation

The script requires a standard PyData stack alongside the GUDHI library for topological structures.

pip install numpy pandas matplotlib scikit-learn gudhi ipywidgets

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Core Usage Guide

1. Data Initialization & Setup

The input pipeline expects CSV format data profiles containing positional coordinates labeled as "Center of the object_0", "Center of the object_1", "Center of the object_2", and a "timestep" field. Filenames should explicitly reference experimental labels ("control" or "epha2a").

from your_script_name import CloudDataManager

# Instantiate the primary manager object
manager = CloudDataManager()

# Ingest an entire folder of embryo configurations
manager.load_groups_from_directory("./data/embryos/")

2. Executing the TDA Pipeline

Run persistence computations across every group structure loaded into the object manager:

# 1. Compute Rips complex diagrams up to dimension H1
manager.compute_all_persistence_diagrams(max_dimension=2, min_persistence=0.0)

# 2. Extract multi-layered persistence landscapes
manager.compute_all_persistence_landscapes(n_layers=5, resolution=100)

3. PCA Trajectory Analysis

Extract properties and compute principal projection trajectories:

# Fit standard scaler and run PCA coordinates
pca_results = manager.compute_pca(
    condition=None,             # Set explicitly to "control" or "epha2a" to isolate 
    properties=[0, 1],          # Include H0 and H1 components
    n_components=2
)

# Render standard developmental paths
fig_traj = manager.plot_trajectories(properties=[0, 1])
fig_traj.show()

4. Vector Profiles & Interactive Visualization

To display vectors showing movement through shape space across consecutive developmental time intervals:

# Plot step-by-step continuous vector arrows
fig_vectors = manager.plot_trajectory_vectors(properties=[0, 1], scale=1.0)
fig_vectors.show()

# Open an interactive notebook slider evaluating path trajectories
manager.slider_plot_trajectory_vectors(properties=[0, 1])

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API Summary Reference Table

Target Method	Main Delegate Class	Description
load_groups_from_directory(path)	CloudDataManager	Ingests structural CSV directories and extracts meta-properties.
compute_all_persistence_diagrams()	CloudGroupTDA	Computes persistence structures via filtration.
compute_all_persistence_landscapes()	CloudGroupTDA	Transforms standard diagrams into vector functional spaces.
build_landscape_matrix()	LandscapeMatrixBuilder	Constructs structured, flatted arrays filtered by conditions.
compute_pca()	CloudGroupPCA	Transforms high-dimensional landscape matrices into low-dimensional PCA space.
plot_trajectory_vectors()	CloudGroupPCA	Visualizes consecutive time shifts as directed spatial vector mappings.
distance_table_from_control_mean()	CloudDataManager	Calculates metric deviations from baseline averages over uniform developmental timesteps.