Vector Coding Analysis Tools

Overview

The Vector Coding Analysis Tools module provides comprehensive analysis of joint coupling and coordination patterns using vector coding techniques. This method quantifies the relationship between two joint angles over time, identifying coordination patterns and phase relationships in human movement.

Features

Coupling Angle Calculation: Quantify coordination between joint pairs
Phase Analysis: Identify in-phase and anti-phase coordination patterns
Time Normalization: Standardize movement cycles for comparison
Visualization Suite: Multiple visualization types for coordination analysis
Statistical Analysis: Quantification of coordination variability
Batch Processing: Analyze multiple movement trials simultaneously
Export Capabilities: Save results in multiple formats

Vector Coding Methodology

Core Concept

Vector coding analyzes the relationship between two angular displacements by: 1. Angle Vector Creation: Represent each joint angle as a vector in polar coordinates 2. Coupling Angle Calculation: Determine the angle between joint angle vectors 3. Phase Classification: Categorize coordination patterns into discrete phases

Mathematical Foundation

For two joint angles θ₁ and θ₂ at each time point:

Vector Representation:

V₁ = (cos(θ₁), sin(θ₁))
V₂ = (cos(θ₂), sin(θ₂))

Coupling Angle:
```
γ = atan2(V₁×V₂, V₁·V₂)
```
Phase Classification:
In-Phase: γ ≈ 0° (coordinated movement)
Anti-Phase: γ ≈ 180° (opposing movement)
Transitions: Intermediate phases

Supported Data Formats

Input Data Requirements

CSV Files: Time-series joint angle data
Column Structure: Frame/Time, Joint1_Angle, Joint2_Angle
Angular Units: Degrees or radians (configurable)
Sampling Rate: Consistent sampling frequency

Example Data Format

frame,joint1_angle,joint2_angle
1,45.2,23.8
2,46.1,24.2
3,47.3,24.8
4,48.2,25.1
...

Analysis Pipeline

1. Data Preprocessing

Loading: Import CSV files with automatic format detection
Validation: Check data integrity and sampling consistency
Filtering: Optional smoothing for noise reduction
Normalization: Standardize data ranges if needed

2. Time Normalization

Cycle Detection: Identify movement cycles
Resampling: Normalize to fixed number of points (default: 101)
Interpolation: Smooth interpolation between data points
Boundary Handling: Proper handling of cycle boundaries

3. Vector Calculation

Angle Vectorization: Convert angles to unit vectors
Coupling Computation: Calculate angle between vector pairs
Phase Determination: Classify coordination patterns
Variability Assessment: Quantify coordination consistency

4. Statistical Analysis

Phase Percentages: Time spent in each coordination pattern
Variability Metrics: Standard deviation of coupling angles
Trend Analysis: Changes in coordination over time
Comparative Statistics: Between-condition comparisons

Visualization Types

Coupling Angle Plots

Circular Plot: Polar plot of coupling angle distribution
Time Series: Coupling angle over normalized time
Phase Regions: Visual separation of coordination phases
Variability Bands: Confidence intervals around mean patterns

Angle-Angle Diagrams

Phase Portraits: Joint angle relationships in phase space
Coordination Patterns: Visual representation of coupling
Movement Trajectories: Path of joint coordination over time
Comparative Overlays: Multiple conditions on same plot

Statistical Visualizations

Phase Distribution: Pie/bar charts of phase percentages
Variability Plots: Box plots and violin plots of coordination
Trend Analysis: Line plots of coordination changes
Heat Maps: Temporal coordination patterns

Usage

GUI Mode (Recommended)

from vaila.run_vector_coding import run_vector_coding

# Launch interactive interface
run_vector_coding()

Programmatic Usage

import pandas as pd
from vaila.run_vector_coding import get_coupling_angle

# Load joint angle data
data = pd.read_csv('joint_angles.csv')

# Extract angle columns
joint1_angles = data.iloc[:, 1].values  # First joint angles
joint2_angles = data.iloc[:, 2].values  # Second joint angles

# Calculate coupling angles
coupling_results = get_coupling_angle(
    file='joint_angles.csv',
    freq=100.0,  # Sampling frequency in Hz
    joint1_name='Knee',
    joint2_name='Ankle',
    save=True,
    savedir='/path/to/results'
)

Batch Processing

import glob
from vaila.run_vector_coding import get_coupling_angle

# Process multiple files
data_files = glob.glob('/path/to/angle_data/*.csv')

for file_path in data_files:
    get_coupling_angle(
        file=file_path,
        freq=100.0,
        joint1_name='Proximal_Joint',
        joint2_name='Distal_Joint',
        save=True,
        savedir='/path/to/vector_coding_results'
    )

Advanced Configuration

Custom Normalization

# Custom time normalization parameters
normalization_config = {
    'n_points': 101,          # Number of normalized time points
    'interpolation_kind': 'cubic',  # Interpolation method
    'boundary_handling': 'periodic'  # How to handle cycle boundaries
}

get_coupling_angle(
    file='joint_data.csv',
    normalization_config=normalization_config
)

Advanced Statistical Analysis

# Configure statistical analysis
stats_config = {
    'phase_bins': 8,           # Number of phase bins for analysis
    'variability_metric': 'std',  # Variability measurement method
    'confidence_interval': 95,   # Confidence interval percentage
    'outlier_detection': True    # Remove statistical outliers
}

coupling_results = get_coupling_angle(
    file='joint_data.csv',
    stats_config=stats_config
)

Applications

Biomechanical Research

Gait Analysis: Examine coordination between lower limb joints
Sports Performance: Analyze technique and coordination patterns
Rehabilitation: Monitor recovery of normal movement patterns
Comparative Studies: Compare coordination between groups

Clinical Assessment

Neurological Disorders: Assess coordination deficits in neurological conditions
Orthopedic Assessment: Evaluate joint coordination post-injury/surgery
Developmental Studies: Track coordination development in children
Geriatric Assessment: Monitor age-related coordination changes

Sports Science

Technique Analysis: Evaluate coordination in athletic movements
Training Effects: Monitor changes in coordination with training
Equipment Effects: Assess how equipment affects movement coordination
Injury Prevention: Identify coordination patterns associated with injury risk

Integration with vailá Ecosystem

This module integrates with other vailá tools:

Motion Capture: Use with cluster and full-body motion capture analysis
Visualization: Compatible with 2D/3D plotting modules for enhanced visualization
Data Processing: Combine with filtering and smoothing tools
Statistical Analysis: Export data for advanced statistical processing

Quality Assurance

Data Quality Checks

Signal Integrity: Verify angle data continuity and range
Sampling Consistency: Ensure consistent sampling rates
Outlier Detection: Identify and handle anomalous data points
Cycle Validation: Verify movement cycle identification

Analysis Validation

Method Verification: Compare with established vector coding literature
Repeatability: Assess consistency across multiple analyses
Sensitivity Analysis: Test robustness to parameter changes
Cross-Validation: Compare results with alternative analysis methods

Troubleshooting

Common Issues

Phase Classification Errors: Check angle data quality and range
Normalization Problems: Verify cycle detection and boundary handling
Statistical Artifacts: Check for sufficient data points per cycle
Visualization Issues: Ensure proper data formatting for plotting

Parameter Optimization

Normalization Points: Use 101 points for standard gait cycle analysis
Phase Bin Number: 8-12 bins typically provide good resolution
Smoothing: Apply light smoothing if data is very noisy
Threshold Values: Adjust based on specific movement characteristics

Version History

v2.0: Added advanced statistical analysis and enhanced visualization
v1.5: Added GUI interface and batch processing capabilities
v1.0: Initial implementation with basic vector coding analysis

Requirements

Core Dependencies

Python 3.8+: Modern Python features
NumPy: Numerical computations
Pandas: Data manipulation
SciPy: Scientific computing
Matplotlib: Visualization

Optional Dependencies

Tkinter: GUI interface (usually included)
Seaborn: Enhanced statistical plotting

References

Vector Coding: Original methodology for joint coordination analysis
Biomechanical Coordination: Principles of inter-joint coordination
Gait Analysis: Application to human locomotion studies
Motor Control: Neural control of coordinated movements