Spatial Clustering analyses

CellTracksColab - Spatial Track Clustering Analysis

Explore Spatial Clustering in Track Data with CellTracksColab: This Colab Notebook is designed to analyze spatial clustering in your track data. Please ensure your data is loaded in the CellTracksColab format for the best results.

Access the Notebook

• CellTracksColab - Track Clustering Analysis:

Assessing Spatial Clustering Using Ripley's L Function

Spatial analysis in this notebook focuses on specific moments or characteristics within each track, revealing unique aspects of spatial distribution in the field of view (FOV).

Choose the Point for Each Track Analysis

This interactive tool allows for comparing and selecting the most suitable analysis point within each track for spatial analysis. Options include:

• "beginning": The initial position of each track.
• "end": The final position of each track.
• "middle": The middle position of each track.
• "average": The average position of all points within each track.
• "median": The median position of all points within each track.

Compute Ripley's L Function for Each FOV

• Analysis Options: Select the point for analysis (beginning, end, middle, average, median).
• r_values Range:
  • Start Value: The minimum distance for "r".
  • End Value: The maximum distance for "r".
  • Number of Points: The number of steps between the start and end values.

Compute Monte Carlo Simulations for Each FOV

• Purpose: To assess the significance of spatial patterns using Monte Carlo simulations.
• Number of Simulations (Nb_simulation): Define the number of simulations for each FOV for statistical confidence.

Visualization and Analysis

• Plot Results for Each FOV: Visualize the outcomes of Ripley's L function.

• Choose a Specific Radius and Plot Results: Focus analysis on a particular spatial scale.
• Comparison of Ripley's L Values Across Conditions: Examine differences across experimental conditions.

• Plot the Analysis Point for Each FOV: Gain deeper insights by visualizing the selected analysis points.

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Interpreting Results from Ripley's L Functions

Ripley's L function is derived from Ripley's K Function.

Understanding Ripley's K Function

Ripley's K function, a vital tool in spatial analysis, elucidates clustering or dispersion patterns of points in a two-dimensional space.

How Ripley's K Function Works

• K_r = ripley_k(points, r, area)
  • points: The coordinates of the points in the dataset.
  • r: The radius within which to count point pairs.
  • area: The total area of the region being analyzed.

Interpretation of K_r

• Greater than Expected: Implies clustering within radius 'r'.
• Less than Expected: Indicates dispersion.
• Negative Values: Could signal calculation errors or data issues.

How Ripley's L Function Works

• Transformation: Stabilizes variance across different 'r' values.
• Calculation: L_r = sqrt(K_r / pi) - r.

Interpretation of L_r

• Near Zero: Implies a random spatial pattern.
• Positive: Suggests clustering.
• Negative: Indicates dispersion.

Understanding the Role of 'r'

• Critical Parameter: Represents the distance threshold for point pairs.
• Influential Choice: Significantly impacts spatial pattern interpretation.
• Analysis of Range: Typically, a range of 'r' values is examined to understand spatial patterns at various scales.

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Utilizing Ripley's K and L functions in CellTracksColab provides valuable insights into the spatial arrangements and interactions of points, making it indispensable for spatial analysis in cell tracking and related fields.