[Feature Request] - Add Centered Arcsine Contrast (CAC) and Additive Arcsine Contrast (AAC)

[jolespin]

Additionally, we create a new framework that enables the development of new transformations by combining proportion conversion with contrast transformations. This framework includes well-known methods such as Additive Log Ratio (ALR) and Centered Log Ratio (CLR) as special cases. Using this framework, we develop two novel transformations—

compositional.pdf

—which show enhanced performance in scenarios with high zero-inflation. Moreover, our findings suggest that ALR and CLR transformations are more effective when zero values are less prevalent. This comprehensive review and the innovative framework provide microbiome researchers with a significant direction to enhance data transformation procedures and improve analytical outcomes.

https://www.csbj.org/article/S2001-0370(24)00374-X/fulltext

[jolespin]

import numpy as np
from scipy.linalg import eigh

def centered_arcsine_contrast(X):
    """
    Perform Centered Arcsine Contrast (CAC) transformation on compositional data.
    
    Parameters:
        X (numpy.ndarray): A 2D array where each row is a compositional sample (proportions sum to 1).
        
    Returns:
        numpy.ndarray: The transformed data with the CAC transformation applied.
    """
    # Ensure X is a NumPy array
    X = np.asarray(X)

    # Compute the arcsine transformation
    X_arcsin = np.arcsin(np.sqrt(X))

    # Compute the centered contrast matrix
    n_features = X.shape[1]
    identity = np.eye(n_features)
    ones_matrix = np.ones((n_features, n_features)) / n_features
    contrast_matrix = identity - ones_matrix

    # Apply the centered contrast transformation
    X_CAC = X_arcsin @ contrast_matrix

    return X_CAC


def additive_arcsine_contrast(X):
    """
    Perform Additive Arcsine Contrast (AAC) transformation on compositional data.
    
    Parameters:
        X (numpy.ndarray): A 2D array where each row is a compositional sample (proportions sum to 1).
        
    Returns:
        numpy.ndarray: The transformed data with the AAC transformation applied.
    """
    # Ensure X is a NumPy array
    X = np.asarray(X)

    # Compute the arcsine transformation
    X_arcsin = np.arcsin(np.sqrt(X))

    # Compute the additive contrast matrix
    n_features = X.shape[1]
    contrast_matrix = np.eye(n_features) - np.ones((n_features, n_features)) / n_features
    contrast_matrix = contrast_matrix[:, :-1]  # Remove the last column to keep the transformation consistent

    # Apply the additive contrast transformation
    X_AAC = X_arcsin @ contrast_matrix

    return X_AAC

Centered Arcsine Contrast (CAC)

• Applies an arcsine square root transformation to stabilize variance.
• Uses a centered contrast matrix to center the data, ensuring that the sum of the transformed components is zero.

Additive Arcsine Contrast (AAC)

• Also applies an arcsine square root transformation.
• Uses an additive contrast matrix, which compares each component relative to the overall composition while removing the last column to maintain proper dimensionality.