fadex-exp 0.1.0

A feature attribution explainability method for dimensionality reduction algorithms.

FADEx

A feature attribution for dimensionality reduction algorithms.

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FADEx is a feature attribution method designed for dimensionality reduction (DR) algorithms. It locally approximates the mapping function of the DR algorithm using a Taylor expansion and derives feature importance scores through a Singular Value Decomposition (SVD). The local approximation is constructed via Radial Basis Function (RBF) interpolation, while the Jacobian matrix is estimated using the finite difference method.

When the data is mapped to a two-dimensional space by the DR algorithm, the importance of each high-dimensional feature $j$ is given by:

$$ \phi_j = \left|v_{1j} x_j\right| + \frac{\lambda_2}{\lambda_1} \left|v_{2j} x_j\right| $$

where $v_{ij}$ denotes the $j$-th entry of the $i$-th right singular vector, $\lambda_i$ is the $i$-th singular value, and $x_j$ is the value of feature $j$.

Installation

Use the following command in your terminal to install the module without the GPU library dependencies:

pip install fadex-exp

If you want to enable GPU acceleration, you need to install the RAPIDS framework. Please follow the official instructions at https://rapids.ai/start.html.

FADEx Class

Class Constructor

The FADEx Class has the following signature:

def __init__(self, high_dim_data: np.ndarray, low_dim_data: np.ndarray, 
                n_neighbors: int = None, feature_names: list = None, 
                classes_names: list = None, RBF_kernel: str = 'cubic',
                pre_dr : int = None, RBF_epsilon : float = 0.001, 
                RBF_degree : float = 1, RBF_smoothing : float = 0, 
                use_GPU : bool = False, dist_sample : int = None):

Required Parameters

high_dim_data (n_samples, n_features) - High dimensional space
low_dim_data (n_samples, 2) - Low dimensional space
n_neighbors - Number of neighbors to consider in the local approximation. When it's None, the entire dataset will be used.

Optional Parameters

feature_names - A list with the feature names.
classes_names - A list with the class for each sample.
RBF_kernel, RBF_epsilon, RBF_degree, and RBF_smoothing - RBFInterpolator parameters.
pre_dr - If provided, a preliminary dimensionality reduction (PCA) is applied to the high-dimensional data, reducing it to pre_dr dimensions before computing the step size in the finite differences method. This is crucial to avoid the curse of dimensionality.
dist_sample - The number of samples to use for distance computation. If set to None, all data points are used. This parameter helps reduce memory consumption.
use_GPU - If True, uses GPU acceleration for computations.

Fit Method

def fit(self, explain_index : int, show : bool = True, width : int = 10, height : int = 8, batch_size : int = 200):

This method applies the FADEx algorithm to a single data instance. When show=True, it displays the feature importance ranking for that specific point, as illustrated below:

Importance Plot

def importance_plot(self, width : int = 10, height : int = 8, n_top : int = 10):

This method applies the FADEx algorithm to the entire dataset, sums the importance values for each feature, and plots a general feature importance ranking, as shown below:

Interactive Plot

def interactive_plot(self, width : int = 10, height : int =8):

This method applies the FADEx algorithm to the entire dataset and displays the results for each individual point in an interactive plot. The points are colored according to their spectral norm's deviation from 1, with red indicating the most distorted points and green indicating the least distorted ones.