Mahalanobisdistorionsbaserad

Mahalanobisdistorionsbaserad is a term found in some Swedish-language technical writings describing a distortion-based approach that uses the Mahalanobis distance to quantify deviations from a reference distribution. The central idea is to assess how much an observation or a reconstructed signal differs from what is considered normal, taking into account the correlations among variables.

Mathematical basis and definition

Given an observation x in R^d, a reference mean vector mu and a covariance matrix Sigma estimated from clean or normal data, the squared Mahalanobis distance is MD^2 = (x − mu)^T Sigma^−1 (x − mu). This distance measures deviation in a space where the variables are decorrelated and scaled by their variability. In a distortion-based framework, MD^2 serves as a distortion score: higher values indicate greater deviation from the expected distribution. Under Gaussian assumptions, MD^2 follows a chi-square distribution with d degrees of freedom, which allows thresholding to flag distortions or anomalies. Robust variants use resistant estimates of mu and Sigma to reduce sensitivity to outliers.

Methodology and variants

Applications typically involve estimating mu and Sigma from a representative training set, possibly after preprocessing or dimensionality reduction (for example, PCA). The distortion score can be used for anomaly detection, quality assessment, or as a component of loss functions in reconstruction tasks where distortions need to be penalized proportionally to their Mahalanobis distance. Variants may incorporate whitening or rely on robust covariance estimators to improve performance in non-Gaussian data.

Applications and limitations

Common uses include multivariate anomaly detection, image or video artifact detection, and signal processing where distortions must be quantified relative to a learned normal model. Limitations include the need for reliable covariance estimation, sensitivity to non-Gaussian data, and potential computational cost in high dimensions.