Fcorr

Fcorr is a statistical measure used to quantify the strength of association between two variables or data sequences. Unlike traditional correlation coefficients that assess only linear relationships, Fcorr is designed to capture both linear and certain non-linear dependencies by operating in a transformed feature space. The method projects the data into a higher-dimensional representation through a feature map or kernel, computes a correlation-like statistic between the transformed variables, and then normalizes the result to lie on a fixed scale, typically between -1 and 1.

Because the measure relies on the chosen feature map, different implementations of Fcorr can emphasize different types of relationships. Common choices include polynomial or kernel-based mappings that reveal monotonic or more complex associations. The result is symmetric with respect to the input variables and, when normalization is applied, invariant to affine scaling of the data.

Fcorr has been used in various domains, including time-series analysis, neuroscience for assessing functional connectivity, genomics to relate expression profiles, and finance to identify linked assets. In practice, Fcorr complements classical measures such as Pearson correlation and Spearman rank correlation, as well as information-theoretic approaches like mutual information.

Limitations include sensitivity to the choice of feature map and the need for adequate sample size to stabilize estimates. Like other data-driven metrics, Fcorr can be affected by noise, non-stationarity, and outliers, though robust variants exist.

See also: Pearson correlation, Spearman correlation, mutual information, coherence, kernel methods.