Feature Extraction

Heike Hofmann and Susan Vanderplas

2024-09-17

The package defines a set of functions of the form extract_feature_XXX where XXX stands for a particular feature to be extracted either directly from a set of aligned signatures or indirectly from peaks and valleys derived from a set of aligned signatures.

Using the function extract_features_all will automatically call all currently implemented functions of the form extract_feature_XXX and return a dataframe (of a single row) for each set of aligned signatures.

There are two types of features implemented at the moment: features, that are based on - only the aligned signatures: D, ccf, rough cor, … - striae extracted from aligned signatures: cms, matches, …

Distance $D$

The Euclidean distance between two aligned signatures $s$ and $t$ is defined as $$d(s,t) = \sqrt{\sum_{i=1}^N\left( s_i - t_i\right)^2}$$, where $i = 1, ..., N$, the length of the aligned signatures. Two signatures $s$ and $t$ of respective lengths $n_s$ and $n_t$ can be aligned by padding one or both of the signatures with missing values NA. The aligned form of signatures $s$ and $t$ then has length $N \ge n_s, n_t$. $d$ is then a measure of the distance between the two vectors. Note that this form of $d$ is not invariant to the resolution $r$, at which signatures $s$ and $t$ are collected. To make the distance invariant to the resolution, we could use $d\cdot r$ as an estimate for the area between the two signatures. However, in cases of degraded signatures (i.e. cases, in which for some reason a signature cannot be extracted from a whole land), we want to also make distance invariant to the length of the signatures involved. We therefore define $$D(s,t) = d(s,t)/N$$ to be the average distance between aligned signatures $s$ and $t$.

Consecutively matching striae (CMS)

Consecutively matching striae is a measure first established by Alfred Biasotti in 1950 (reference). The number of consecutively matching striae is the number of consecutive peaks two signature have in common, i.e. the valleys in between the peaks should not be counted. XXX Currently, the function extract_feature_cms counts both peaks and valleys XXX Generally, a CMS of 6 or higher is considered to be strongly indicative of a match (need another citation for this).

Countable features

All features that return a count in one way or the other, such as cms, noncms, matches, nonmatches, … are accompanied by functions that scale these integers by the signature length (to make these numbers independent from length) and return values scaled to millimeter. The corresponding variables then have an appendix of _per_mm.