CTS_seeds: Extract all possible minimal tracer combinations to identify...

In fingerPro: A Comprehensive Package for Sediment Source Unmixing

Extract all possible minimal tracer combinations to identify the most discriminant.

Description

This function generates a list of all possible minimal tracer combinations and serves as a crucial initial step (a "seed") in building a consistent tracer selection within a sediment fingerprinting study. This analysis systematically explores various minimal tracer combinations and solves the resulting determined systems of equations to assess the **variability** of each combination. The **dispersion of the solution** directly reflects the **discriminant capacity** of each tracer combination: a lower dispersion indicates a higher discriminant capacity. While traditional methods like Discriminant Function Analysis (DFA) also identify discriminant tracer combinations, this function provides solutions that are **not restricted to the physically feasible space (0 < wi < 1)**. This unconstrained approach is valuable for identifying problematic tracer selections that might otherwise be masked when using constrained unmixing models, as discussed by Latorre et al. (2021).

Usage

CTS_seeds(data, iter = 1000, seed = 123456)

Arguments

data	Data frame containing sediment source and mixtures. Users should ensure their data is in a valid format by using the check_database() function before running this function.
iter	The number of iterations for the variability analysis. Increase 'iter' to improve the reliability and accuracy of the results. A sufficient number of iterations is reached when the output no longer changes significantly with further increases.
seed	An integer value used to initialize the random number generator. Setting a seed ensures that the sequence of random numbers generated during the unmixing is reproducible. This is useful for debugging, testing, and comparing results across different runs. If no seed is provided, a random seed will be generated.

Details

The Consistent Tracer Selection (CTS) method, as described by Latorre et al. (2021), begins by considering all possible sets of $n-1$ tracers, where $n$ is the number of sources. Each of these sets forms a determined system of linear equations that can be solved. To account for the variability within the sources, each tracer set is iteratively solved. This process involves sampling the source average values from a t-distribution, reflecting the discrepancy between the true mean and the measured mean due to finite observations. The maximum dispersion observed in the average apportionments for each tracer set is then used as a criterion to rank them, with lower dispersion indicating higher discriminant capacity. This initial step is crucial for identifying multiple discriminant solutions within the dataset, a problem often unexplored by traditional tracer selection methods.

Value

The function returns a data frame summarizing all possible tracer combinations. The data frame includes the following columns for a scenario with three sources: 'tracers', 'w1', 'w2', 'w3', 'percent_physical', 'sd_w1', 'sd_w2', 'sd_w3', and 'max_sd_wi'. Each row represents a tracer combination, detailing its corresponding solution ($w_i$), the percentage of solutions that are physically feasible (0 < w_i < 1), the standard deviation of the results (sd_w_i), and the maximum dispersion among all sources (max_sd_w_i). The solutions are sorted in descending order, with the solution having the lowest dispersion appearing first. This highlights the most discriminant combinations.

References

Latorre, B., Lizaga, I., Gaspar, L., & Navas, A. (2021). A novel method for analysing consistency and unravelling multiple solutions in sediment fingerprinting. *Science of The Total Environment*, *789*, 147804.

fingerPro documentation built on Aug. 27, 2025, 5:11 p.m.