Table 2 Synthetic data: compositional.

Method	MULTIPLIER 1.1		MULTIPLIER 1.5		MULTIPLIER 2.0		UNIFORM—NO HET		PARETO—4 MILD HET		PARETO—0.7 HIGH HET
Method	Median AUC	Mean AUC	Median AUC	Mean AUC	Median AUC	Mean AUC	Median AUC	Mean AUC	Median AUC	Mean AUC	Median AUC	Mean AUC
MultiLOO-ISN	0.502	0.502	0.565	0.586	0.684	0.705	0.543	0.562	0.556	0.578	0.629	0.653
LOO-ISN	0.503	0.505	0.586	0.598	0.726	0.733	0.559	0.585	0.571	0.601	0.637	0.650
SSN - m	0.498	0.497	0.559	0.577	0.676	0.695	0.541	0.562	0.553	0.575	0.619	0.632
KNN log(N),P	0.503	0.503	0.582	0.596	0.714	0.730	0.556	0.579	0.567	0.595	0.642	0.656
KNN 5,\(\sqrt{N}\)	0.504	0.502	0.582	0.597	0.717	0.732	0.556	0.579	0.568	0.595	0.644	0.657
Optics 5	0.494	0.477	0.541	0.533	0.633	0.624	0.510	0.525	0.521	0.536	0.546	0.573
Optics \(\sqrt{N}\)	0.491	0.489	0.556	0.565	0.673	0.686	0.532	0.555	0.545	0.569	0.595	0.616
OTS euclidean	0.503	0.503	0.577	0.591	0.704	0.718	0.553	0.574	0.566	0.590	0.635	0.648
OTS cosine	0.499	0.500	0.504	0.504	0.499	0.503	0.498	0.497	0.496	0.495	0.509	0.514
mOTS cosine	0.499	0.499	0.503	0.506	0.497	0.505	0.494	0.493	0.491	0.491	0.519	0.525
mOTS euc	0.504	0.503	0.581	0.595	0.714	0.729	0.554	0.578	0.569	0.595	0.637	0.655
mOTS glob	0.502	0.503	0.551	0.571	0.642	0.672	0.532	0.550	0.547	0.564	0.614	0.631
Spoutlier -l	0.503	0.501	0.576	0.590	0.703	0.720	0.551	0.575	0.561	0.589	0.634	0.646
Cook’s max	0.501	0.502	0.575	0.594	0.703	0.720	0.554	0.574	0.564	0.589	0.637	0.652
Cook’s med	0.502	0.503	0.580	0.593	0.712	0.718	0.555	0.578	0.566	0.592	0.630	0.644

Bold values indicate the top performer of each column.
Summarization of methods’ Median and Mean performances per Mult parameter—if the average abundances for the cases individual are \(10\%\), \(50\%\) or \(100\%\) more - and Data Heterogeneity—from no to mild and high. High multipliers and more heterogeneity yield better AUC. With a Mult of 1.1, outlier detection is not better than random guessing. Notably, there is an appreciable performance gain passing from mild to elevate heterogeneity, but the difference from no to mild heterogeneity is limited. KNN’s methods and LOO-ISN are consistently among the best in every scenario, with Cook’s distance and euclidean-based Spoutlier methods closely following. Furthermore, cosine OTS, both OTS cosine and mOTS cosine, have worse performance than their euclidean counterparts. LOO-ISN achieves the top performance, 0.726, in terms of Median AUC, in the \(Mult=2.0\) scenario. This method has a 0.221 performance increment from \(Mult=1.1\) to \(Mult=2.0\), highlighting the multiplier as the primary driver of performance.

Search