When analyzing microbial communities, an active and computational challenge concerns the categorization of 16S rRNA gene sequences into operational taxonomic units (OTUs). Established clustering tools use a one pass algorithm in order to tackle high numbers of gene sequences and produce OTUs in reasonable time. However, all of the current tools are based on a crisp clustering approach, where a gene sequence is assigned to one cluster. The weak quality of the output compared to more complex clustering algorithms, forces the user to post-process the obtained OTUs. Providing a membership degree when assigning a gene sequence to an OTU, will help the user during the post-processing task. Moreover it is possible to use this membership degree to automatically evaluate the quality of the obtained OTUs. So the goal of this work is to propose a new clustering approach that takes into account uncertainty when producing OTUs, and improves both the quality and the presentation of the OTUs results.
Studying the structure of the communities in an ecosystem is central in environmental microbiology [Hugoni et al., 2013; Roux et al., 2011]. The biosphere’s diversity can be determined by amplifying and sequencing specific phylogenetic markers (e.g. 16S rRNA). From there, these amplicons need to be clusterized in ”species” named Operational Taxonomic Units (OTUs) [Chen et al., 2013; Li et al., 2012; Mahe´ et al., 2014; Westcott and Schloss, 2015]. As the volume of sequences has drastically increased in recent times, new clustering tools have emerged to treat the data in reasonable time. The currently used algorithms are, from the point of view of algorithmic complexity, the fastest available that do not produce random results. However, due to their simplicity, the reliability of the results are often discussed. These tools being essentially black boxes, their sensitivity to the sequence order, clustering threshold and structure of the data makes it that the users have no way of knowing whether better Operational Taxonomic Units (OTUs) could have been obtained with different parameters or even whether they correctly represent the data. In these circumstances, there is no choice but to blindly trust them.
Distance-based greedy clustering algorithm such as the ones implemented in OTUclust [Albanese et al., 2015], VSEARCH [Rognes et al., 2016], CD-HIT [Li and Godzik, 2006] or USEARCH [Edgar, 2010] all share the same base algorithm as shown in Algorithm 1.
Output: A set of OTUs to which the sequences are assigned 1 Clusters = ; 2 foreach sequence S do 3 foreach known cluster C do 4 Compute distance(S; C) 5 end 6 if a suitable cluster exists then 7 Assign S to it
9 Create a new cluster with S as the center 10 end 11 end 12 Return Clusters
While more sophisticated algorithms [Antoine et al., 2014; Gath and Geva, 1989; Pe´rez-Sua´rez et al., 2013; Hariz et al., 2006; Antoine et al., 2012] could produce better results quality-wise, their runtime would render them unusable on millions of sequences. As the quality of the OTUs is important, we have to find a way to improve it without increasing the runtime. The different available implementations use a variety of heuristics to counterbalance the simplicity of the algorithm but, to the best of our knowledge, no approach has tried to add a measure of uncertainty to the process. This is why, in order to help increase the quality and trustworthiness of the clustering, we propose to add uncertainty to this simple algorithm through the use of fuzzy clustering. 2.1
Distance-based greedy clustering algorithms, such as the one in VSEARCH, produce a number of OTUs and assign each sequence to one of them. The OTU to which a sequence is said to belong to is usually the first one to be encountered that is sufficiently close, i.e. within the specified threshold. This creates two problems :
An OTU either includes or does not include a sequence Having a sequence associated to a single OTU is expected as the ultimate output of the algorithm. For this reason, algorithms can stop after finding the first OTU that is close enough to a sequence, which speeds the computation up. However, not considering all the OTUs a sequence could be assigned to increases the sensitivity to the order - a weakness of these algorithms - and reduces the quality of the clustering. Indeed, what if two different OTUs are close enough ? Giving priority to the first generated OTU only creates a bias that no heuristic - such as sorting the sequences - could hope to overcome.
Moreover, by using strict thresholds, it is possible to have two nearly identical sequences such that one belongs to a particular OTU while the other does not. This strictness makes it so an OTU partitions the set of sequences into two sets inside of which sequences are considered the same regardless of their distance to the center of the OTU. This lack of distinction between sequences that are isolated and sequences on the border of OTUs hides information that could help understand the data.
While these would not be problems were the clustering optimal, the need for fast algorithms gives rise to results that are not always trustworthy. The OTUs being presented as absolute, the end user has no choice, should consider them correct and cannot know whether the algorithm has encountered ambiguity. We believe that being less strict in the way the OTUs partition sequences would help produce better results from the end user’s point of view. 2.2
To help increase the quality of the clustering and maximize the information that can be gathered from the data, we propose to add uncertainty to the clustering by means of fuzzy sets.
We define a membership function fC (S) that, for an OTU C, associates a membership value to a sequence S. Usually, this value is either 0 or 1. Here, we propose to have fC (S) take its value in f 1n0 j n = 0::10g. This value represents the degree of membership and, as such, 1 means that the sequence certainly belongs to the OTU while 0 means that the sequence certainly does not belong to it. Other values represent uncertainty and are used to express that the sequence nearly belongs to the OTU. This membership value can easily be computed from the distance between the sequence and the center of the OTU using two thresholds t1 and t2 such that t1 t2. If the distance is less than the threshold t1, the membership value is 1. If the distance is greater than t2 the value is 0. If the distance is between t1 and t2, it increases gradually.
Using fuzzy OTUs allows us to discern the difference between sequences close to the OTU and sequences extremely far. Using the parameters t1 and t2, we can tune the “detection radius” around OTUs to gather information that would normally be discarded by the clustering algorithm. 3
Having a non-binary membership function produces OTUs that partition the sequences into multiple sets. If we consider only the sequences that belong (more or less) to an OTU, the repartition of their membership values provides information on the topology of the OTU. An ideal OTU would contain only sequences with a membership value of 1, meaning a group of sequences has been perfectly regrouped with a good threshold and no sequence lies ambiguously on the border. More realistically, a good OTU would contain many sequences with high membership values and little sequences with low values. A bad OTU with the majority of its sequences having low membership values could mean that the algorithm has chosen as a center a sequence on the border of a group or, even worse, between two distinct groups.
We can quickly evaluate the quality of an OTU with this repartition. If we suppose that each sequence lowers the quality of the OTU depending on its membership value, we can use the following formula :
Quality(OT U ) = 1
Pi9=1 !i # sequences with membership value i 0:1 # sequences in the OTU with !i being the “cost” of having a sequence with membership value i 0:1. In our previous examples, and with the following values of !i
we obtain a quality of respectively 0.71 and 0.26 for OTU1 and OTU2, showing OTU1 is better.
A problem arises with singletons that always have perfect quality but these can safely be treated separately. 4
A sequence can belong to multiple OTUs due to fuzzy membership. However, in the end, we want each sequence to be assigned to a single OTU. Hence, we have to choose one of the possible OTUs. We have two types of values left from the clustering process : membership and quality. The first one is based on the distance between the OTU and the sequence and the second one is used to recognize bad OTUs. Choosing the OTU with the best membership value is akin to running VSEARCH. Choosing the OTU with the best quality tends to create bigger OTUs that absorb distant sequences. To better compromise, we can use a linear combination of both values : quality + membership
Increasing the importance of the quality reduces the number of OTUs containing sequences. When is low, the “best” OTUs quality-wise absorb very close sequences that would have been attributed to other OTUs. When gets too high, the best OTUs start absorbing all the sequences around them, effectively acting like an increase of the distance threshold.
Distance-based greedy algorithms are good at clustering objects that are easy to cluster. Groups of very similar sequences that are different from the rest of the dataset are supposed to birth a new OTU while isolated singletons should be identified to be either removed or treated separately. A problem arises when groups of sequences are close to each other but not enough to be the same OTU. In this case and supposing the algorithm ideally chooses the centers of the OTUs, sequences can lie just between these OTUs. In the current implementations, these ambiguous sequences that must be assigned are usually put in OTUs of their own, increasing the number of OTUs and reducing the overall quality of the clustering.
Using fuzzy clustering allows us to identify these ambiguous sequences. Using the previously mentioned choice strategy, they can be assigned to a good OTU even though they lie slightly outside of the distance threshold. However, their ambiguousness may be significant for the user. It is thus important to highlight their existence and the various fuzzy OTUs they could have alternatively been assigned to. We used our algorithm on a dataset containing 5977 sequences of length between 900 and 3081 for an average of 1442 and taxonomies extracted from the SILVA database. We used a threshold of 0.97 (97% similarity) for determining new OTUs and a threshold of 0.95 for fuzzy membership. For the choice of the OTU for each sequence, we present the results of three strategies : best quality ( = 1 and = 0), compromise ( = 0:5 and = 0:5) and distance ( = 0 and = 1). The comparison with VSEARCH is done using identical parameters when applicable.
The program, dataset and corresponding taxonomy are available on http://projets.isima.fr/sclust/ Expe.html. 6.2
To measure the effects of introducing uncertainty to the clustering, we consider the following metrics : centered on isolated sequences near good OTUs. That isolation lowers their quality and the good OTUs absorb their sequences.
The distance between two sequences in the taxonomy is defined as the sum of the lengths of the path from their nearest commonality. For example, if a sequence is classified as ”bacteria;proteobacteria;betaproteobacteria” and the other is classified as ”bacteria;proteobacteria;alphaproteobacteria ”, their distance is 2 as each of them is at a distance 1 from their commonality ””bacteria;proteobacteria”. 6.3
First, let us begin with the results obtained using the default values for –maxaccepts and –maxrejects in Table 3.
Then, the results obtained using –maxaccepts 10000 and –maxrejects 10000 in Table 4. 6.4
Results show that the choice strategy affects every metric relevant to the quality of the clustering : number of OTUs, singletons and pairs, average misclassification. The fuzzy approach uses slightly more memory than VSEARCH but all choice strategies are similar on this metric. When using the default –maxaccepts and –maxrejects values, computation time is lower for VSEARCH. However, when using higher values for these parameters – and thus more precise clustering - the computation time is the same for both approaches.
Using the quality also lowers the number of singletons and increases the number of pairs. This most likely means that singletons were created close to either good clusters or one another. The fuzzy approach allows the algorithm to merge those sequences that were slightly too far from the center with their corresponding OTU. The increase in the number of pairs appears to be due to the merging of singletons lying too close to one another.
The average taxonomy distance in OTUs is shown to vary wildly. Using only the quality to choose OTUs increases this number as the “best” OTUs attract all the sequences in their fuzzy surroundings. This causes some sequences belonging to different species to be classified together. However, using a compromise between quality and distance lowers this metric as the best clusters only absorb sequences that are sufficiently close to them and should probably be together while rejecting the sequences that are too different. 7
We observe that the experimental results confirm that adding uncertainty to the clustering helps improve the quality of the output by reducing the number of singletons. Using fuzzy clusters, we are able to extend the clustering threshold to gather additional information on the OTUs’s surroundings and use it to quickly assess their quality. This quality can be used together with the distance to choose an OTU for each sequence. The resulting output contains less singletons and misclassifications. Being able to choose the weight of both distance and quality allows for additional tuning.
As previously mentioned, the fuzziness also makes it possible to detect ambiguous sequences and clusters. In our opinion, this is where further work is required. An ambiguous sequence could be arbitrarily assigned to a nearby OTU, become the center of its own OTU or even be considered as an error and deleted but these operations imply such a knowledge of the domain that interactions with the human user become necessary. However, on datasets containing millions of sequences, the number of alerts would render manual treatment impractical or even impossible. Automatizing this treatment would require being able to adapt to the type of data, domain and preferences of the user. We suggest that machine learning techniques be introduced in the process to automatically learn how to handle these ambiguities.
We observe that increasing the importance of the quality in the OTU choice strategy lowers the final number of OTUs. This is due to the fact that some OTUs are initially created This work was supported by the European Union’s “Fonds Europe´en de De´veloppement Re´gional (FEDER)” program and the Auvergne-Rhone-Alpes region.