#### BACKGROUND:

Classification is the problem of assigning each input object to one of a finite number of classes. This problem has been extensively studied in machine learning and statistics, and there are numerous applications to bioinformatics as well as many other fields. Building a multiclass classifier has been a challenge, where the direct approach of altering the binary classification algorithm to accommodate more than two classes can be computationally too expensive. Hence the indirect approach of using binary decomposition has been commonly used, in which retrieving the class posterior probabilities from the set of binary posterior probabilities given by the individual binary classifiers has been a major issue.

#### METHODS:

In this work, we present an extension of a recently introduced probabilistic kernel-based learning algorithm called the Classification Relevance Units Machine (CRUM) to the multiclass setting to increase its applicability. The extension is achieved under the error correcting output codes framework. The probabilistic outputs of the binary CRUMs are preserved using a proposed linear-time decoding algorithm, an alternative to the generalized Bradley-Terry (GBT) algorithm whose application to large-scale prediction settings is prohibited by its computational complexity. The resulting classifier is called the Multiclass Relevance Units Machine (McRUM).

#### RESULTS:

The evaluation of McRUM on a variety of real small-scale benchmark datasets shows that our proposed Naïve decoding algorithm is computationally more efficient than the GBT algorithm while maintaining a similar level of predictive accuracy. Then a set of experiments on a larger scale dataset for small ncRNA classification have been conducted with Naïve McRUM and compared with the Gaussian and linear SVM. Although McRUM's predictive performance is slightly lower than the Gaussian SVM, the results show that the similar level of true positive rate can be achieved by sacrificing false positive rate slightly. Furthermore, McRUM is computationally more efficient than the SVM, which is an important factor for large-scale analysis.

#### CONCLUSIONS:

We have proposed McRUM, a multiclass extension of binary CRUM. McRUM with Naïve decoding algorithm is computationally efficient in run-time and its predictive performance is comparable to the well-known SVM, showing its potential in solving large-scale multiclass problems in bioinformatics and other fields of study.

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