BackgroundProtein function prediction is to assign biological or biochemical functions to proteins, and it is a challenging computational problem characterized by several factors: (1) the number of function labels (annotations) is large; (2) a protein may be associated with multiple labels; (3) the function labels are structured in a hierarchy; and (4) the labels are incomplete. Current predictive models often assume that the labels of the labeled proteins are complete, i.e. no label is missing. But in real scenarios, we may be aware of only some hierarchical labels of a protein, and we may not know whether additional ones are actually present. The scenario of incomplete hierarchical labels, a challenging and practical problem, is seldom studied in protein function prediction.ResultsIn this paper, we propose an algorithm to Predict protein functions using Incomplete hierarchical LabeLs (PILL in short). PILL takes into account the hierarchical and the flat taxonomy similarity between function labels, and defines a Combined Similarity (ComSim) to measure the correlation between labels. PILL estimates the missing labels for a protein based on ComSim and the known labels of the protein, and uses a regularization to exploit the interactions between proteins for function prediction. PILL is shown to outperform other related techniques in replenishing the missing labels and in predicting the functions of completely unlabeled proteins on publicly available PPI datasets annotated with MIPS Functional Catalogue and Gene Ontology labels.ConclusionThe empirical study shows that it is important to consider the incomplete annotation for protein function prediction. The proposed method (PILL) can serve as a valuable tool for protein function prediction using incomplete labels. The Matlab code of PILL is available upon request.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-014-0430-y) contains supplementary material, which is available to authorized users.

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Clustering suffers from the curse of dimensionality, and similarity functions that use all input features with equal relevance may not be effective. We introduce an algorithm that discovers clusters in subspaces spanned by different combinations of dimensions via local weightings of features. This approach avoids the risk of loss of information encountered in global dimensionality reduction techniques, and does not assume any data distribution model. Our method associates to each cluster a weight vector, whose values capture the relevance of features within the corresponding cluster. We experimentally demonstrate the gain in perfomance our method achieves with respect to competitive methods, using both synthetic and real datasets. In particular, our results show the feasibility of the proposed technique to perform simultaneous clustering of genes and conditions in gene expression data, and clustering of very high-dimensional data such as text data.

Nearest neighbor classi cation assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions with nite samples due to the curse of dimensionality. Severe bias can be introduced under these conditions when using the nearest neighbor rule. We propose a locally adaptive nearest neighbor classi cation method to try to minimize bias. We use a Chisquared distance analysis to compute a exible metric for producing neighborhoods that are highly adaptive to query locations. Neighborhoods are elongated along less relevant feature dimensions and constricted along most in uential ones. As a result, the class conditional probabilities tend to be smoother in the modi ed neighborhoods, whereby better classi cation performance can be achieved. The e cacy of our method is validated and compared against other techniques using a variety of simulated and real world data.

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