Minimalist ensemble algorithms for genome-wide protein localization prediction
© Lin et al.; licensee BioMed Central Ltd. 2012
Received: 26 December 2011
Accepted: 3 July 2012
Published: 3 July 2012
Computational prediction of protein subcellular localization can greatly help to elucidate its functions. Despite the existence of dozens of protein localization prediction algorithms, the prediction accuracy and coverage are still low. Several ensemble algorithms have been proposed to improve the prediction performance, which usually include as many as 10 or more individual localization algorithms. However, their performance is still limited by the running complexity and redundancy among individual prediction algorithms.
This paper proposed a novel method for rational design of minimalist ensemble algorithms for practical genome-wide protein subcellular localization prediction. The algorithm is based on combining a feature selection based filter and a logistic regression classifier. Using a novel concept of contribution scores, we analyzed issues of algorithm redundancy, consensus mistakes, and algorithm complementarity in designing ensemble algorithms. We applied the proposed minimalist logistic regression (LR) ensemble algorithm to two genome-wide datasets of Yeast and Human and compared its performance with current ensemble algorithms. Experimental results showed that the minimalist ensemble algorithm can achieve high prediction accuracy with only 1/3 to 1/2 of individual predictors of current ensemble algorithms, which greatly reduces computational complexity and running time. It was found that the high performance ensemble algorithms are usually composed of the predictors that together cover most of available features. Compared to the best individual predictor, our ensemble algorithm improved the prediction accuracy from AUC score of 0.558 to 0.707 for the Yeast dataset and from 0.628 to 0.646 for the Human dataset. Compared with popular weighted voting based ensemble algorithms, our classifier-based ensemble algorithms achieved much better performance without suffering from inclusion of too many individual predictors.
We proposed a method for rational design of minimalist ensemble algorithms using feature selection and classifiers. The proposed minimalist ensemble algorithm based on logistic regression can achieve equal or better prediction performance while using only half or one-third of individual predictors compared to other ensemble algorithms. The results also suggested that meta-predictors that take advantage of a variety of features by combining individual predictors tend to achieve the best performance. The LR ensemble server and related benchmark datasets are available at http://mleg.cse.sc.edu/LRensemble/cgi-bin/predict.cgi.
KeywordsProtein subcellular localization Ensemble algorithms Classifiers Logistic regression
Functions of proteins are closely correlated with their subcellular locations. For example, Assfalg et al.  showed that there exists strong correlation between localization and proteins fold and localization can be utilized to predict structure class of proteins. It is thus desirable to accurately annotate subcellular location of proteins to elucidate their functions. In the past ten years, dozens of protein localization algorithms have been proposed based on different information sources such as amino acid composition, sorting signals, functional motifs, conserved domains, homology search, and protein-protein interaction . A variety of machine learning techniques, such as SVM and K-nearest neighbour classifiers, have been used in these prediction algorithms. Although existent methods have achieved success at different degrees, a comprehensive evaluation study has shown that many of the reported prediction accuracies are far from being sufficient for genome wide protein localization prediction .
Recently, several research groups proposed to apply ensemble or integration of algorithms to protein localization prediction [4–8]. Liu et al.  proposed weighted and adaptive weighted voting algorithms in which the overall accuracy of a standalone algorithm is used as the weight. Laurila and Vihinen  proposed an integrated method (PROlocalizer) which combines the predictions of multiple specialized binary localization prediction algorithms such as TMHMM and Phobius. Park et al.  developed a Linear Discriminant Analysis (LDA) method (ConLoc) to assign LDA optimal weights for weighted voting. Assfalg et al.  proposed two ensemble localization algorithms; one is a scored voting scheme based on the ranks of the prediction accuracy of the predictors; the other chose J48 decision tree (DT) classifier as the integration scheme. Shen and Burger  proposed a two-layer decision tree method to improve the prediction accuracy of a single subcellular location. Most of these ensemble algorithms integrated 10 or more standalone prediction methods for localization prediction without considering their relationships such as redundancy and complementarity. This makes these ensemble algorithms computationally intensive. Furthermore, incorporation of unnecessary predictors into an ensemble algorithm may overfit the training data and result in degradation of its prediction performance, which has been reported recently for ensemble mitochondrion predictors .
In this paper, we evaluated 9 standalone localization prediction algorithms and analyzed their bias and relationships in the prediction space of the resulting ensemble algorithms. We found that ensemble algorithms based on the combination of several specific predictors achieved comparable prediction performance as using all 9 predictors, suggesting that a high degree of redundancy exists among all individual predictors. We thus proposed a minimalist ensemble prediction algorithm for subcellular localization prediction and evaluated its performance on two data sets, which showed high performance and significant reduction of computational complexity and running time.
Standalone protein localization predictors
Features used in localization prediction algorithms
Amino acid composition
Known domains or motifs
In addition to amino acid sequence information, protein-protein interaction has been known as external information correlated to protein subcellular localization. A number of algorithms have been developed to utilize PPI features to predict protein localization (Hishigaki et al. , Lee et al.  and Shin et al. ). Recently, our group developed NetLoc , a kernel-based logistic regression (KLR) method, which can effectively extract PPI features to predict protein localization. Considering that NetLoc simply used PPI as its features, we integrated NetLoc into our ensemble algorithms to compare the ensemble performances with and without a PPI-based predictor. In our experiments, PPI data of NetLoc is based on the whole Saccharomyces cerevisiae physical PPI dataset obtained from BioGRID database . We exclude proteins overlapped with our Yeast datasets from the PPI dataset to ensure independency between the training and testing datasets.
Mapping of subcellular locations
Different localization predictors may have different subcell resolutions. In order to compare their performances on genome wide datasets, we applied a location mapping scheme to map the subcellular locations of standalone predictors to unified 5 locations in the ensemble algorithms, including Cytosol, Mitochondrion, Nucleus, Secretory (secretory pathway), and Others. Six classes of subcellular locations are mapped to Secretory according to : extracellular, plasma membrane, endoplasmic reticulum, golgi apparatus, lysosomal, and vacuolar. Except for Cytosol, Mitochondrion, Nucleus, and Secretory, the remaining subcellular locations are categorized as Others. For example, for CELLO, the following subcellular locations are mapped to Secretory: extra, plas, er, vacu, golgi, and lyso; chlo, pero, and cytos are mapped to Others. For WoLFPSORT, E.R., extr, plas, golg, lyso, and vacu are mapped to Secretory; chlo, cysk, and pero are mapped to Others.
Symbols in the formula are explained as follows: for a protein j, the prediction results of nine predictors in the order of predictor 1 to predictor 9 are Cytosol, Nucleus, Nucleus, Mitochondrion, Nucleus, Cytosol, Nucleus, Nucleus, and Nucleus, while the real localization of protein j is Cytosol. In this case, the majority votes (predictions) are for Nucleus, the number of the majority votes is denoted as , which is 6; the number of the second majority votes is denoted as , which is 2; the number of the correct votes is denoted as , which is 2; the prediction result of predictor i is denoted as ; the number of predictors having the same prediction result with predictor i is denoted as . From the formula, we can see that predictor 1 and predictor 6 have the same positive contribution, which is 2*6-2 = 10; predictor 4 has minor negative contribution, which is −5; predictors 2,3,5,7,8,9 have the most negative contribution, which is −10. If the dataset used to learn contribution scores has N proteins, then the final contribution score of a predictor is summation of its N contributions. We normalized the final contribution scores (CS) with the formula: (CS – μ)/σ, where μ and σ are mean and standard deviation of contribution scores among predictors.
Minimalist ensemble prediction algorithm
Existing ensemble algorithms tend to include as many as possible component classifiers for better prediction performance. However, including redundant predictors not only increases computational complexity and collecting effort, but also may lead to over-fitting . Moreover, predictors with poor performance could mislead the ensemble algorithms especially those using majority voting schemes. It is thus desirable to find the minimal subset of predictors for achieving equally good or better prediction performance.
Several strategies can be used to find the minimal set of predictors: exhaustive search of all possible combinations of component predictors, feature selection, and selecting top k most accurate predictors. We did an exhaustive search for all combinations of K individual predictors to build different ensemble algorithms. It shows that combining 6 out of 9 predictors can achieve the best performance when the logistic regression classifier was used to integrate the predictions. However, exhaustive search is a time consuming process especially when the set of available predictors is large. Top-K accuracy selection method is straightforward and fast, but has the limitation of neglecting the redundancy among individual predictors.
Here we proposed a minimalist ensemble design method to approximate the smallest set of predictors with the best possible prediction accuracy. The rationale is to find the smallest subset of predictors whose predictions are highly correlated to the real locations. The minimalist ensemble design problem is similar to feature selection when the prediction labels of individual predictors are considered as features. Here, we chose the correlation based feature subset evaluator (CfsSubsetEval)  as the attribute evaluator to evaluate correlation between a feature subset and the class. Greedy-Stepwise method is used to search optimal feature subsets in different size of K through the space: the starting point of search is set as the set with all available predictors (assume size N). Each time Greedy-Stepwise algorithm will remove one feature or predictor from the set which would produce a reduced set with the highest possible CfsSubsetEval Score. We continue the process until set size is 1, while along the way the predictors in the set with size K are recorded as the output of our minimalist ensemble algorithm. After the K individual predictors are selected based on the training dataset, their predicted localizations for all proteins in the training dataset will be used as features, and a machine learning based classifier, such as naive Bayes, logistic regression, or decision trees is used to train a classifier to predict the final subcellular localization. This method used to select minimalist set of individual predictors can also be used for building ensemble algorithms based on weighted voting or LDA.
The distributions of proteins in different locations for the test datasets
Evaluation of individual predictors and ensemble algorithms
where TP, TN, FP, FN means true positive, true negative, false positive and false negative predictions. It should be noted that since localization prediction is a multi-class classification problem, MCC can only be calculated for each location while an overall accuracy can be calculated for each prediction method for a given dataset. In our experiments, 10-fold cross-validation was used to evaluate all the ensemble algorithms.
Results and discussion
Evaluation of individual predictors
Prediction performance (MCC Scores) of individual predictors for the Yeast Low-Res dataset
LR with 8 predictors without NetLoc
LR with all 9 predictors
Prediction performance (MCC Scores) of individual predictors for the Yeast High-Res dataset
LR with 5 predictors without NetLoc
LR with all 6 predictors
Prediction performance (MCC Scores) of individual predictors for the Human dataset
LR with all 8 predictors
For the Yeast dataset (Tables 3, 4), most algorithms have better performance on predicting Mitochondrion proteins. For the Yeast High-Res dataset (Table 4), we can see that all predictors except NetLoc showed poor performance on predicting proteins localized to secretory pathway compartments especially golgi, and cell periphery. This suggests that PPI can be an effective feature for predicting low-resolution compartments. Predictors with relatively high accuracy on the Yeast Low-Res Secretory proteins, such as CELLO and WoLFPSORT, don’t have corresponding performance on predicting proteins localized to ER, Golgi, Vacuole in the Yeast High-Res dataset which are highly overlapped with the Yeast Low-Res Secretory proteins (Table 3). This means those predictors have difficulties in distinguishing smaller compartments of secretory pathway. YLoc and MultiLoc2 have very different performances between the Yeast Low-Res and High-Res datasets, which could be due to the use of different training datasets. For the Human dataset (Table 5), the Secretory proteins (which are exclusively Extracellular proteins) are the easiest for YLoc, MultiLoc2, and WoLFPSORT, which may suggest that these proteins have more distinct features such as secretory pathway signals than the Yeast Secretory proteins. As shown in Table 1, YLoc, MultiLoc2, and WoLFPSORT all use sorting signals as one of their features. The variation of prediction performance of the individual predictors implies that an ensemble algorithm may be able to integrate their strengths and achieve better overall performance.
From Tables 3, 4, 5 we can compare the performances between logistic regression (LR) ensemble algorithms and their element predictors on the three test datasets. We can see that LR ensemble has better overall accuracy than the best element predictor over the three datasets; for the Yeast Low-Res dataset and Yeast High-Res dataset, LR ensemble have more than 10% improvement over the best element predictors when integrating all available element predictors. However, LR ensemble does not always have the best performance on each compartment. This is because the ensemble training process is to optimize the overall accuracy while performance of certain compartment(s) could be compromised. We can also see that when all of the element predictors failed on certain compartments, such as Golgi and Cell Periphery in the Yeast High-Res dataset, LR ensemble doesn’t have any improvement on predicting those compartments.
Prediction performance of the optimal ensemble algorithms using exhaustive search
We also evaluated the ensemble performance on the Human dataset with all combinations of predictors including YLoc, MultiLoc2, WoLFPSORT, CELLO, SubLoc, Subcell, BaCelLo and KnowPred. However, relatively limited accuracy improvement over the best individual predictor has been achieved by the LR ensemble compared to the Yeast dataset. One reason is that the ensemble algorithm for the Yeast dataset includes NetLoc which uses protein-protein correlation network information for localization prediction. This distinctive feature makes it complementary to the other algorithms, which leads to significant performance boosting. Another reason may be that the strengths and bias of different predictors are enlarged or reduced to different degrees on different datasets, which may result in the change of complementary relationship among predictors. The varying complementary relationship thus leads to different prediction accuracy of the ensemble composed of the same set of predictors on different datasets.
Contributions of individual predictors to the ensemble algorithm
Prediction performance of the minimalist ensemble algorithm
To test the performance of our minimalist LR ensemble algorithm with K component predictors, we run the minimalist algorithm to generate the combination of predictors for each K to build the minimalist ensemble algorithms and then tested them on the Yeast Low-Res and Human datasets. The results in Figure 1 show that for the LR ensemble method, our minimalist ensemble algorithm can achieve near-optimal performance for any given K value. We also found that using 3–4 individual predictors can obtain near-best performance for all possible K values on the Yeast Low-Res dataset. This means that our minimalist ensemble algorithm can use 1/2 to 1/3 of individual predictors used by existing ensemble algorithms to achieve similar performance while remarkably reducing the computational effort.
The most frequent predictors selected by the minimalist algorithm with size of each K (noted by M) during the 10-fold cross-validation and the best combination of K predictors (noted by B) according to the exhaustive search result of the logistic regression ensemble on the Yeast dataset
Number of predictors
Comparison of computational complexity
The computational complexity of the ensemble involves the effort to collect prediction results from individual predictors either from local software running or from web servers and the total running time. Since most of the predictors are available only via web servers which are sometimes offline, it is desirable to have fewer component predictors. As demonstrated in Figure 1, the minimalist algorithm can efficiently find the key component predictors. Since only 4 predictors are needed for the ensemble algorithm to achieve comparable performance of using 9 predictors, about 1/2 to 2/3 amount of computation time to collect prediction results can be saved.
Comparison of different ensemble schemes
Figure 3(a) and (b) showed the performance of the ensemble algorithms with or without including the PPI based predictor NetLoc. It is observed that ensemble algorithms without NetLoc have much less improvement over the best individual predictors, which means that these ensemble algorithms except weighted voting can automatically take advantage of the unique/beneficial component predictors (such as NetLoc which uses a unique protein-protein interaction features) to improve the performance. From Figure 3(b) we also noticed that LDA ensemble’s performance could degrade dramatically when too many redundant predictors are included without including predictor(s) with distinct property such as NetLoc.
Comparison with other ensemble algorithms
Comparison of the performance of ConLoc and Minimalist LR ensemble algorithm with 13 predictors on the Yeast Low-Res dataset
The best element predictor of ConLoc: SherLoc
LR ensemble with 13 predictors as used in ConLoc
LR + minimalist algorithm to select K out of 13 predictors in ConLoc, K = 4
Comparison of the performance of ConLoc and Minimalist LR ensemble algorithm with 13 predictors on the Human dataset
The best element predictor of ConLoc: Proteome Analyst
LR ensemble with 13 predictors used in ConLoc
LR + minimalist algorithm to select K out of 13 predictors used in ConLoc, K = 3
To investigate the redundancy among ConLoc’s 13 predictors, we applied our minimalist algorithm to select K out of the 13 predictors and tested them on the Yeast Low-Res dataset and the Human dataset. The results (Tables 7 and 8, column 5) showed that for the Yeast Low-Res dataset, using only 4 predictors can achieve equally good performance as using all the 13 predictors. The most frequent 4 predictors selected by our minimalist algorithm during the 10-fold cross-validation are CELLO, Proteome Analyst, PTS1Prowler, and SherLoc. For the Human dataset, using only 3 predictors can achieve better performance than using all the 13 predictors. The most frequent 3 predictors selected by our minimalist algorithm during the 10-fold cross-validation are Proteome Analyst, PTS1Prowler, and SherLoc.
We also tested PROlocalizer which is an integration algorithm based mainly on binary classifiers. However, the server was able to generate prediction results for only 399 out of 1305 proteins in our Human dataset. The overall prediction accuracy of PROlocalizer on those 399 proteins is 0.81 while the standalone predictor YLoc alone has an overall accuracy 0.84 on the same dataset. We argue that it is difficult to construct a reliable protocol-based ensemble algorithm such as PROlocalizer when the predictions of individual predictors are still not reliable leading to accumulation of errors along its sequential inference steps. Instead, the machine learning based ensemble methods can learn complementary rules among the predictors to function as a “protocol” to determine protein localization.
Although many protein localization prediction algorithms have been developed, the prediction performance remains low and the features used to predict localizations are still limited. Ensemble algorithms have shown some promise to take advantage of a variety of features by combining individual predictors. However, combining as many as possible individual predictors, which is the most common strategy, has the drawback of high running complexity and low availability as well as risk of performance degradation. The result of our minimalist ensemble algorithm showed that it is possible to significantly reduce the number of individual predictors in a given ensemble algorithm while maintaining comparable performance. It is also observed that the best component algorithm set tends to keep predictors with unique features, which indicates that new features are the key to further improve the prediction accuracy for localization prediction. The success of our minimalist ensemble algorithm based on feature selection and logistic regression showed that supervised ensemble algorithms based on machine learning can effectively capture the complex relationships among individual predictors and achieve better performance than the voting methods.
We found that our ensemble algorithm works best when predictors with unique features are combined. For example, the PPI based NetLoc algorithm can significantly improve the ensemble performance, which is however limited by the fact that many proteins do not have PPI information. It should be also noted that the PPI information and ensemble predictor itself are species specific. So our ensemble predictor trained on human/yeast dataset may not work well for proteins of other species. However, the design methodology of minimalist ensemble predictors can be used to develop predictors tailored to specific organisms or available training datasets.
This work was supported by the National Science Foundation Career Award (Grant BIO-DBI-0845381).
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