- Open Access
Fast subcellular localization by cascaded fusion of signal-based and homology-based methods
© Mak et al; licensee BioMed Central Ltd. 2011
- Published: 14 October 2011
The functions of proteins are closely related to their subcellular locations. In the post-genomics era, the amount of gene and protein data grows exponentially, which necessitates the prediction of subcellular localization by computational means.
This paper proposes mitigating the computation burden of alignment-based approaches to subcellular localization prediction by a cascaded fusion of cleavage site prediction and profile alignment. Specifically, the informative segments of protein sequences are identified by a cleavage site predictor using the information in their N-terminal shorting signals. Then, the sequences are truncated at the cleavage site positions, and the shortened sequences are passed to PSI-BLAST for computing their profiles. Subcellular localization are subsequently predicted by a profile-to-profile alignment support-vector-machine (SVM) classifier. To further reduce the training and recognition time of the classifier, the SVM classifier is replaced by a new kernel method based on the perturbational discriminant analysis (PDA).
Experimental results on a new dataset based on Swiss-Prot Release 57.5 show that the method can make use of the best property of signal- and homology-based approaches and can attain an accuracy comparable to that achieved by using full-length sequences. Analysis of profile-alignment score matrices suggest that both profile creation time and profile alignment time can be reduced without significant reduction in subcellular localization accuracy. It was found that PDA enjoys a short training time as compared to the conventional SVM. We advocate that the method will be important for biologists to conduct large-scale protein annotation or for bioinformaticians to perform preliminary investigations on new algorithms that involve pairwise alignments.
- Subcellular Localization
- Cleavage Site
- Spectral Space
- Sorting Signal
- Subcellular Localization Prediction
Motivation of subcellular localization prediction
For a protein to function properly, it must be transported to the correct organelles of a cell and folded into correct 3-D structures. Therefore, knowing the subcellular localization of a protein is one step towards understanding its functions. However, the determination of subcellular localization by experimental means is often time-consuming and laborious. Given the large number of un-annotated sequences from genome projects, it is imperative to develop efficient and reliable computation techniques for annotating biological sequences.
In recent years, impressive progress has been made in the computational prediction of subcellular localization. A number of approaches have also been proposed in the literature. These methods can be generally divided into four categories, including predictions based on sorting signals [1–6], global sequence properties [7–10], homology [11–13] and other information in addition to sequences [14, 15]. Methods based on sorting signals are very fast, but they typically suffer from low prediction accuracy. Homology-based methods are more accurate, but they are very slow. Therefore, fast and reliable predictions of subcellular localization still remain a challenge.
Approaches to subcellular localization prediction
Signal-based methods predict the localization via the recognition of N-terminal sorting signals in amino acid sequences. PSORT, proposed by Nakai in 1991 , is one of the early predictors that use sorting signals for protein’s subcellular localization. PSORT and its extensions – WoLF PSORT [3, 4] – derive features such as amino acid compositions and the presence of sequence motifs for localization prediction. In the late 90’s, researchers started to investigate the application of neural networks  to recognize the sorting signals. In a neural network, patterns are presented to the input layer of artificial neurons, with each neuron implementing a nonlinear function of the weighted sum of the inputs. Because amino acid sequences are of variable length, the input to the neural network is extracted from a short window sliding over the amino acid sequence. TargetP [17, 18] is a well-known predictor that uses neural networks.
Another type of approaches relies on the fact that proteins of different organelles have different global properties such as amino-acid composition. Based on amino-acid composition and residue-pair frequencies, Nakashima and Nishikawa  developed a predictor that can discriminate between soluble intracellular and extracellular proteins. Another popular predictor based on amino acid composition is SubLoc . In SubLoc, a query sequence is converted to 20-dim amino-acid composition vector for classification by support vector machines (SVMs). Recently, Xu et al.  proposed a semi-supervised learning technique (a kind of transductive learning) that makes use of unlabelled test data to boost the classification performance of SVMs. One limitation of composition-based methods is that information about the sequence order is not easy to represent. Some authors proposed using amino-acid pair compositions (dipeptide) [8, 9, 20] and pseudo amino-acid compositions  to enrich the representation power of the extracted vectors.
The homology-based methods use the query sequence to search protein databases for homologs [11, 12] and predict the subcellular location of the query sequence as the one to which the homologs belong. This kind of method can achieve very high accuracy when homologs of experimentally verified sequences can be found in the database search . A number of homology-based predictors have been proposed. For example, Proteome Analyst  uses the presence or absence of the tokens from certain fields of the homologous sequences in the Swiss-Prot database as a means to compute features for classification. In Kim et al. , an unknown protein sequence is aligned with every training sequences (with known subcellular locations) to create a feature vector for classification. Mak et al.  proposed a predictor called PairProSVM that uses profile alignment to detect weak similarity between protein sequences. Given a query sequence, a profile is obtained from PSI-BLAST search . The profile is then aligned with every training profile to form a score vector for classification by SVMs.
Some predictors not only use amino acid sequences as input but also require extra information such as lexical context in database entries  or Gene Ontology entries  as input. Although studies have shown that this type of method can outperform sequence-based methods, the performance has only been measured on data sets where all sequences have the required additional information.
Limitations of existing approaches
Among all the methods mentioned above, the signal-based and homology-based methods have attracted a great deal of attention, primarily because of their biological plausibility and robustness in predicting newly discovered sequences. Comparing these two approaches, the signal-based methods seem to be more direct, because they determine the localization from the sequence segments that contain the localization information. However, this type of method is typically limited to the prediction of a few subcellular locations only. For example, the popular TargetP [5, 6] can only detect three localizations: chloroplast, mitochondria, and secretory pathway signal peptide. The homology-based methods, on the other hands, can in theory predict as many localizations as available in the training data. The downside, however, is that the whole sequence is used for the homology search or pairwise alignment, without considering the fact that some segments of the sequence are more important or contain more information than the others. Moreover, the computation requirement will be excessive for long sequences. The problem will become intractable for database annotation where tens of thousands of proteins are involved.
Our proposal for addressing the limitations
Our earlier report  has demonstrated that computation time of subcellular localization based on profile alignment SVMs can be substantially reduced by aligning profiles up to the cleavage site positions of signal peptides, mitochondrial targeting peptides, and chloroplast transit peptides. Although 20-fold reduction in total computation time (including alignment, training and recognition time) has been achieved, the method fails to reduce the profile creation time, which will become a substantial part of the total computation time when the database becomes large. In this paper, we propose a new approach that can reduce both the profile creation time and profile alignment time. In the new approach, instead of cutting the profiles, we shorten the sequences by cutting them at the cleavage site locations. The shortened sequences are then presented to PSI-BLAST to compute the profiles. To further reduce the training and recognition time of the classifier, we propose replacing the SVMs by kernel perturbation discriminants.
Fusion of signal- and homology-based methods
Truncation of profiles/sequences
I: Truncating Profiles. Given a query sequence, we pass it to PSI-BLAST  to determine a full-length profile (PSSM and PSFM ). The profile is then truncated at the cleavage site position. The truncated profile is aligned with each of the training profiles to create a vector for classification. Note that the training profiles are also created by the same procedure.
II: Truncating Sequences. Given a query sequence, we truncate it at the cleavage site and pass the truncated sequence to PSI-BLAST to determine a short-length profile. The profile is then aligned with all of the training profiles to create a vector for classification. All training profiles are also created by the same procedure.
Note that as the time taken by PSI-BLAST search (profile-creation time) is proportional to the query sequence, Scheme II is expected to provide more computation saving than Scheme I. However, as the sequences are truncated at an early stage, important information may be lost if cleavage site prediction is inaccurate. The “Results and Discussion” Section provides experimental evidences suggesting that Scheme II can provide significant computation saving without suffering from severe information loss.
Cleavage site prediction
Grouping of amino acids according to their hydrophobicity and charge/polarity .
TargetP is one of the most popular signal-based sub-cellular localization predictors and cleavage site predictors. Given a query sequence, TargetP can determine its subcellular localization and will also invoke SignalP , ChloroP , or a program specialized for mTP to determine the cleavage site of the sequence. TargetP requires the N-terminal sequence of a protein as input. During prediction, a sliding window scans over a query sequence; for each segment within the window, a numerically encoded vector is presented to a neural network to compute the segment score. The cleavage site is determined by finding the position at which the score is maximum. The cleavage site prediction accuracy of SignalP on Eukaryotic proteins is around 70%  and that of ChloroP on cTP is 60% (±2 residues) .
Only the entries of Eukaryotic species, which were annotated with “Eukaryota” in the OC (Organism Classification) fields in Swiss-Prot, were included.
Entries annotated with ambiguous words, such as “probable”, “by similarity” and “potential”, were excluded because of the lack of experimental evidence.
Sequences annotated with “fragment” were excluded.
For signal peptides, mitochondria, and chloroplast, only sequences with experimentally annotated cleavage sites were included.
Breakdown of eukaryotic dataset derived from the Swiss-Prot database (release 57.5).
Number of Proteins
PDA and SVM for multi-class classification
We used perturbational discriminant analysis (PDA)  and support vector machines (SVMs)  for classification. The formulation of PDA can be found in the Appendix. During the training phase, N training profiles were obtained by Scheme I or Scheme II. Pair-wise profile-alignments were then performed to create an N × N symmetric score matrix K, which were then used to train the PDA and SVM classifiers as follows.
One-vs-rest PDA and SVM classifier
Cascaded fusion of PDA and SVM
where 1 is an N- dim vector of all 1’s and p is a perturbation parameter. During recognition, an unknown sample x is projected onto a (C – 1)-dim PDA space spanned by [a 1,…,a C--1] using
g(x) = Â T k(x) + [b 1,…, b C– 1]T, g(x) ∊ ℜ C –1 .
We used 5-fold cross validation to evaluate the performance. The overall prediction accuracy, the accuracy for each subcellular location, and the Matthew’s correlation coefficient (MCC)  were used to quantify the prediction performance. MCC allows us to overcome the shortcoming of accuracy on unbalanced data .
We measured the computation time on a Core 2 Duo 3.16GHz CPU running Matlab and SVMlight. The computation time was divided into profile creation time, alignment time, classifier training time, and classification time.
Performance of cleavage site prediction
Cleavage-site prediction accuracies achieved by TargetP and CSitePred. For TargetP, (P) and (N) mean using the ‘Plant’ and ‘Non-plant’ option of the predictor, respectively. TargetP will invoke SignalP, ChloroP, or a program specialized in predicting mTP for cleavage site prediction. CSitePred is based on conditional random fields.
Cleavage Site Predictor
Cleavage Site Prediction Accuracy (%)
The prediction accuracy of chloroplasts by TargetP shown in Table 3 is significantly lower than that in . There are two reasons for this difference: (1) our dataset has sequence identity lower than that of  and (2) we consider predicting precisely the ground-truth sites as correct predictions whereas  considers predictions within ±2 positions of the ground-truth sites as correct predictions. In fact, if we relaxed the criterion of correct prediction to ±2 ground-truth positions, the prediction accuracy on chloroplasts achieved by TargetP increases to 47.06%.
To evaluate the effect of incorrect cleavage site prediction on the accuracy of subcellular localization, sensitivity analysis was performed by truncating SP, mTP, and cTP at the ground-truth cleavage sites and plus/minus several positions of the ground-truths. Specifically, the sequence cut-off positions are 16, 8, and 2 amino acids upstream and 2, 16, 32, and 64 amino acids downstream from the ground-truth cleavage site.
Apparently, mTP and cTP are more sensitive to the error of cleavage site prediction, which agrees with the fact that the signals of mTP and cTP are weaker. Localization performance of these sequences degrades when the cut-off position drifts away significantly the ground-truth cleavage site. But the overall accuracy can be maintained at above 95% even if the drift is as large as –16 and +64 positions from the ground-truth. Moreover, a forward drift of 64 positions from the ground truth cleavage site leads to a higher overall accuracy when compared to that of a backward drift of 16 positions, which suggests that cutting sequences before their cleavage sites may lose useful information in the signal pep-tides while including extra (may be irrelevant) information by cutting sequences after their cleavage sites is not detrimental to subcellular location accuracy.
Average computation time to create a profile by PSI-BLAST using sequences of different length as input. In Scheme I, full-length sequences are presented to PSI-BLAST and the resulting profiles are truncated at the predicted cleavage sites. In Scheme II, truncation is applied to the sequences before presenting to PSI-BLAST. In both cases, CRFs (CSitePred) were used to predict the cleavage sites.
Input to PSI-BLAST
Profile Creation Time (second)
Subcellular Localization Accuracy
Sequences truncated at predicted cleavage sites
Profile-Alignment time and subcellular localization accuracy for different sequence cut-off positions in Scheme II. In the first column, “Full length” means that no sequence truncation was applied. “TargetP(P)” and “Tar-getP(N)” mean that the cutoff position is determined by TargetP using the “Plant” option and “Non-plant” option, respectively. CSitePred is a cleavage site predictor based on conditional random fields.
Seq. Cutoff position
Alignment Time for Each Profile (sec.)
Subcellular Localization Accuracy (%)
Determined by TargetP(P)
Determined by TargetP(N)
Determined by CSitePred
SVM versus PDA
The computation time and performance of different classifiers in the subcellular localization task. The classification time is the time to classify a profile-alignment score vector with dimension equal to the number of training vectors. The training time is the time required to train a classifier, given a profile-alignment score matrix K. In PDAproj+SVM, PDA was applied to project the samples in the input space to a (C - 1)-dim space (C = 4 here); the projected vectors were then classified by RBF-SVMs.
Training Time (sec.)
Classification Time (sec.)
Compared with state-of-the-art predictors
Subcellular localization performance achieved by different classifiers. The second column specifies the cleavage site predictors that were used for determining the positions at which the amino sequences were truncated. Notice that TargetP can perform both cleavage site prediction and subcellular localization. For Rows 4 and 5, TargetP was used as a cleavage site predictor, where “TargetP(P)” and “TargetP(N)” mean selecting plant or non-plant option in TargetP, respectively. For Rows 6–8 “CRF” means that conditional random fields were used for cleavage site prediction.
Cleavage Site Predictor
Classification Accuracy (%)
Matthew’s correlation coefficient (MCC)
Because ChloroP is weak in predicting the cleavage sites of chloroplasts (see Table 3), it is not a good candidate for assisting PairProSVM. This is evident by the low subcellular localization accuracy of chloroplasts in Table 7 when TargetP is used as a cleavage site predictor. However, TargetP is fairly good at predicting the subcellular location of chloroplasts when it is used as a localization predictor.
Among the four classes in Table 7, the subcellular localization accuracies of mitochondria and chloroplasts are generally lower than that of Ext and Cyt/Nuc. The reason may be that these transit peptides are less well characterized and their motifs are less conserved than those of secretary signal peptides .
Table 7 also suggests that the TargetP(N) is very effective in assisting PairProSVM, leading to the highest prediction accuracy (92.6%) among all subcellular localization predictors. In particular, except for predicting Chl, TargetP in combination with PairProSVM can surpass the other methods in subcellular localization accuracy and MCC.
This paper has demonstrated that homology-based sub-cellular localization can be speeded up by reducing the length of the query amino acid sequences. Because shortening an amino acid sequence will inevitably throw away some information in the sequence, it is imperative to determine the best truncation positions. This paper shows that these positions can be determined by cleavage site predictors such as TargetP and CSitePred. The paper also shows that as far as localization accuracy is concerned, it does not matter whether we truncate the sequences or truncate the profiles. However, truncating the sequence has computation advantage because this strategy can save the profile creation time by as much as 6 folds.
This appendix derives the formulations of kernel discriminant analysis. The key idea lies in the equivalency between the optimal projection vectors in the Hilbert space, spectral space and empirical space.
Input, Hilbert, spectral, and empirical Spaces
The construction of the empirical space for vectorial and non-vectorial data are quite different. For the former, the elements of K are a simple function of the corresponding pair of vectors in X. For the latter, the elements in K are similarities between the corresponding pairs of objects.
The kernel matrix K can be factorized with respect to the basis functions in H: K = ΦT Φ, where . Alternatively, it can be factorized via spectral decomposition: where .
where λ i is the i-th element of the diagonal of Λ.
Note that K = ET E, i.e., . Therefore, .
where we have used the relationships w = Φ a and v = Ea .
Orthogonal hyperplane principle (OHP)
Assume that the dimension of H is M and that the training data in H are mass-centered. When M >N, all of the N training vectors will fall on an ( M –1)-dim data hyperplane. Mathematically, the data-hyperplane is represented by its normal vector p such that Φ T p = 1. The optimal decision-hyperplane in H (represented by w) must be orthogonal to the data-hyperplane:
wT p = 0 ⇒ αT ΦT p = 0 ⇒ αT1 = 0.
Kernel Fisher discriminant analysis (KFDA)
where 1 is an N- dim vector with all elements equal to 1 and and are between-class and within-class covariance matrices in E space, respectively.
Perturbational discriminant analysis (PDA)
The FDA and KFDA are based on the assumption that the observed data are perfectly measured. It is however crucial to take into account the inevitable perturbation of training data. For the purpose of designing practical classifiers, we can adopt the following perturbational discriminant analysis (PDA).
where η is a scalar whose value can be determined through the optimal solution in K space as follows.
Note that unlike Eq. 6, Eq. 8 does not require spectral decomposition, thus offering a fast close-form solution. Also, Eq. 6 suggests that ρ has more regularization effect on the minor components with small eigenvalues than on the major components with large eigenvalues. This serves well the purpose of regularization. Consequently, a PDA classifier will use less proportion of minor (and risky) components and more of major components. Therefore, the parameter p plays two major roles: (1) it can assure the Mercer condition and invertibility of the kernel matrix; and (2) it can suppress the weights assigned to the risker and less resilient components.
where y i = 1 when x i ∊ C + and y i = –1 when x i ∊ C –. Since K is invertible, we have a opt = K–1(y–b 1). Eqs. 6 and 8 suggest that perturbation in the spectral space can be represented by shifting the diagonal of K by p. Therefore, taking the perturbation in the spectral space into account, we have
a opt = (K + ρ I)–1 (y –b 1). (11)
Note that the solutions of a and b in Eqs. 11 and 12 are equivalent to the least-squares SVM , although the way to derive the solutions are different.
This work was in part supported by The Hong Polytechnic University (G-U877) and Research Grant Council of the Hong Kong SAR (PolyU 5264/09E). This work is based on our presentation “Truncation of Protein Sequences for Fast Profile Alignment with Application to Subcellular Localization” in IEEE BIBM’2010, Hong Kong.
This article has been published as part of Proteome Science Volume 9 Supplement 1, 2011: Proceedings of the International Workshop on Computational Proteomics. The full contents of the supplement are available online at http://www.proteomesci.com/supplements/9/S1.
- von Heijne G: A new method for predicting signal sequence cleavage sites. Nucleic Acids Research 1986,14(11):4683–4690. 10.1093/nar/14.11.4683PubMed CentralPubMedView ArticleGoogle Scholar
- Nakai K, Kanehisa M: Expert system for predicting protein localization sites in gram-negative bacteria. Proteins: Structure, Function, and Genetics 1991,11(2):95–110. 10.1002/prot.340110203View ArticleGoogle Scholar
- Horton P, Park KJ, Obayashi T, Nakai K: Protein Subcellular Localization Prediction with WoLF PSORT. Proc. 4th Annual Asia Pacific Bioinformatics Conference (APBC06) 2006, 39–48.Google Scholar
- Horton P, Park K, Obayashi T, Fujita N, Harada H, Adams-Collier C, Nakai K: WoLF PSORT: protein localization predictor. Nucleic acids research 2007,35(Web Server issue):585–587.View ArticleGoogle Scholar
- Emanuelsson O, Nielsen H, Brunak S, von Heijne G: Predicting subcellular localization of proteins based on their N-terminal amino acid sequence. J. Mol. Biol. 2000,300(4):1005–1016. 10.1006/jmbi.2000.3903PubMedView ArticleGoogle Scholar
- Emanuelsson O, Brunak S, von Heijne G, Nielsen H: Locating proteins in the cell using TargetP, SignalP, and related tools. Nature Protocols 2007,2(4):953–971. 10.1038/nprot.2007.131PubMedView ArticleGoogle Scholar
- Hua SJ, Sun ZR: Support vector machine approach for protein subcellular localization prediction. Bioinformatics 2001, 17: 721–728. 10.1093/bioinformatics/17.8.721PubMedView ArticleGoogle Scholar
- Huang Y, Li YD: Prediction of protein subcellular locations using fuzzy K-NN method. Bioinformatics 2004, 20: 21–28. 10.1093/bioinformatics/btg366PubMedView ArticleGoogle Scholar
- Park KJ, Kanehisa M: Prediction of protein subcellular locations by support vector machines using compositions of amino acids and amino acid pairs. Bioinformatics 2003,19(13):1656- 1663. 10.1093/bioinformatics/btg222PubMedView ArticleGoogle Scholar
- Nakashima H, Nishikawa K: Discrimination of intracellular and extracellular proteins using amino acid composition and residue-pair frequencies. J. Mol. Biol. 1994, 238: 54–61. 10.1006/jmbi.1994.1267PubMedView ArticleGoogle Scholar
- Mott R, Schultz J, Bork P, Ponting C: Predicting protein cellular localization using a domain projection method. Genome research 2002,12(8):1168–1174. 10.1101/gr.96802PubMed CentralPubMedView ArticleGoogle Scholar
- Scott M, Thomas D, Hallett M: Predicting subcellular localization via protein motif co-occurrence. Genome research 2004,14(10a):1957–1966. 10.1101/gr.2650004PubMed CentralPubMedView ArticleGoogle Scholar
- Mak MW, Guo J, Kung SY: PairProSVM: Protein Subcellular Localization Based on Local Pairwise Profile Alignment and SVM. IEEE/ACM Trans. on Computational Biology and Bioinfor-matics 2008,5(3):416–422.View ArticleGoogle Scholar
- Nair R, Rost B: Inferring sub-cellular localization through automated lexical analysis. Bioinformatics 2002, 18: S78-S76. 10.1093/bioinformatics/18.suppl_1.S78PubMedView ArticleGoogle Scholar
- Chou K, Shen H: Recent progress in protein subcellular location prediction. Analytical Biochemistry 2007, 370: 1–16. 10.1016/j.ab.2007.07.006PubMedView ArticleGoogle Scholar
- Baldi P, Brunak S: Bioinformatics : The Machine Learning Approach. 2nd edition. MIT Press; 2001.Google Scholar
- Nielsen H, Engelbrecht J, Brunak S, von Heijne G: A neural network method for identification of prokaryotic and eukaryotic signal perptides and prediction of their cleavage sites. Int. J. Neural Sys. 1997, 8: 581–599. 10.1142/S0129065797000537View ArticleGoogle Scholar
- Nielsen H, Engelbrecht J, Brunak S, von Heijne G: Identification of prokaryotic and eukaryotic signal peptides and prediction of their cleavage sites. Protein Engineering 1997, 10: 1–6. 10.1093/protein/10.1.1PubMedView ArticleGoogle Scholar
- Xu Q, Hu DH, Xue H, Yu W, Yang Q: Semi-supervised protein subcellular localization. BMC Bioinformatics 2009., 10: Google Scholar
- Yuan Z: Prediction of protein subcellular locations using Markov chain models. FEBS Letters 1999, 451: 23–26. 10.1016/S0014-5793(99)00506-2PubMedView ArticleGoogle Scholar
- Chou KC: Prediction of protein cellular attributes using pseudo amino acid composition. Proteins: Structure, Function, and Genetics 2001, 43: 246–255. 10.1002/prot.1035View ArticleGoogle Scholar
- Nair R, Rost B: Sequence conserved for subcellular localization. Protein Science 2002, 11: 2836–2847.PubMed CentralPubMedView ArticleGoogle Scholar
- Lu Z, Szafron D, Greiner R, Lu P, Wishart DS, Poulin B, An-vik J, Macdonell C, Eisner R: Predicting subcellular localization of proteins using machine-learned classifiers. Bioinformat-ics 2004,20(4):547–556. 10.1093/bioinformatics/btg447View ArticleGoogle Scholar
- Kim JK, Raghava GPS, Bang SY, Choi S: Prediction of subcellular localization of proteins using pairwise sequence alignment and support vector machine. Pattern Recog. Lett. 2006,27(9):996–1001. 10.1016/j.patrec.2005.11.014View ArticleGoogle Scholar
- Altschul SF, Madden TL, Schaffer AA, Zhang J, Zhang Z, Miller W, Lipman DJ: Gapped BLAST and PSI-BLAST: A new generation of protein database search programs. Nucleic Acids Res 1997, 25: 3389–3402. 10.1093/nar/25.17.3389PubMed CentralPubMedView ArticleGoogle Scholar
- Wang W, Mak MW, Kung SY: Speeding up Subcellular Localization by Extracting Informative Regions of Protein Sequences for Profile Alignment. In Proc. Computational Intelligence in Bioinformatics and Computational Biology. Montreal; 2010:147–154.Google Scholar
- Mak MW, Kung SY: Conditional Random Fields for the Prediction of Signal Peptide Cleavage Sites. In Proc. ICASSP. Taipei; 2009:1605–1608.Google Scholar
- Lafferty J, McCallum A, Pereira F: Conditional random fields: Probabilistic models for segmenting and labeling sequence data. Proc. 18th Int. Conf. on Machine Learning 2001.Google Scholar
- von Heijne G: Patterns of amino acids near signal-sequence cleavage sites. Eur J Biochem 1983, 133: 17–21. 10.1111/j.1432-1033.1983.tb07424.xPubMedView ArticleGoogle Scholar
- Bendtsen JD, Nielsen H, von Heijne G, Brunak S: Improved prediction of signal peptides: SignalP 3.0. J. Mol. Biol. 2004, 340: 783–795. 10.1016/j.jmb.2004.05.028PubMedView ArticleGoogle Scholar
- Emanuelsson O, Nielsen H, von Heijne G: ChloroP, a neural network-based method for predicting chloroplast transit pep-tides and their cleavage sites. Protein Science 1999, 8: 978–984. 10.1110/ps.8.5.978PubMed CentralPubMedView ArticleGoogle Scholar
- Nielsen H, Brunak S, von Heijne G: Machine learning approaches for the prediction of signal peptides and other protein sorting signals. Protein Eng 1999, 12: 3–9. 10.1093/protein/12.1.3PubMedView ArticleGoogle Scholar
- Menne KML, Hermjakob H, Apweiler R: A comparison of signal sequence prediction methods using a test set of signal peptides. Bioinformatics 2000, 16: 741–742. 10.1093/bioinformatics/16.8.741PubMedView ArticleGoogle Scholar
- Kung SY: Kernel Approaches to Unsupervised and Supervised Machine Learning. In Proc. PCM, LNCS 5879. Edited by: Muneesawang P. Springer-Verlag; 2009:1–32.Google Scholar
- Vapnik VN: Statistical Learning Theory. New York: Wiley; 1998.Google Scholar
- Matthews BW: Comparison of predicted and observed secondary structure of T4 phage lysozyme. Biochim. Biophys. Acta. 1975, 405: 442–451.PubMedView ArticleGoogle Scholar
- Tsuda K: Support vector classifier with asymmetric kernel functions. In Proc. ESANN. Bruges, Belgium; 1999:183–188.Google Scholar
- Mika S, Ratsch G, Weston J, Scholkopf B, Mullers KR: Fisher discriminant analysis with kernels. In Neural Networks for Signal Processing IX Edited by: Hu YH, Larsen J, Wilson E, Douglas S. 1999, 41–48.Google Scholar
- Kung S, Mak M: PDA-SVM Hybrid: A Unified Model For Kernel-Based Supervised Classification. Journal of Signal Processing Systems for Signal, Image, and Video Technology 2011. To appearGoogle Scholar
- Suykens JAK, Vandewalle J: Least squares support vector machine classifiers. Neural processing letters 1999,9(3):293–300. 10.1023/A:1018628609742View ArticleGoogle Scholar
- Wu CH, McLarty JM: Neural Networks and Genome Informatics. Elsevier Science; 2000.Google Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.