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Decision trees for hierarchical multilabel classification A case study in functional genomics

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Work by Hendrik Blockeel Leander Schietgat Jan Struyf Katholieke Universiteit Leuven (Belgium) Amanda Clare University of Aberystwyth (Wales) Sašo Džeroski Jozef Stefan Institute Ljubljana (Slovenia)

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Overview Hierarchical Multilabel Classification task description Predictive Clustering Trees for HMC the algorithm: Clus-HMC Evaluation on yeast datasets

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Hierarchical multilabel classification (HMC) Classification predict class for unseen instances based on (classified) training examples HMC instance can belong to multiple classes classes are organised in a hierarchy Example toy hierarchy Advantages efficiency skewed class distributions hierarchical relationships 1 (1) 3 (5) 2 (2) 2/1 (3) 2/2 (4)

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Predictive clustering trees ~ decision trees [Blockeel et al. 1998] each node (including leaves) is a cluster tests in nodes are descriptions of clusters Heuristic minimize intra-cluster variance maximise inter-cluster variance Can be extended to perform HMC distance measure d (quantifies similarity) prediction function p (maps a cluster in a leaf onto prediction)

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Instantiating d Class labels are represented in a vector v i = [1,1,0,1,0] (1) (2) (3) (4) (5) Distance between vectors is defined as the component-wise Euclidean distance: d(x 1,x 2 ) = √ ∑ k w k (v 1,k – v 2,k ) 2 1 (1) 3 (5) 2 (2) 2/1 (3) 2/2 (4) (w k = w depth(c k ) ) Example S i = {1,2,2/2}, S j = {2} d Eucl ([1,1,0,1,0],[0,1,0,0,0]) = sqrt(w + w²)

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Instantiating p Each leaf contains multiple classes (organised in a hierarchy) Which classes to predict? binary classification: predict positive if the instance ends up in a leaf with at least 50% positives multilabel classification: skewed class distributions Threshold an instance ending up in some leaf is predicted to belong to class c i if v i t i, with v i the proportion of instances in the leaf belonging to c i, and t i some threshold by varying threshold, we obtain different points on the precision-recall curve

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Clus-HMC algorithm Pseudo code stopping criterion

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Experiments in yeast functional genomics Saccharomyces cerevisiae or baker’s/brewer’s yeast MIPS FunCat hierarchy function of yeast genes 12 data sets [Clare 2003] Sequence structure (seq) Phenotype growth (pheno) Secondary structure (struc) Homology search (hom) Microarray data cellcycle, church, derisi, eisen, gasch1, gasch2, spo, expr (all) 1 METABOLISM 1/1 amino acid metabolism 1/2 nitrogen and sulfur metabolisms … 2 ENERGY 2/1 glycolysis and gluconeogenesis …

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Experimental evaluation Objectives Comparison with C4.5H [Clare 2003] Evaluation of the improvement obtainable with HMC trees over single classification trees Evaluation with precision-recall curves precision recall advantages = TP / Yes = TP / (TP+FP) = TP / + = TP / (TP+FN)

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Comparison with C4.5H C4.5H = hierarchical multilabel extension of C4.5 [Clare 2003] Designed by Amanda Clare Heuristic: information gain adaptation of entropy (sum of all classes) Prediction: most frequent set of classes + significance test Clus-HMC method Tuning: different F-tests on validation data, choose F-test with highest AUPRC

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Comparison between Clus-HMC and C4.5H Average case

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Comparison between Clus-HMC and C4.5H Specific classes 25 wins (II), 6 losses (IV) III IIIIV

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Comparing rules e.g. predictions for class 40/3 in “gasch1” data set C4.5H: two rules Clus-HMC (most precise rule) IF 29C_Plus1M_sorbitol_to_33C_Plus_1M_sorbitol_ __15_minutes <= 0.03 AND constant_0point32_mM_H202_20_min_redo <= 0.72 AND 1point5_mM_diamide_60_min <= -0.17 AND steady_state_1M_sorbitol > -0.37 AND DBYmsn2_4__37degree_heat___20_min <= -0.67 THEN 40/3 IF Heat_Shock_10_minutes_hs_1 <= 1.82 AND Heat_Shock_030inutes__hs_2 <= -0.48 AND 29C_Plus1M_sorbitol_to_33C_Pl us_1M_sorbitol___5_minutes > -0.1 THEN 40/3 IF Nitrogen_Depletion_8_h <= -2.74 AND Nitrogen_Depletion_2_h > -1.94 AND 1point5_mM_diamide_5_min > -0.03 AND 1M_sorbitol___45_min_ > -0.36 AND 37C_to_25C_shock___60_min > 1.28 THEN 40/3 Precision: 0.52 Recall: 0.26 Precision: 0.56 Recall: 0.18 Precision: 0.97 Recall: 0.15

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HMC vs. single classification Method Average case

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HMC vs. single classification Specific classes numbers are AUPRC(Clus-HMC) – AUPRC(Clus-SC) HMC performs better!

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Conclusions Use of precision-recall curves to optimize the learned models and to evaluate the results Improvement over C4.5H HMC compared to SC Comparable predictive performance Faster Easier to interpret

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References Hendrik Blockeel, Luc De Raedt, Jan Ramon, Top-down induction of clustering trees (1998) Amanda Clare, Machine learning and data mining for yeast functional genomics, Doctoral dissertation (2003) Jan Struyf, Sašo Džeroski, Hendrik Blockeel, Amanda Clare, Hierarchical multi- classification with predictive clustering trees in functional genomics (2005)

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