short lectures notes
Data Fusion Tutorial Jane looks foR help! [BC]2 Basel, June 9, 2015 jane’s personal hairball! Hi jane. NAR just published 176 new bio databases*! Ohhh! What’s wrong? How about stiching them in a single data table? I could work this out, but not for every different data source out there. .... Messy. Think about all different edge types! I have no idea how to Make anything useful. TRMT61A RecA_monomer-monomer_interface Tried it. A nightmare! Think of GO annotationS in the data table of yeast phenotypes! TOP3B NFX1 PMS1 GBP2 RAD52 RPL11 Homologous Recombination Repair Double-Strand Break Repair TP53 POLD4 RAD54B POLD1 ACACB RPA1 RPA4 EIF5A DNA Repair RAD9B CRYAB RPA2 PMS2 POLR2K RFC5 TERF2IP MND1 TOP3A Meiotic Recombination MUS81 ATR BIOCARTA_ATM_PATHWAY MYO18A RPA3 RFC3 BIOCARTA_ATRBRCA_PATHWAY UBE2I MSH3 PRKDC RAD9A POLD3 BARD1 FANCD2 RFC1 AIRE PCNA WRN ZNF280B EME1 DNAJA3 TERF2 CDK2 RFC2 RFC4 Told you! EXO1 ACACA MLH1 MLH3 XRCC2 XRCC5 DMC1 DNA_recomb/repair_RecA MDC1 MRE11A CSNK1D RAD51 APEX2 Homologous recombination MSH5 DNA_recomb/repair_Rad51_C FANCL SEC14L5 RAD51D C10orf2 POLD2 MSH2 H2AFX FANCF CSNK1E XRCC6 ATM PPP1CC JUN FANCE CHEK2 FANCA RAD51AP1 RBBP8 RAD51B FIGN TP53BP1 FEN1 CHEK1 SSBP1 UIMC1 Homologous recombination repair of ... SHFM1 LIG1 MSH5-C6orf26 FANCG RAD51C HSPA9 RAD54L FANCC MED6 XRCC4 Mismatch repair COPB2 NBN BRCA2 BLM TOPBP1 XRCC3 DNA_recomb_RecA/RadB_ATP-bd BRCA1 RAD50 MSH6 BRIP1 MSH4 PALB2 Meiosis BARD1 signaling events GYS1 Fanconi anemia pathway CSTF1 FAM175A ANAPC2 * Fernandez-suarez & galperin, nucleic acids research, 2013. Large-scale data fusion by collective matrix factorization Tutorial at the Basel Computational Biology Conference, Basel, Switzerland, 2015 These notes include introduction to integrative data analysis with examples from collaborative filtering and systems biology, and Orange workflows that we will construct during the tutorial. Tutorial instructors: Marinka Zitnik and Blaz Zupan, with the help from members of Bioinformatics Lab, Ljubljana. Welcome to the hands-on Data Fusion Tutorial! This tutorial is designed for data mining researchers and biologists with interest in data analysis and large-scale data integration. We will explore latent factor models, a popular class of approaches that have in recent years seen many successful applications in integrative data analysis. We will describe the intuition behind matrix factorization and explain why factorization approaches are suitable when collectively analyzing many heterogeneous data sets. To practice data fusion, we will construct visual data fusion workflows using Orange and its Data Fusion Add-on. If you haven’t already installed Orange, please follow the installation guide at http://biolab.github.io/datafusion-installation-guide. * See http://helikoid.si/recomb14/zitnik-zupan-recomb14.png for our full award-winning poster on data fusion. 1 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 1: Everything is a Matrix In many data mining applications there are plenty of potentially beneficial data available. However, these data naturally come in various formats and at different levels of granularity, can be represented in totally different input data spaces and typically describe distinct data types. Gene interaction network can easily be converted to a matrix. Each wighted edge in a network corresponds to a matrix entry. gacT ga cT ge mA rdi A rac N rac J rac I xa cA rac M For joint predictive modeling of heterogeneous data we need a generic way to encode data that might be fundamentally different from each other, both in type and in structure. An effective way to organize a data compendium is to view each data set a matrix. Matrices describe dyadic relationships, which are relationships between two groups of objects. A matrix relates objects in the rows to objects in the columns. Examples of data matrices commonly used in the analysis of biological data include degrees of protein-protein interactions from the STRING database that are represented in a gene-to-gene matrix: gemA gacT rdiA gemA racN rdiA racJ racN racM racJ racI racI xacA xacA racM Binary matrices can be used to associate Gene ontology terms with cellular pathways: alg7 alg13 alg14 alg1 Ontology terms Part of N-Glycan biosynthesis pathway Fructose and mannose metabolism dpm1 dpm2 dpm3 Protein N-linked glycosylation (GO:0006487) Orthology Dolichol kinase (K00902) Alpha-mannosidase II (K01231) Oligosaccharyltransferase complex (K12668) Ontology GO:0004168 GO:0004572 GO:0008250 Pathways Binary relations between two object types can be represented with a binary matrix. 2 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 research articles with Medical Subject Headings (MeSH): Papers cited in PubMed are tagged with MeSH terms. We can use one large binary matrix to encode relations between research articles and MeSH terms. Medical Subject Headings MeSH terms Literature Cell separation Cytoplasmic vesicles/metabolism Ethidium/metabolism Immunity/innate Mutation Phagocytes/cytology Phagocytes/immunology* Phagocytosis* or membership of genes in pathway, one column for each pathway: Part of N-Glycan biosynthesis pathway alg7 alg13 alg14 alg1 alg2 Pathways Fructose and mannose metabolism alg11 dpm1 dpm2 dpm3 alg12 Genes Just like the relations between MeSH terms and scientific papers, we can encode pathway memberships of genes in one large matrix that has genes in rows, pathways in commons. alg3 alg9 GPI-anchor biosynthesis The structure of Gene Ontology can be represented with a real-valued matrix whose elements represent distance or semantic similarity between the corresponding ontological terms: Part of Gene Ontology graph Response to external biotic stimulus Defense response Response to other organisms Defense response to other organism Response to bacterium Defense response to bacterium Gene Ontology terms Response to biotic stimulus Re oth spon s er org e to an ism s Response to external stimulus Re to spon str es se s Response to stress Gene Ontology terms Any ontology can be represented with a square matrix. We use ontology to measure distances between its entities, and encode these distances in a distance matrix. Response to bacterium Defense response 3 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 2: The Challenge Suppose we would like to identify genes whose mutants exhibit a certain phenotype, e.g., genes that are sensitive to Gram negative bacteria. In addition to current knowledge about phenotypical annotations, i.e. data encoded in a gene-tophenotype matrix, which might be incomplete and contain some erroneous information, there exists a variety of circumstantial evidence, such as gene expression data, literature data, annotations of research articles etc. An obvious question is how to link these seemingly disparate data sets. In many applications there exists some correspondence between different input dimensions. For example, genes can be linked to MeSH terms via gene-to-publication and publication-to-MeSH-term data matrices. This is an important observation, which we exploit to define a relational structure of the entire data system. The data excerpt on the right comes from a gene prioritization problem where our goal was to find candidates for bacterial response genes in a social amoeba Dictyostelium. Other than for a few seed genes, there was not any data from which we could directly infer the bacterial phenotype of mutants. Hence, we considered circumstantial data sets and hoped that their fusion would uncover interesting new bacterial response genes. Gram neg. defective Aberrant spore color Aberrant spore color Decreased chemotaxis Gram pos.defective The major challenge for such problems is how to jointly model multiple types of data heterogeneity in a mutually beneficial way. For example, in the scheme below, can information about the relatedness of MeSH terms and similarity between phenotypes from the Phenotype Ontology help us to improve the accuracy of recognizing Gram negative defective genes? Phenotype Ontology Mutant Phenotypes Timepoints spc3 swp1 kif9 alyL Genes nagB1 gpi shkA nip7 Publications Pubmed data Phenotype data MeSH terms Expression data MeSH terms MeSH Ontology MeSH annotations 4 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 3: Recommender Systems Sparse matrices and matrix completion have been thoroughly addressed in the area of machine learning called recommender systems. Several methods from this field form foundation for matrix-based data fusion. Hence, we diverge here from fusion to recommender systems, and for a while, from biology to movies. How would you decide which movie to recommend to a friend? Obviously, a useful source of information might be ratings of the movies your friend had seen in the past, i.e. one star up to five stars. Movie recommender systems primarily use user ratings information from which they estimate correlations between different movies and similarities between users and infer a prediction model which can be used to make recommendations about which movie a user should see next. For example, in the figure below we see a movie ratings data matrix containing information for four users and four movies. Notice that in a real setting such matrices can contain information for millions of users and hundreds of thousands of movies. However, each individual user typically sees only a small proportion of all the movies and rates even fewer of them. Hence, data matrices in recommender systems are typically extremely sparse, e.g., it is common that up to ~99% of matrix elements are unknown. This characteristic together with a strong relational structure of the data, i.e. “you might enjoy movies, which users similar to you, are enthusiastic about” and “you might like movies that are similar to the movies you have already seen and rated favorably.” The movie rating matrix has users in rows and movies in columns. We made this explicit in this simple graph: object types are represented as nodes (User, Movie) and an edge is labeled with a matrix that relates them. ss W eng ar o ers Br f th id e Th e W Wo a rl e M rs ds at rix Re lo ad e d Is there an analogy between recommender systems and challenges in systems biology? We will answer these questions in the next lessons. User Pa John, Kate, Alex and Mike rated a selection from four movies, Passengers, War of the Worlds, Bride Wars and The Matrix Reloaded. John, for example, has seen Passengers and Bride Wars, and did not like them so much. Which of the two other movies, if any, he should see? John Kate Alex Mike 2 3 5 4 4 4 5 5 Movie 5 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 4: Matrix Factorization and Completion Taking our four-by-four movie ratings matrix we can try to factorize it into a product of two much smaller latent matrices called latent factors. One latent matrix describes latent profiles of the users and the other matrix contains latent data representation of the movies. L1 L2 John 0.2 0 Kate Pa Two-factorization of a user-movie rating matrix from the previous page. Factorization rank of 2 was used. Should factorization rank be the same for both latent matrices? ss W eng ar of ers Br th ide e Th W Wo a rl e M rs ds at rix Re loa de d For example, each of our four users is described by a latent profile of length two and similarly, each movie is explained via two latent components, i.e. L1 and L2. The dimensionality of a latent model is typically called factorization rank. 0 0.5 Alex 0.5 0 Mike L1 6.3 0 1.1 8 L2 3.9 10.7 0 3.3 0 0.5 Latent model, that is, the two latent matrices are complete, hence their product is also a complete matrix. This product (matrix on the right) is an estimate of an original matrix (matrix on the left). How good is our reconstruction? Which of the two movies should be recommend to Mike? Pa ss W eng ar of ers Br th id e Th e W Wo a rl e M rs ds at rix Re lo ad e d The challenge of matrix factorization stems from the difficulty of estimating the latent matrices in a way that their matrix product minimizes some measure of discrepancy between the input data matrix and its reconstruction obtained by factorization. Importantly, reconstructed matrix is complete, i.e. all of its elements are defined, which we exploit for making predictions. John 2 Kate Alex 3 5 4 Mike 4 1.3 4 5 5 ~ ~ 0 0.2 1.6 2 5.4 0 1.7 3.2 0 0.6 4 2 5.4 0 1.7 6 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 5: Matrix Tri-Factorization d ss W eng ar of ers Br th id e Th e W Wo a rl e M rs ds at rix Re lo ad e U1 U2 John 0.2 0.3 Kate 0.8 0.2 M1 M2 Alex 0.7 1.2 U1 -4.4 9.1 M1 0.9 0.2 0.2 1 Mike 0.8 1.2 U2 6.7 -5.8 M2 0.6 0.8 0.1 0.7 Pa Similarly to the previous lesson, the goal of matrix ti-factorization is to estimate three latent matrices that provide a quality approximation of observed entries in the input data matrix. By selecting sufficiently small factorization rank, we compress the data, which ensures generalization and consequently prediction of how a given user would enjoy a particular movie he has not seen before. Just like for twofactorization, in trifactorization the latent matrices are complete. So is their product (the matrix on the right). This product is also an estimate of the original matrix. How good is our estimate? Which movie should be recommended to Mike? Pa ss W eng ar of ers Br th id e Th e W Wo a rl e M rs ds at rix Re lo ad e d The backbone matrix (a 2x2 matrix in the middle) could be seen as a compressed version of original user-movies rating matrix. It has “meta” users in rows and “meta” movies in columns. We can use the two recipe matrices (left and right matrix) to transform the backbone matrix back to the original user-movies space. So far, we found a decomposition of the movie ratings matrix into two latent matrices. An alternative approach is to factorize it into three latent matrices; one latent matrix that expresses the degrees of user membership to each of the latent components, i.e. user recipe matrix; another latent matrix with memberships of movies to movie-specific latent components, i.e. movie recipe matrix. A third matrix, i.e. a backbone matrix, captures the interactions between latent components specific to the users, i.e. U1, U2, and components specific to the movies, i.e. M1, M2. John 2 Kate Alex 3 5 4 Mike 4 1.1 0.3 0.2 1.2 4 5 5 ~ ~ 1.7 4.5 0.2 2.1 4.1 0.5 0.9 4.5 1.5 4.8 0.1 1.9 7 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 6: Tri-Factorization in Orange In Orange workflows its components (widgets) load or process data and pass the information to other widgets. Widgets inputs are on its left, and outputs on its right. Try adding a Data Table widget to display an input data set and any of the latent factors! Let's try matrix tri-factorization in practice. We construct a visual workflow in Orange, a data mining suite. The workflow loads movie ratings, represents them with a data matrix, tri-factorizes it and explores the latent factors. In this tutorial we organize the data sets using a structure that we call a data fusion graph. It shows the relational structure of entire data collection. Each distinct type of objects, e.g., users, movies, is represented with a node and each data set corresponds to an edge that relates two types of objects, e.g., movie ratings data relate users with the movies. In Latent Factors widget one can select any of the latent matrices and then explore them further, say, through hierarchical clustering. 8 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 7: Collective Matrix Factorization and Sharing of Latent Factors Orange workflow on this page adds another data source: movie genres. How does that effect the results of the movie clustering? In the previous lesson we analyzed a single data set. Ultimately, we would like to collectively tri-factorize many heterogeneous data sets across different input spaces. Suppose we have collected information about movie genres. This is a relation that relates movies to genres, hence our data fusion graph gets an additional node, i.e. genres, and an edge linking movies with genres. To fuse heterogeneous data at large scales we need to define the kind of knowledge that can be transferred between related data matrices, types of objects and prediction tasks. Data fusion algorithms typically rely on one of the following three assumptions: Relation transfer: We build the relational map called a data fusion graph of all the relations considered in data fusion and relax the assumptions about independently and identically distributed relations. Object type transfer: We assume that there exists a common feature space shared by the input spaces, which can be used as a bridge to transfer knowledge. Parameter transfer: We make use of latent model parameterization and assume that heterogeneous input spaces have shared latent parameters and hyperparameters. In collective matrix factorization we achieve data fusion by sharing latent matrices across related data sets. In our running example we reuse the movie recipe matrix in both decompositions of user-to-movie as well as movie-to-genre matrices. Importantly, collective matrix factorization estimates the latent matrices for all data sets in a compendium simultaneously, which ensures transfer of knowledge between data, i.e. data fusion, and presents many unique opportunities from the application perspective and challenges in algorithmic design. 9 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 8: More Complex Fusion Schemes, Data Sampling and Completion Scoring So far we fused at most two data sets. Let’s proceed by constructing a larger data compendium. There are many other sources of information that might be informative for movie recommendation, for example, user demographics profiles, movie casting, information about movie directors and screenplays, scenery, etc. We construct an Orange workflow that considers four data sources, i.e. movie ratings, movie casting, genres and relationships between actors, and fuse them via collective matrix factorization. This data fusion configuration is already a complex one. We are using four different data sources. Try having a Fusion Graph widget window open, so that you can see the data fusion schema as it shapes up when adding the data sets. A simple way to assess the benefits of integrative data analysis over the analysis of a single homogeneous data set is to measure the quality of predictions made by data fusion versus the quality of prediction model inferred from a part of data collection. The assessment is fair if we evaluate predictions for data that are hidden from the algorithm during prediction model inference. There are four different ways of partitioning a data matrix into a training and a test set: 10 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 In predictive modeling tasks, such as movie recommendation, where we regress against the target variable, i.e. movie rating, we can evaluate model quality by reporting a variety of measures, including the root mean squared error (RMSE). A lower RMSE value indicate a better model. Alternatively, if our goal would be to rank the movies from what the model believes are the most enjoyable to the least enjoyable for a given user, we would use the area under curve (AUC). How does the quality of reconstruction change when adding or removing data sets from the fusion schema? Try it out! Should RMSE always decrease with new data sources being added? 11 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 9: “Meta Genes” - Latent Profiling Until now we focused on non-biological data. We now apply a latent factor model to gene expression data. The microarray data for this example is from an influential paper by DeRisi, Iyer, and Brown (Science 1997), who explored the metabolic and genetic control of gene expression on a genomic scale. The authors used DNA microarrays to study temporal gene expression of almost all genes in baker’s yeast Saccharomyces cerevisiae during the metabolic shift from fermentation to respiration. Expression levels were measured at seven time points during the diauxic shift, e.g. T1 to T7. Experiments V4 T1 T2 T3 T4 T5 T6 T7 V3 V2 Genes Gene expression V5 V1 T1 T2 T3 T4 T5 T6 T7 Timepoints As we will see in this and in the next lessons, collective matrix factorization is a generic and flexible tool for integrative data analysis in different domains, e.g., recommender systems and functional genomics. What is similar between matrix-based movie recommendation system and data fusion in molecular biology? Everything! We’ll use the same set of Orange widgets for bio data fusion. All tricks that we have learned so far apply. We construct an Orange workflow that reads the expression data into Orange using Table to Relation widget, tri-factorizes the data, and explores the estimated latent data representation using various Orange widgets, such as Linear Projection, Scatter Plot and Multi-dimensional Scaling (MDS). 12 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 By factorizing gene expression data we obtained three latent data matrices: a gene recipe matrix, an experiment recipe matrix, and a backbone matrix that relates both recipe matrices in the latent space. It is common in matrix factorization algorithms to interpret the experiment recipe matrix as a matrix that reports on expression of “meta genes,” i.e. “genes,” whose profiles are obtained from the original gene expression profiles by a linear (or, nonlinear, depending on a latent factor model) transformation. Similarly, one can see the gene recipe matrix as a matrix that reports on expression of genes in “meta experiments,” i.e. “experiments,” which cannot be interpreted in an intuitive manner but which can improve the quality of prediction models applied to them, e.g., clustering of genes based on their recipe matrix and enrichment analysis of detected clusters. Combination of hierarchical clustering and GO enrichment analysis is a cool way to explore results of data fusion. Genes in the data set we are exploring are also function-labeled. Any other ideas how to use latent matrices? Classification, perhaps? And then estimation of AUC in cross-validation? 13 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 10: The Yeast Case Study Next, we collectively analyze eight data sets from molecular biology of yeast S. cervisiae (load the data sets from http://bit.ly/1Gb8SJ7). We organize them in a data fusion graph with six object types and eight edges, one for each data set. This schema looks boring. But it offers so much for the patient one! Try adding matrix sampling and RMSEbased evaluation! Or clustering with gene set enrichment. Or data projection based on any of the latent matrices. 14 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 11: Latent Matrix Chaining The concept of chaining latent matrices is important because it allows us to profile objects in the latent space of any other object type based on the connectivity in the data fusion graph. In the simplest scenario, where object types are adjacent in the fusion graph, e.g., “Genes” and “Experiments” from Lesson 9, chaining construct data profiles of one object type, e.g., genes, in the latent space of another object type, e.g., experiments, by multiplying the recipe matrix of the first object type by the backbone matrix of the data set. The resulting profile matrix has objects of the first type, e.g., genes, in rows and the latent components of the second type, e.g., experiments, in columns. However, the power of chaining becomes apparent when we would like to profile objects whose types are not direct neighbors in the fusion graph, such as “Genes” and “Literature Topics,” i.e. MeSH terms, in the fusion graph from Lesson 10. To profile genes in the latent space of literature topics chaining starts with the recipe matrix of genes and multiplies it by backbone matrices of gene-to-literature and literatureto-literature-topic data sets on the path from “Genes” to “Literature Topics” in the fusion graph. This procedure yields profiles of genes in the latent space of literature topics. Latent matrix chaining constructs dense profiles that include the most informative features obtained by collectively compressing data via matrix factorization. Intuitively, chaining is able to establish links between genes and literature topics even though relationships between these object types are not available in input data. A conceptual presentation of profiling of genes in the latent space of MeSH terms. The MeSH-based gene profiles are constructed by multiplying latent factors on the path from one to another object type. Topics of yeast biology Literature Topic G en e lit er at ur e Literature Chain of latent matrices Gene Gene Gene Literature topic = x Literature topic x = Gene profile matrix 15 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 In Orange we chain the latent matrices of a data system using the Chaining widget. Chaining widget allows us to select a start object type and a target object type (highlighted in orange below) in the latent fusion graph. It then computes the chains associated with selected nodes from the fusion graph. The so obtained profile matrices can be used for further data analysis. Chaining and construction of relations for objects that were originally not related in any input data set comes as an extra benefit of matrix-based data fusion. Try exploring the chaining results by feeding them into a data table first, and then push them through unsupervised or supervised analysis pipeline. 16 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 12: Case Studies in Data Fusion Identification of the mechanisms of action of chemical compounds is a crucial task in drug discovery. We have integrated 6 data sets to improve prediction pharmacologic actions of chemical compounds (IEEE TPAMI 2015). 2 Pharmacologic Action Θ1 1 R12 R13 3 PMID Chemical R14 R15 4 6 Depositor R46 Depositor Category 5 Substructure Fingerprint Root layer We have fused 11 systemslevel molecular data sets to predict disease-disease associations (Sci Reports 2013). ... gastric lymphoma crescentic glomerulonephritis ... 146 Hodgkin’s lymphoma Cushing’s syndrome Largest disease class Level 1 cancer inherited metabolic disorders nervous system diseases respiratory system diseases cardiovascular system disease 51 bile duct disease hemolytic-uremic syndrome Level 2 immune system diseases cognitive disorders acquired metabolic diseases metabolic diseases cancer 18 pulpitis periodontitis Level 3 ... Disease class size: a single disease two diseases three or more diseases 18 6 abetalipoproteinemia, lung metastasis dysgerminoma serous cystadenoma factor XIII deficiency Plasmodium falciparum malaria eighteen diseases 17 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 5 Data fusion of 11 data sets substantial raised the accuracy of gene function predictions, also when compared to kernel-based data integration approach (IEEE TPAMI 2015). 4 R45 5 MeSH Descriptor PMID IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. X, NO. X, OCTOBER 2013 11 R14 TABLE 1 R42 3 Cross-validated F11 and AUC accuracy scores for fusion by matrix factorization (DFMF), kernel-based method (MKL), random forests (RF) and relational learning-based matrix factorization (tri-SPMF). Experimental R13 1 Prediction task Condition 2 DFMF F12 AUC Gene R12 100 D. discoideum genes 1000 D. discoideum genes R16 Whole D. discoideum genome Pharmacologic actions F1 0.799 0.801 GO Term R62 6 0.826 0.831 0.663 6 MKL AUC 0.781 0.787 0.800 0.639 0.823 0.849 0.834 RF 0.788 0.798 0.821 0.811 F1 AUC 0.761 0.767 0.782 0.643 0.785 0.788 0.801 0.819 tri-SPMF F1 AUC 0.731 0.756 0.778 0.641 0.724 0.741 0.787 0.810 TABLE 2 KEGG Gene Ontology term-specific cross-validated F1 and AUC accuracy scores for fusion by matrix factorization Pathway (DFMF), kernel-based method (MKL), random forests (RF) and relational learning-based matrix factorization (tri-SPMF). Terms in Gene Ontology belong to one of three namespaces, biological process (BP), molecular function (MF) or cellular component. GO term name Term identifier Namespace Size 0007190 0006935 0043327 0006909 0009617 0016337 0003779 0003796 0003700 1.0 0.835 0.8 0.830 Averaged F1 score Prioritization of genes in a quest to identify the most promising candidates for bacterial response in Dictyostelium fused 13 input data sets. Out of 9 top-rated candidates, 8 predictions were confirmed in the wet lab (submitted, 2015). Averaged F1 score Activation of adeny. cyc. act. Chemotaxis Chemotaxis to cAMP Phagocytosis Response to bacterium Cell-cell adhesion Actin binding Lysozyme activity Seq.-spec. DNA bind. t. f. a. (a)0.6 A 0.4 0.0 Tri-factorization R12 , R12 A 1 A-B Rof12matrix , R13R 12 , R13 , 1 11 58 21 33 51 14 43 4 79 0.834 0.981 0.922 0.956 0.899 0.883 0.676 0.782 0.956 Step 1. Compressive data fusion 0.820 Data fusion graph A 0.781 0.786 0.862 0.901 0.761 0.856 0.658 0.750 0.901 RF AUC 0.758 0.538 0.798 0.789 0.785 0.728 0.642 0.754 0.732 0.601 0.724 0.767 0.619 0.761 0.725 0.737 0.625 0.759 tri-SPMF F1 AUC 0.729 0.804 0.838 0.836 0.817 0.799 0.671 0.747 0.892 0.731 0.810 0.815 0.810 0.831 0.834 0.682 0.625 0.852 E B 5.4 BMatrix Factor Initialization Study We studied the effect of matrix factor initialization on DFMF by observing the reconstruction error after one and after twenty iterations of optimization procedure, the latter being about one fourth of the iterations Collective matrix D C requiredC forfactorization the optimization algorithm to converge when predicting gene functions. We estimated the error relative to the optimal (k1 , k2 , . . . , k6 )-rank approximation given by the SVD. For iteration v and F G G matrix Rij the error was computed by: 0.810 0.0 0.2 0.4 0.6 0.8 1.0 Proportion of 1 included in the model (b) D Fig. 5. Adding newB data sources (a) or incorporating Backbone Recipe matrix of of A A-B more matrix object-type-specific constraints in ⇥1 (b) both increase the accuracy of matrix factorization-based Recipe F matrix of B models for gene function prediction task. A 0.770 0.794 0.835 0.892 0.788 0.867 0.664 0.774 0.894 F1 data representation E (a) 0.844 0.980 0.910 0.932 0.870 0.861 0.781 0.750 0.948 MKL F1 AUC to held-out constraints to zero so that they did not affect the cost function during optimization. Fig. 5b shows that including additional information on genes in the form of constraints improves the predictive (c) performance of DFMF for gene function prediction. Fused latent A 0.825(b) 0.815 B 0.2 BP BP BP BP BP BP MF MF MF DFMF F1 AUC Errij (v) = ||Rij (v) (v) (v) ||2 Gi Sij (GT j ) dF (Rij , [Rij ]k ) , (14) dF (Rij , [Rij ]k ) function prediction in x x = ~ ~ Fig. 5a, where we started with Data set relating only the target data source R and then added either B A Reconstructed (v) (v) (v) 12 objects of type A matrix A-B where Gi , Gj and Sij were matrix factors obof type B R13 or ⇥1 or both. Similar effects wereto objects observed tained after v iterations of factorization algorithm. Step 3. Similarity Step 2. Object profiling by when we studied other combinations of data sources estimation chaining of latent matrices In Eq. (14), dF (Rij , [Rij ]k ) = ||Rij Uk ⌃k VkT ||2 (not shown here for brevity). Notice also that due to denotes the Frobenius distance between Rij and its (d) (f) (e) Chains latent starting at A ensembling the cross-validated variance ofof F is small. 1 matrices Seed by genes the SVD, where k = k-rank approximation given A i i A max(ki , kj ) is the approximation rank. Errij (v) is a ii Chains Candidate 5.3 Sensitivity to Inclusion of Constraints iii pessimistic measure of quantitative accuracy because gene iv A B ii v We varied the sparseness of gene constraint matrix ⇥1 of the choice of k. This error measure is similar vi Similarity scoring Similarity score Scored aggregation vii candidate gene by holding out a random subset ofiii protein-protein E B to the error of the two-factor non-negative matrix A G inChain of viii latent matrices Seed ix teractions. We set the entries of ⇥ that corresponded factorization from [17]. 1 genes A C D C F iv A Object type D F v A D vi A D vii A E viii A D F ix A E G F Similarity score matrix B C Step 4. Gene ranking (g) Profiling of objects of type A in the latent space of C A C = A A C = D x F x C x = Profile matrix A C Candidate genes Similarity scoring Similarity score aggregation Scored candidate genes Similarity score matrices 18 Data Fusion Tutorial In drug toxicity prediction the task was to distinguish between compounds that represent little or no health concern and those with the greatest likelihood to cause adverse effects in humans (CAMDA 2013). Highthroughput and toxicogenomic screening coupled with a plethora of circumstantial evidence provide a challenge for improved toxicity prediction and require appropriate computational methods that integrate various biological, chemical and toxicological data. Fusion of 29 data sets allowed us to improve prediction accuracy well above that achieved by standard supervised approaches (Sys Biomed 2014). 12 9 Hematology, biochemistry, liver weight Sample metadata R6;12 R5;12 R5;9 [BC]2 Basel, June 9, 2015 R7;9 R6;9 R8;9 11 Drug type 6 Sample from rat in vivo repeated dose study 5 Sample from rat in vivo single dose study R1,5 Gene from rat in vivo single dose study R7,10 R8,10 10 R2,6 Drug Θ R4,10 R2,10 1,1 R3,10 2 Gene from rat in vivo repeated dose study R1,13 R4,8 R3,7 Θ10,10 R1,10 1 8 Sample from human in vitro study R10;11 R6,10 R5,10 7 Sample from rat in vitro study 3 Θ2,2 R2,13 R10;14 14 4 Gene from human in vitro study Gene from rat in vitro study Θ4,4 Θ3,3 R3,13 R4,13 DILI potential 13 GO term Θ13,13 19 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 13: Related Work on Data Fusion Lanckriet, Gert R.G., et al. A statistical framework for genomic data fusion. Bioinformatics 20.16 (2004): 2626-2635. The first study to propose a kernel-based integration as a way of intermediate data integration. Schadt, Eric E., et al. An integrative genomics approach to infer causal associations between gene expression and disease. Nature Genetics 37.7 (2005): 710-717. This study integrated DNA variation and gene expression data to identify drivers of complex traits. Aerts, Stein, et al. Gene prioritization through genomic data fusion. Nature Biotechnology 24.5 (2006): 537-544. The paper describes Endeavour, a tool to prioritize candidate genes underlying biological processes or diseases, based on their similarity to known genes involved in these phenomena. Mostafavi, Sara, et al. GeneMANIA: a real-time multiple association network integration algorithm for predicting gene function. Genome Biology 9.Suppl 1 (2008): S4. GeneMANIA is a tool that integrates multiple functional association networks and predicts gene functions using label propagation. Zitnik, Marinka, et al. Discovering disease-disease associations by fusing systemslevel molecular data. Scientific Reports 3 (2013). A study of relationships between diseases based on evidence from fusing available molecular interaction and ontology data. Wang, Bo, et al. Similarity network fusion for aggregating data types on a genomic scale. Nature Methods 11.3 (2014): 333-337. Fusion of cancer patient similarity networks by combining mRNA expression, DNA methylation and microRNA expression data. Zitnik, Marinka, and Zupan, Blaz. Matrix factorization-based data fusion for druginduced liver injury prediction. Systems Biomedicine 2.1 (2014): 16-22. An application of a data fusion approach for prediction of drug toxicity in humans using 29 data sets provided by the CAMDA 2013 Challenge. Ritchie, Marylyn D., et al. Methods of integrating data to uncover genotypephenotype interactions. Nature Reviews Genetics 16.2 (2015): 85-97. This review explores emerging approaches for data integration including multi-staged, metadimensional and factor analysis. Zitnik, Marinka, and Zupan, Blaz. Data fusion by matrix factorization. IEEE Transactions on Pattern Analysis and Machine Intelligence 37.1 (2015): 41-53. An introduction and formalization of collective matrix factorization as presented in this tutorial. The paper also provides mathematical derivation of optimization approach. 20 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 14: Related Tools for Data Fusion 21 Data Fusion Tutorial [BC]2 Basel, June 9, 2015 Lesson 15: Data Fusion in Python We have developed a scripting library in Python, which implements collective matrix factorization and completion, and is suitable for fusion of large data compendia. The official source code repository is at http://github.com/marinkaz/scikit-fusion. 22
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