Modeling Gene Transcriptional Regulation by Means of … · 2018-08-09 · Modeling Gene Transcriptional Regulation by Means of Hyperplanes Genetic Clustering Fabrizio Frasca , Matteo

Modeling Gene Transcriptional Regulationby Means of Hyperplanes Genetic Clustering

Fabrizio Frasca∗, Matteo Matteucci†, Marco Masseroli‡ and Marco Morelli§∗†‡Dipartimento di Elettronica, Informazione e Bioingegneria

Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milan, Italy§Center for Genomic Science of IIT@SEMM,

Istituto Italiano di Tecnologia (IIT), 20139 Milan, Italy∗Email: [email protected] †Email: [email protected]

‡Email: [email protected] §Email: [email protected]

Abstract—In the wide context of biological processes reg-ulating gene expression, transcriptional regulation driven byepigenetic activity is among the most effective and intriguing ones.Understanding the complex language of histone modifications andtranscription factor bindings is an appealing yet hard task, giventhe large number of involved features and the specificity of theircombinatorial behavior across genes. Genome-wide regressionmodels for predicting mRNA abundance quantifications fromepigenetic activity are interesting in an exploratory framework,but their effectiveness is limited as the relative predictive powerof epigenetic features is hard to discern at such level of resolution.On the other hand, an investigative analysis cannot rely on priorbiological knowledge to perform sensible grouping of genes andlocally study epigenetic regulative processes. In this context, weshaped the “gene stratification problem” as a form of epigeneticfeature-based hyperplanes clustering, and proposed a geneticalgorithm to approach this task, aiming at performing data-driven partitioning of the whole set of protein coding genes ofan organism based on the characteristic relation between theirexpression and the associated epigenetic activity. We observedhow, not only the hyperplanes described by the resulting parti-tions significantly differ from each other, but also how differentepigenetic features are of diverse importance in predicting geneexpression within each partition. This demonstrates the validityand biological interest of the proposed computational method andthe obtained results.

Keywords—Gene expression, Epigenetic transcriptional regula-tion, K-planes regression, Genetic clustering

I. INTRODUCTION

Gene expression regulation is an essential, yet very sophis-ticated mechanism to increase or decrease the production rateof gene products such as proteins or, more generally, RNA.This regulatory phenomenon is important for both simple andmore complex forms of life, providing the ability to dynami-cally adapt to mutating environmental conditions and enablingcellular differentiation. Gene regulation actually involves thecoordination of several complex mechanisms acting at differentlocations and stages of the expression of a gene. Among thebiological processes most effective in this task there are theones involved in transcription initiation [1], the majority ofthem occurring at the epigenetic level, i.e., just acting ‘ontop’ of the genome by means of chemical modifications andprotein bindings. In this context, the main role is played by thecombinatorial interactions between transcription factors [2],[3], and histone modifications [4], [5] (respectively TF and

HM in the following). The challenge of understanding howhistone modifications and transcription factors regulate geneexpression in a cell is particularly enticing as many humandiseases have been shown to be caused by the alteration of theexpression levels of some genes by abnormalities in TF andHM combinatorial patterns [3].

Recent advancements in sequencing technologies, alongwith joint efforts from laboratories and research centers allover the world, have enabled extensive genome-wide mea-surements of epigenetic processes and the sharing of suchmeasurements in an organized and catalogued manner. TheENCODE (ENCyclopedia Of DNA Elements) consortium isbuilding a comprehensive parts list of functional elements inthe human genome [6]; it has set up a large repository tomake the results of various sequencing experiments publiclyavailable, along with essential metadata dealing with experi-ment settings and quality. Currently, the ENCODE repositoryhosts measurements from Chromatine Immuno-Precipitationsequencing (ChIP-seq) experiments for a large number ofepigenetic ‘features’ such as TFs and HMs.

Taking advantage of such available data, attempts havebeen made to conceive statistical predictive models for themRNA abundance of a cell from corresponding ChIP-seqdata on TFs and HMs at a genome-wide level [7]–[9]. Theimportance of genome-wide models as a powerful explorativeframework has been remarked in [10], as they allow drawingmore general and fundamental conclusions on the roles andinterplay of TFs and HMs. On the other hand, these two classesof features seem to be statistically redundant for this task.In [10] statistical redundancy has been well distinguished fromfunctional redundancy and has been shown how redundancyat genome-wide level breaks down at the resolution of groupsof ontology-classified biological processes, where variations inthe relative predictive power of TFs and HMs are observed.Thus, it is interesting and useful to design statistical modelsstill on a genome-wide scale, but taking into account thecharacteristics of these epigenetic features to have differentrelative predictive capabilities for different gene subsets.

The comprehension of important epigenetically-driven dy-namics in the mRNA production of a cell can be cast as thetask of finding groups of HMs and TFs which sufficientlywell explain measured mRNA quantifications for groups ofgenes. In this case, it is important to stress not only how

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the information about the mRNA gene quantifications mustconsistently drive the gene partitioning procedure, but also howboth the grouping for genes and epigenetic features shouldarise directly from data, when analysis is carried out withinvestigative purposes. With respect to the first point, wedo not aim at finding genes with similar input patterns orexpression levels, but rather, genes with common kinds ofcorrelations between their epigenetic status and expression. Asfor the second point, focusing on ontology-classified biologicalpathways is not suitable, if not in contrast, with an exploratoryanalysis, as it requires prior biological knowledge on the cellunder study.

It is then within the general context of regression analysis,where we frame the described problem, considering genes ofinterest as samples, epigenetic measurements as input featuresand mRNA quantifications as target values. In this context, andaiming at retaining maximum model interpretability, findinggroups of genes/samples corresponds to clustering hyper-planes, each representing the solution of the ordinary leastsquares problem over a certain group of genes.

In this paper, we present the application of a geneticalgorithm to perform such clustering of hyperplanes. Then,we show how we perform forward step-wise feature selectionto extract the most predictive features for each partition found.Furthermore, we explore the dissimilarities between the sepa-rated hyperplanes and investigate the possibility of enhancinggenome-wide prediction capabilities by means of the clusteringperformed by the evolutionary procedure.

The remainder of this paper is organized as follows. InSection II we describe related works. Section III is devotedto the discussion of the data used - including how they areretrieved and preprocessed - and the design choices concerningthe genetic algorithm. In Section IV we analyze and validatethe results of the partitioning procedure in terms of featurerankings, model dissimilarities and possible improvements onthe regression task. Finally, conclusions in Section V.

II. RELATED WORKS

The problem we are addressing is similar to what in theliterature is termed as k-plane clustering, or more generally aspiece-wise linear affine model fitting. One of the most commonapproaches of this kind is the hinging hyperplane method [11],which can be considered as a more refined version of theregression tree one, aiming at overcoming the drawbacksof this last, such as convergence to suboptimal solutions.Considered the hinge function as the maximum or minimumof two affine functions, the objective is to approximate theregression function as a sum of these hinge functions. Anotherpossibility is given by the bounded error approach [12], inwhich the objective is to learn a piecewise linear regressionfunction such that, for every point in the training set, theabsolute difference between the target value and the predictedvalue is less than �. This kind of problem is referred as themaximum feasible sub-system problem, shown to be NP-hardin [12], where solution is approached by means of severalproposed heuristics.

These techniques are mainly designed to fit a supposednon-linear dynamic with piecewise linear functions in order toretain interpretability of the results, but are not well suited

to learn possibly discontinuous functions, as it might bethe case of our study. In our case, we are not interestedin approximating a non-linear dynamic; whereas we aim atlearning different linear models in a scenario where dynamicsare likely to be overlapped, mixed, and partially lying on sub-dimensional manifolds.

A more suited approach was proposed in [13] and istermed as k-plane regression. Its objective is fitting possiblydiscontinuous functions based on a clustering approach. Themain idea is to partition the input points and to learn a linearmodel for each of those partitions. K-plane regression finds apredefined number of hyperplanes such that each point in thetraining set is close to one of the hyperplanes, and all points inthe k-th partition are as closest as possible in the input featurespace. That is to say partitions are found by minimizing thefollowing objective function:

E(Θ) =K−1∑k=0

∑i∈Θ(k)

(ti − w̃Tk x̃i)2 + γ‖xi − µk‖22 (1)

where K is the pre-defined number of clusters, Θ(k) representsthe set of samples in cluster k according to Θ - input feature x̃iand target value ti, (i ∈ Θ(k)), wk is the weight vector of theleast square solution for those points, µ terms refer to centroidsin the feature space and γ is a user defined parameter decidingthe relative weight of the two terms in the objective function.The ‘tilde’ notation is used to indicate the inclusion of the biasterm in the regression. The error function E(Θ) is minimizedby an Expectation-Maximization (EM) procedure. The secondpart of the equation, i.e., the term related to the closeness of thepoints belonging to the same partition, was introduced in [13]to avoid EM finding suboptimal solutions, and to enforce foundpartitions not to contain points from disjoint regions of theinput feature space.

In the context of transcriptional regulation modeling, possi-ble multi-functionality of epigenetic markers for different genesubsets has been addressed in [14] with a mixture of sparselinear models. The authors focused on four hematopoieticcell types, considering mRNA abundance quantifications asa function of histone mark signals and transcription factorbinding affinities. By resorting to a Maximum A Posteriori(MAP) version of the EM algorithm, an ensemble of bayesianelastic nets is fitted on data. Not only the model parametersare estimated, but also the posterior probabilities (or respon-sibilities) for each observation to belong to a certain model.In so doing, however, genes are not ‘sharply’ grouped, sincea precise partitioning of the gene set into distinct regulativedynamics is not defined. Rather, the expression for a gene ismodeled by the weighted sum of the outputs of all the fittedlinear models.

Differently from [14], in our work we would like, instead,to perform a ‘sharp’ partitioning, defining clusters of genessharing a common kind of epigenetic regulative behavior. Thisis the reason why our method is more similar to the approachof k-plane regression proposed in [13], where, however, weexplicitly drop the second term of the objective function inEquation 1. Indeed, our prime objective is the separation ofoverlapped gene expression dynamics and not just the piece-wise linear approximation of a more complex function; in ourcase, partitions spanning over disjoint regions of the feature

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space are not necessarily to be avoided. Enforcing closenessbetween points being partitioned is difficult in our domain,due to the lack of a sensible distance measure in the high-dimensional space of the epigenetic features, and potentiallydangerous, since we have no reason to believe gene parti-tions induce non-intersecting convex hulls in the input space.Furthermore, to cope with the issue of suboptimality in thesolution found via the EM procedure, we focused on a geneticclustering approach. This is mainly due to the intrinsic parallelnature of the search-space exploration and the capability ofmore finely controlling such exploration by tuning the geneticalgorithm’s hyper-parameters, so to ensure enough ‘biologicaldiversity’.

III. MATERIALS AND METHODS

A. Biological data

To study the relation between epigenetic features - par-ticularly HMs and TF bindings - and cell transcriptionalactivities, we focused on the interesting K562 immortalizedhuman leukemic cell-line, for which ChIP-seq experimentshave been performed for a large amount of TFs, and re-sults are available in the ENCODE repository. To study thecells in their stationary normal status, we disregarded anyexperiment conducted in response to any chemical treatment,and considered only good quality experiments. The ENCODEproject standards define ‘audits’ metadata to report qualityissues. We discarded experiments with at least one of thefollowing audits: “AUDIT ERROR: extremely low read depth,extremely low read length”, “AUDIT NOT COMPLIANT: in-sufficient replicate concordance, missing input control, severebottlenecking, unreplicated experiment”. Furthermore, we dis-carded all TF experiments having at least one of the fol-lowing audits: “AUDIT WARNING: insufficient read depth”,“AUDIT NOT COMPLIANT: insufficient read depth”. Thesequality filters gave ChIP-seq experiment data for 247 differentepigenetic markers, i.e., 237 TFs and 10 HMs.

Genes are our units of measurements, represent single ob-servations of epigenetic quantities under study, and correspondto points in the (high-dimensional) feature space. We used theGENCODE v24 gene annotation, considering only (human)protein coding genes associated with an Entrez Gene ID, i.e.,a set of 19, 077 genes. For each of them GENCODE providesthe coordinates of all known alternative transcript isoforms.

As gene transcriptional activity data, we considered maturemessenger-RNA (mRNA) gene quantifications from ENCODEK562 polyadenylated RNA-seq experiments as output targetresponse values. We averaged the FPKM (fragments per kilo-base of exons per million) quantifications of three RNA-seqexperiments conducted in similar conditions which showedgood internal replicate concordance and high correlationsbetween each other (Pearson correlation coefficient on thenatural logarithm of FPKM values greater than 0.92).

B. Data preparation

As far as epigenetic signals are concerned, for each TFand HM we considered processed data in the form of calledpeaks, whose goodness relies on the way the peak callingprocedure has been performed. The ENCODE consortium hasdefined standards for this procedure, so it was possible to

retrieve robust peaks for each feature. We indeed considered“conservative IDR thresholded peaks” for TFs and “replicatedpeaks” for HMs. Given the high number of features, using peakdata greatly reduces computational and storing requirementswithout waiving information content; in fact, peak data arerefined and partly de-noised as the peak calling procedure alsotakes into account an input control signal.

To characterize the epigenetic status of a gene for a specificfeature (TF or HM), we considered the maximum peak en-richment signal attained by peaks within a symmetric windowregion of length 10 kbases centered on the gene transcriptionstart site (TSS); this is in accordance with the observationreported in [7] that signals close to a TSS (roughly, in a genepromoter) are the most informative. Each gene usually hasdifferent RNA transcript isoforms, each with its own TSS.Among all TSSs of a gene, we chose the one associated withthe most expressed gene transcript, according to the averageisoform transcript quantifications, provided, together with genequantifications, by ENCODE RNA-seq experiments.

With the described data, we constructed a dataset that weused to fit statistical models and evolve our genetic algorithm.We refer to such dataset as D = (X,T ), i.e., the ensembleof an input epigenetic signal matrix X and a target geneexpression vector T . X is a matrix of dimension n × m,where n is the total number of genes under analysis andm is the number of epigenetic features, with n = 19, 077and m = 247. The element i,j of the matrix X representsthe maximum peak enrichment value found for the epigeneticfeature j in the promoter of gene i, with i ∈ {0, . . . , n−1} andj ∈ {0, . . . ,m − 1}. The target vector T is a column vectorof dimensions n × 1, whose element i is the average FPKMmRNA quantification of gene i, with i ∈ {0, . . . , n− 1}.

C. Data preprocessing

Before performing genetic hyperplanes clustering and fit-ting of linear regression models, on the dataset D we executedsome data-cleaning and transformation procedures.

First, D was also considered in a ‘transformed’ versionD̃ = (X, T̃ ), which is the same dataset as D but with the targetvector T transformed according to: T̃ =

√ln(1 + T ). The

complete modeling pipeline was run on both the two datasetversions. Log-linear regression was already applied in [10].The further squaring operation on the log-target values wasapplied because it was observed to help genome-wide leastsquare fitting in terms of enhanced average R2 scores in k-fold cross validation (k = 10).

Second, both D and D̃ datasets were purged from outliers,considered as points with both high regression leverage andassociated high residual. Considered the leverage threshold land the residual thresholds (r, r̃), with r = (rlower, rupper)and r̃ = (r̃lower, r̃upper), for D and D̃, respectively, k-foldcross-validation (k = 5) was performed in fitting a genome-wide linear regression model, and repeated for N = 10 times.Each time a gene with leverage higher than l is found to beassociated with a residue greater than r (or r̃) in absoluteterms, then it is added to the set of outliers. In our study weset l to 0.3, r = (−255.17, 271.65) and r̃ = (−1.15, 1.18).These values correspond to the 1st and 99th percentiles ofthe residues for the two linear models fitted on the entire

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datasets D and D̃, respectively. This procedure led to thepurged datasets Dp and D̃p, where the design matrices andtarget vectors have np and ñp rows, with np = 19, 065 andñp = 19, 072.

D. Genetic hyperplanes clustering

The primary objective of the genetic algorithm (GA in thefollowing) we developed is to extract a partitioning of genessuch that partition-wise linear fitting minimizes the overallregression error. In the context of genetic algorithms, eachindividual encodes one possible solution to the optimizationproblem. In other words, fixed the number of partitions beingsought to C, one individual corresponds to a C-way par-titioning of the gene set and, thus, we would like to findthe individual Θ whose encoded partitioning maximizes thefollowing fitness function:

Φ(Θ) = −C−1∑c=0

∑i∈Θ(c)

|ti − w̃Tc x̃i| (2)

where Θ(c) represents the set of genes in partition c accordingto the partitioning induced by individual Θ, ti is the elementi of the considered target vector, and yi,d = w̃Tc x̃i is theprediction computed for the input sample xi by the linearmodel mc learned on Θ(c).

The description of the GA characteristics follows; pleaserefer to Algorithm 1 for the outline of the overall clusteringprocedure. Several terms describing GAs are borrowed frombiology; to avoid annoying clashes with the same termsinvolved in our application domain, we emphasize all thosecomputational terms relating GAs that could generate misun-derstandings (e.g., gene in biology vs. gene in evolutionarycomputation).

Encoding: The encoding is the way we describe an indi-vidual of the GA, i.e., the way we represent a possible solutionto our optimization problem. An individual is classicallyrepresented with a chromosome, i.e., a string of some objects,e.g., characters, numbers, etc. An element of the string istermed as gene, and the values a gene can assume are called

Algorithm 1 Hyperplanes Genetic Clustering1: procedure HYPGENCLUST(D, C, P, L, ω, r, o,m0,mL, e)2: t← 03: initialize P with P random individuals reflecting a C-

way partitioning4: Θ∗ ← arg maxΘ∈P Φ(Θ,D)5: while neither S1(t, L) nor S2(ω,Θ∗) is met do6: P ′ ← {Elitism(P, e)}7: while |P ′ | < P do8: (i1, i2)← DetTournamentSelection(P, r)9: O ← UniformCrossover((i1, i2), o)

10: m(t)← LinearScheduler(m0,mL, L, t)11: O ← UniformSNV LikeMutation(O,m)12: P ′ ← P ′ ∪ O13: t← t+ 114: P ← P ′

15: Θ∗ ← arg maxΘ∈P Φ(Θ,D)16: return Θ∗

alleles. The encoding that is adopted in this study is verynatural and straightforward. Let Θ be an individual describinga partitioning of the dataset Dp, then:

- its chromosome consists in a string of length np;

- the gene at locus i in the chromosome represents thepartition to which gene i in Dp has been assigned;

- an allele ai associated with gene i is such that ai ∈{0, . . . , C − 1}

Selection: Both Ranked Roulette Wheel Selection and De-terministic Tournament Selection were tested. The latter oneshowed to be more effective in the sense that, by ensuringgreater diversity in the solution population, led to faster con-vergence of the optimization procedure. Deterministic Tour-nament Selection takes as input P and r, where P is thecurrent population and r is the percentage of individuals in thepopulation taking part in a tournament. It randomly sampleswithout replacement two tournaments, i.e., two subsets ofP , called P1 and P2, of cardinality b|P| × rc. It computesand stores the fitness values of all the individuals in the twotournaments, F1,F2, and takes the individuals with best fitnessin P1 and P2, say i11 i12. In the case the two selected individualsequal each other, it chooses the individual i22 from P2, i.e., theone with second best fitness. Those two individuals will bemated. The value for r was chosen as 0.1.

Crossover: Single Point Crossover and Uniform Crossoverstrategies were attempted. The latter one revealed to be muchmore effective, speeding up the convergence of the algorithm.This was probably due, again, to a greater ‘diversity’. Somemeasurements on the average Hamming distance betweenindividuals were taken during the evolution of the GA, andthose confirmed this last intuition. This latter strategy led topopulations with a greater average Hamming distance betweenindividuals than the former one. Uniform Crossover takes asinputs the two individuals being mated i1 i2 and the numberof descendants to be generated, o. Each new descendant hasa chromosome built in this way: allele at locus l, say al, canuniformly assume one of the values of the parents, i.e., a1lor a2l . In other words, al takes value a

1l with 0.5 probability

and a2l with 0.5 probability. Uniform Crossover returns theoffspring O as the set of the o computed descendants. Thevalue for o was set to 1, as it, in principle, gives morepopulation ‘diversity’, and was shown not to slow downcomputation, in practice.

Mutation: The choice for the mutation operator arose quitenaturally because of the way the encoding has been designed.Uniform Single-Nucleotide-Variant-like Mutation takes as in-put an individual i and a probability of mutation m. Foreach gene in its chromosome: with probability (1 − m) thegene is kept as is, with probability m its allele is uniformlymutated to one of the possible alleles, i.e., to one value inthe set A = {0, . . . , C − 1}. It returns the (possibly) mutatedindividual. The mutation probability m was generally keptlow, given the length of the chromosomes. In particular, alinear scheduler was used to make the mutation probabilitydecrease as the algorithm was reaching convergence. Giventwo mutation probability extremes, m0,mL ∈ [0, 1], withm0 > mL, the mutation probability at time t is given by:

m(t) = m0 + (mL −m0

L)× t, t ∈ {0, . . . , L} (3)


where L denotes the maximum time horizon allowed for theconvergence of the algorithm. m0 and mL values were set to0.003 and 0.002. Greater values were observed to make theevolution too much noisy.

Elitism: A minimum quantity of elitism was applied justas a safety net in the case too much introduced ‘diversity’in the population would possibly bend the evolution awayfrom the best currently found solution. A parameter e controlsthe proportion of best found solutions that are injected inthe new population by overriding the selection and matingprocess. Even the e value was kept low, as the focus is just toensure to keep few best overall solutions between subsequentgenerations. e was set to 0.01 with a population of cardinality|P| = 200 (two elite individuals preserved at each generation).

Population size: The population size was set to P = |P| =200. This mild value was observed to be enough to avoid thealgorithm to rapidly get caught in a poor local optimum, butat the same time was observed to be small enough to allowreasonable computational times.

Stopping criterion: The GA has been equipped with amaximum time horizon value of L generations and a furtherparameter, ω. The evolution process is iterated in time untilone of the two following conditions hold:

S1: L generations have been performed;S2: the fitness function of the best individual, Φ(Θ∗) has

not increased during the last ω iterations.

The S2 condition is actually evaluated only when at least ωgenerations have been performed. At time t̄, t̄ ≥ ω, we canrewrite the condition as

Φ(Θ∗; t) ≤ Φ(Θ∗; t− 1)∀t ∈ {t̄− ω + 1, . . . , t̄}. (4)

IV. RESULTS

In this section we report and evaluate the obtained results;these depend on the number of clusters we would like thealgorithm to extract, i.e., what we termed C. This parameteris not guessable a priori; in our work we ran the algorithm forthree different values of C, namely 2, 3, 5. We ran the GA andanalyzed its results for both Dp and its transformed version D̃p.Hyperplanes clustering of Dp should in principle be an easiertask under the hypothesis that mingled, yet different expressiondynamics exist. Target transformations might indeed compactthese latter ones, and make partitioning harder. Nevertheless,the illustrated target transformation seems to be necessary toreasonably fit linear models to the considered kind of data andobtain acceptable coefficients of determination (R2).

The whole parameter setting of the GA is the following:

Selection . . . . . . . . . . . . . . . . . .DeterministicTournamentCrossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UniformMutation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .SNV − LikeNumber of partitions: . . . . . . . . . . . . . . . . . . . . . . . C = 2, 3, 5Population size: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P = 200Optimization horizon: . . . . . . . . . . . . . . . . . . . . . . . L = 1, 600Stopping criterion window: . . . . . . . . . . . . . . . . . . . . ω = L/4Tournament size ratio: . . . . . . . . . . . . . . . . . . . . . . . . . . r = 0.1Offspring size (for one mating): . . . . . . . . . . . . . . . . . . .o = 1Mutation extremes: . . . . . . . . . . . .m0 = 0.003,mL = 0.002Elitism ratio: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e = 0.01

Fig. 1: Trend of the fitness function (refer to Equation 2) forbest and average individual in the setting Dp, C = 3 duringthe evolution process, stopped due to meeting of condition S2.

For all the experiments, we observed that the optimizationprocedure ended before reaching the maximum time horizonL. Figure 1 represents the GA evolution process for C = 3 onDp and its convergence, depicting the trend for the best andaverage fitness value in the population overtime.

A. Enhanced easiness of linear fitting

Our first approach to assess the validity of the foundclusters consisted in studying the average performance oflinear models on them. Consider a solution Θ∗ inducing apartitioning of the dataset into C clusters. From now onthey are termed as ‘computed’ clusters. For computed clusterΘ∗(c), with c ∈ {0, . . . , C − 1}, we randomly sampled asubset of Dp (or D̃p) of same cardinality, call it DSp , asthe ‘random’ counterpart and then we 5−folds cross-validatedlinear models on both Θ∗(c) and DSp , yielding, respectively,two average coefficients of determination R̄2

dand R̄2

S. For

each partition c, this procedure was repeated 20 times, eachtime storing, separately, the two average performance scores.Such procedure has the precise objective to assess whether theGA has managed to find a partitioning into clusters for whichthe linear fitting problem is actually easier and more stable(less variance in regression scores) w.r.t. the whole dataset.Such characteristics would suggest a reasonably good data un-mingling.

For the Dp dataset and for all the choices of C, linearregression on clusters has always shown to obtain better scoresand to be more robust. For each cluster, the mean of theaverage coefficients of determination is always higher thanthe one computed on the randomly sampled subset DSp , andtheir range of variation is always narrower. This behavior isdepicted in Figure 2 and quantified in Table I for C = 3 inDp. In this setting, the cluster cardinalities are the following:|cluster 0| = 8, 393, |cluster 1| = 2, 985, |cluster 2| = 7, 687.As far as D̃p dataset is concerned, we observed how oneextracted cluster for each choice of C always has an higher


(a) 0: computed vs. random (b) 1: computed vs. random (c) 2: computed vs. random

Fig. 2: Boxplotted average R2s for linear models on computed clusters contrasted with those attained on randomly sampledsubsets of same cardinalities (setting Dp, C = 3). Medians are elongated in order to more easily read their associated value.Negative scores attained on the random cluster 1 are probably due to the fact that such model is fitted on a smaller number of(randomly sampled) points, as |cluster 1| = 2, 985.

TABLE I: Mean and standard deviations for average R2 scorescomparisons (as mean± std). Refer to subsection IV-A.

Dp, C = 3 computed randomly sampled

cluster0 0.22± 0.01 0.13± 0.04cluster1 0.43± 0.02 −0.42± 0.33cluster2 0.20± 0.04 0.12± 0.08

mean for the average coefficients of determination, whilethe other clusters have means comparable with those of therandomly sampled D̃Sp . In any case, the variations in regressionscores are always much smaller, confirming the robustness ofthe partitioning found. Table I reports the mean and standarddeviations of the average coefficients of determination for eachcluster found in the setting Dp, C = 3.

B. Feature importance

Our second assessment concerns feature importance. Werecall the objective of our study is not only partitioning thegene set, but, hopefully, to have such partitions characterizedby distinct transcriptional regulation mechanisms, i.e., wewould like to have clusters for which different characteristicepigenetic features are mostly predictive w.r.t. other clusters.We hence proceeded to the computation of feature rankingsfor each of the clusters extracted.

Let Θ∗ be a solution inducing a partitioning of the datasetinto C clusters. For each cluster Θ∗(c), c ∈ {0, . . . , C−1}, weperformed step-wise forward feature selection, and constructeda ranking for the top-10 predictive features according to thiscriterion. The feature rankings computed on the Dp datasetgenerally showed to be different from each other. This wastrue especially for a lower value of C, i.e., 2, 3. With C = 5we observed, instead, how rankings encounter larger overlaps,though being generally different. We take as an example C =3, whose clusters top-10 rankings are reported in Table II.

TABLE II: Feature rankings for the setting Dp, C = 3, top-10

Dp, C = 3 cluster0 cluster1 cluster2

1st H3K79me2 SNRNP70 H3K79me2

2nd H3K36me3 TAF7 ZZZ3

3rd GTF2A2 POLR2AphosphoS2 H3K36me3

4th KAT8 HNRNPUL1 SNRNP70

5th POLR2AphosphoS2 WDR5 HINFP

6th AGO1 GTF2F1 BCLAF1

7th ZNF639 H3K79me2 GTF2F1

8th CEBPB POLR2A ZBTB11

9th TAF7 MBD2 ZNF24

10th BRD4 KAT8 TEAD2

For cluster 1, transcription factor SNRNP70 was observedto be the most predictive, while the top predictive features inthe other clusters are histone modifications. Also, consider howthe predictive features WDR5 and HNRNPUL1 for cluster 1are absent in the top-10 positions of the other two clusters.Cluster 0 and cluster 2 differ, although the two histonemodifications H3K79me2 and H3K36me3 are among the toppredictive features in both of them. Indeed, most of top-ranked TFs of one cluster are not found in the top-10 rankingof the other one. This suggests that, even though the twomentioned HMs account for top predictive information in thesetwo clusters, they enhance the model accuracy when combinedwith different sets of transcription factors.

From a biological perspective, cluster 1 is well char-acterized by the presence of the leukemia-involved MYC-recruiter transcription factor WDR5 [15] and from the im-portance assumed by mRNA-binding proteins, i.e., SNRPN70and HNRNPUL1. The involvement of the former one in thesplicing process has been shown in [16]. In cluster 0, thetop predicting features are directly linked with gene activeexpression: H3K79me2 and H3K36me3 are activators [17],and GTF2A2 is part of the polymerase complex playing animportant role in transcription activation [18]. Finally, cluster 2


reports, besides the already mentioned histone marks, HINFP,which has been shown to play a role in DNA methylation andtranscription repression [19].

As for D̃p dataset, variations in rankings are still observed,but they are much less evident: compacting of the target valuesdoes not allow a clear and interpretable hyperplanes clustering.

C. Model diversity

A further analysis is based on the evaluation of modeldissimilarity. In the following, model dissimilarity is assessedby comparing slopes and specific weights assigned to featuresby each of the models. The maximization of the fitnessfunction does not directly include the maximization of themodel dissimilarity; hence, if models fitted on different clustersare found to be dissimilar, this is a reasonable confirmation ofthe goodness of the partitioning.

Evaluation of the model dissimilarity consists in the diver-sity of the models parameters. For this purpose, we computedthe Pearson correlation coefficient between models’ weightvectors. Let Θ∗ be a solution inducing a partitioning of thedataset into C clusters. For each cluster Θ∗(c), c ∈ {0, . . . , C−1}, we fitted a linear model on it and considered its weightvectors as wc. Call W the set of the weight vectors: W ={wc, c ∈ {0, . . . , C − 1}}. For each pair of weight vectors(wc1 ,wc2),wc1 ,wc2 ∈ W and c1 6= c2, we computed thePearson correlation coefficient %c1,c2 . The Pearson correlationcoefficient is always bounded between values −1 and +1;the closer the value is to +1, the more the models describesimilar input-response relations. For a value approaching 0, thehyperplanes described by the models tend to be orthogonal.Lastly, the closer the value is to −1, the more the models areanti-correlated, meaning they describe a completely oppositekind of input-response relation.

For dataset Dp and C = 2, the models fitted on the twoclusters have a Pearson correlation coefficient %0,1 = 0.34. ForC = 3, the two hyperplanes described by cluster 0 and cluster1 are nearly orthogonal as %0,1 = 0.09. As for the correlationbetween the other clusters, we have: %1,2 = 0.39, %0,2 = 0.26.With C = 5, a total number of 10 correlation coefficientsare computed. Most of them are near to zero, suggesting thatmany hyperplanes are nearly orthogonal; consider for instance%0,4 = −0.03. Consistent results are found for dataset D̃p.

A second approach to the evaluation of model dissimilarityconsists in the direct comparison of models’ weight vectors,at least for the top-predictive features. In order to fairlycompare those weights, we performed feature normalizationby aligning the min and the max values for each of their valuedistributions. We then fitted linear models on the normalizeddatasets and compared the values assumed in different modelsby the same feature-weights. Great variations were observedamong clusters, again conveying the dissimilarity between themodels. Table III compares the weights assigned to the top-rank features in cluster 0 and cluster 1, the ones describing themost hyperplanes with the most dissimilar slopes for C = 3.

D. An oracle-based approach

In this last subsection of the result analysis we show howthe partition produced by the GA could be used to construct

TABLE III: Feature weights for the three most predictivefeatures in cluster 0 and cluster 1 in the setting Dp, C = 3.

Dp, C = 3 cluster0 cluster1

H3K79me2 9.52 51.32

H3K36me3 6.02 13.69

GTF2A2 1.27 40.99

SNRNP70 1.45 276.25

TAF7 −0.29 23.66POLR2AphosphoS2 4.28 78.61

a predictive model for the mRNA abundance quantifications,with enhanced performances w.r.t. a single linear model. Thesetting is the following. Consider dataset D̃p and a train-test split: D̃p = D̃p

train ∪ D̃ptest

, D̃ptrain ∩ D̃p

test= {},

where the test set was constructed by randomly sampling10% of genes from the original dataset. The genetic algo-rithm procedure is launched on D̃p

trainand a solution Θ∗

is returned, defining a partition on that train set, i.e., a setC = {Θ∗(c), c ∈ {0, . . . , C − 1}}. On each partition in C,a linear model is fitted, generating the ensemble of modelsM = {Mc, c ∈ {0, . . . , C−1}}. Then, the task is to optimallypredict genes in D̃p

testby making use ofM, hopefully better

than how a genome-wide model would do, that is, a singlelinear model fitted on the whole D̃p

train. Under the assumption

that the partitioning induced by Θ∗ is actually meaningful alsofor genes in the test set, then, given a query point q ∈ D̃p

test,

the steps for predicting its associated response value are thefollowing:

1. assign q to its most representative cluster, named c̄

2. predict the response value for q as the output of Mc̄,i.e., yc̄q = w̃

Tc̄ x̃q

The most representative cluster is, in principle, the one whoseprediction from the associated model is the closest to the realresponse value tq associated with q. Unfortunately, step 1. isnot a trivial task if the value tq is not known a priori. Thisis true even for points in the train set. Anyhow, supposing tohave an oracle $ capable of assigning the best possible clusterto all the query points in D̃p

test, we can accordingly define an

upper-bound on the regression performance of any ensemblemodel based on M. The oracle’s decision function takes thefollowing form:

f$(xq;M) = w̃Tc̄ x̃q, c̄ = arg minc∈{0,...,C−1}

|tq − ycq| (5)

where we remark how the response tq is actually hidden, andknown only to $.

We evaluated the performance of $ in the setting D̃p, C =2, 3, 5. The genome-wide model, termed as γ, scored R2γ =0.74 on D̃p

test, where the oracle always scored better coef-

ficient of determinations, with better performance for largervalues of C. Scores are R2$ = 0.79 for C = 2, R

2$ = 0.83

for C = 3 and R2$ = 0.86 for C = 5.

Note how the scores obtained by the oracle can be usedto choose the best value for C a posteriori. For instance, one


Fig. 3: Residue plots for $ and γ on D̃ptest

, C = 5.

can choose the value of C corresponding to an elbow for R2$scores, averaged over several random test-train splits.

In order to further characterize the behavior of the oraclepredictor with respect to the genome-wide model, we com-pared the residues of both of them for C = 5 - the testedchoice associated with best score. They are considered as thedifferences between target and predicted values over all thegenes in D̃p

test, and are reported in Figure 3. Predictions from

$ were found to be more accurate than those from γ on 92.0%of test genes. It can also be observed how they are relativelyless dispersed, as confirmed by a smaller standard deviation:σR$ = 0.30 vs. σRγ = 0.41.

V. CONCLUSIONS

In this work we proposed the application of a geneticalgorithm to cluster protein coding genes according to therelation between their epigenetic status and expression. Thehyperplanes corresponding to the found partitions revealed tobe dissimilar in terms of slope and specific importance ofepigenetic marks. The found gene partitioning showed alsoto be potentially effective in enhancing expression predictioncapabilities for unseen genes. The upper bound on regressionperformance for the ensemble of linear models fitted on eachcomputed cluster has been indeed estimated to be significantlyhigher that those from a single linear regression model.

Future work will address a more profound biological vali-dation of the results and characterization of the found gene sub-sets. The procedure will be also applied to measurements con-ducted on different cell-lines, probing the ability of the algo-rithm to detect tissue-related dissimilarities in epigenetically-driven regulative dynamics. Further analyses will focus onvalidating the robustness of the proposed genetic clusteringapproach w.r.t. classical EM-based procedures applied, forinstance, in [13] and [14]. Interesting will also be to extendthe proposed algorithm to fitting elastic nets as in [14], ratherthan simple ordinary least squares models. This is motivated bythe so-called ‘grouping effect’ that characterizes the formers,that is, highly correlated variables tend to be either includedor excluded from the model in groups [20]. This feature isof interesting application in our domain, in which, from an

exploratory perspective, hundreds of - possibly correlated -epigenetic markers are included as monitored variables.

ACKNOWLEDGMENT

This work was supported by the Advanced ERC Grant“Data-Driven Genomic Computing (GeCo)” project (2016-2021), funded by the European Research Council.

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tory elements in the human genome,” Annu Rev Genomics Hum Genet,vol. 7, pp. 29–59, 2006.

[2] P. J. Farnham, “Insights from genomic profiling of transcription factors,”Nat Rev Genet, vol. 10, no. 9, pp. 605–616, 2009.

[3] J. M. Vaquerizas, S. K. Kummerfeld, S. A. Teichmann, and N. M. Lus-combe, “A census of human transcription factors: function, expressionand evolution,” Nat Rev Genet, vol. 10, no. 4, pp. 252–263, 2009.

[4] S. Berger, “The complex language of chromatin regulation duringtranscription,” Nature, vol. 447, no. 7143, pp. 407–412, 2007.

[5] S. K. Kurdistani, S. Tavazoie, and M. Grunstein, “Mapping globalhistone acetylation patterns to gene expression,” Cell, vol. 117, no. 6,pp. 721–733, 2004.

[6] ENCODE Project Consortium, “An integrated encyclopedia of DNAelements in the human genome,” Nature, vol. 489, pp. 57–74, 2012.

[7] C. Cheng, K.-K. Yan, K. Y. Yip, J. Rozowsky, R. Alexander, C. Shou,and M. Gerstein, “A statistical framework for modeling gene expressionusing chromatin features and application to modENCODE datasets,”Genome Biol, vol. 12, no. 2, p. 15, 2011.

[8] Z. Ouyang, Q. Zhou, and W. H. Wong, “ChIP-seq of transcriptionfactors predicts absolute and differential gene expression in embryonicstem cells,” Proc Natl Acad Sci, vol. 106, no. 51, pp. 21521–21526,2009.

[9] R. Karlić, H.-R. Chung, J. Lasserre, K. Vlahoiviček, and M. Vingron,“Histone modification levels are predictive for gene expression,” ProcNatl Acad Sci, vol. 107, no. 7, pp. 2926–2931, 2010.

[10] B. et al., “Predicting expression: the complementary power of histonemodification and transcription factor binding data,” Epigenetics Chro-matin, vol. 7, p. 36, 2014.

[11] L. Breiman, “Hinging hyperplane for regression, classification andfunction approximation,” IEEE Trans Inf Theory, vol. 39, pp. 999–1013,1993.

[12] E. Amaldi and M. Mattavelli, “The MIN PFS problem and piecewiselinear model estimation,” Discrete Appl Math, vol. 118, pp. 115–143,2002.

[13] N. Manwani, “K-plane regression,” Inf Sci (Ny), vol. 292, pp. 39–56,2015.

[14] T. G. do Rego, H. G. Roider, F. A. T. de Carvalho, and I. G. Costa,“Inferring epigenetic and transcriptional regulation during blood celldevelopment with a mixture of sparse linear models,” Bioinformatics,vol. 28, no. 18, pp. 2297–2303, 2012.

[15] L. R. Thomas and W. P. Tansey, “Interaction with WDR5 promotestarget gene recognition and tumorigenesis by MYC,” Mol Cell, vol. 58,no. 3, pp. 1–13, 2015.

[16] D. J. Adams, L. van der Weyden, A. Mayeda, S. Stamm, B. J. Morris,and J. E. Rasko, “ZNF265 - a novel spliceosomal protein able to inducealternative splicing,” Cell Biol, vol. 154, no. 1, pp. 25–32, 2001.

[17] A. J. Bannister and T. Kouzarides, “Regulation of chromatin by histonemodifications,” Cell Res, vol. 21, no. 3, p. 381395, 2011.

[18] D. J. Mitsiou and H. G. Stunnenberg, “TAC, a TBP-sans-TAFs complexcontaining the unprocessed TFIIAalphabeta precursor and the TFI-IAgamma subunit.,” Mol Cell, vol. 6, pp. 527–537, 2000.

[19] M. Sekimata, A. Takahashi, A. Murakami-Sekimata, and Y. Homma,“Involvement of a novel zinc finger protein, MIZF, in transcriptionalrepression by interacting with a methyl-CpG-binding protein, MBD2,”J Biol Chem, vol. 276, no. 46, pp. 42632–42638, 2001.

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2018 International Joint Conference on Neural Networks (IJCNN)Table of ContentsWelcome Message from the ChairTechnical Papers: Table of ContentsMonday, July 92: Machine LearningN-18690N-18700N-18776N-18085N-18301N-18777

8k-1: Signal processing, image processing, and multi-mediaN-18718N-18144N-18590N-18610N-18808N-18823

1-2: Neural Networks ModelsN-19003N-18990N-19085N-18356N-18183N-18148

2c: Self-organizing mapsN-18508N-18649N-18546N-18869N-18220N-18215

CDS-CI: Special Session on Computational IntelligenceN-18034N-18753N-19071N-18197N-18716N-18959

SS16-1: Special Session on Hybrid Neural Intelligent Models and ApplicationsN-18093N-18321N-18720N-18755N-18117N-18487

SS1: Special Session Non-iterative Approaches in LearningN-18237N-18503N-18149N-18032N-18607N-18719

SS38: Neural Approaches for Natural LanguageN-18694N-18754N-18804N-18903N-18711N-19126

2r-2s: Hybrid learning and Computational power of neural networksN-18473N-18772N-18337N-19079N-18642N-19098

1h-1: Spiking neural networksN-18057N-18295N-18469N-18867N-18702N-18228N-18299

6c-1: Neuromorphic hardwareN-19022N-19066N-18632N-19063N-18995

Best-Reg: Best PapersN-18836N-18890N-18803N-18010N-18782

SS16-2: Special Session on Hybrid Neural Intelligent Models and ApplicationsN-19117N-18562N-18490N-18926N-18927

2k-1: Mixture models, ensemble learning, and other meta-learning or committee algorithmsN-28011N-18994N-18580N-28017N-28008N-18646

1a-1: Feedforward neural networksN-18118N-18842N-18170N-18761N-18100N-18106

WT1: Workshop on Computational Intelligence and Smart CitiesN-18279N-18385N-19009N-18934N-18923

POS1: Poster Session 1N-18003N-18014N-18017N-18018N-18019N-18025N-18038N-18040N-18043N-18067N-18071N-18080N-18092N-18095N-18110N-18111N-18128N-18135N-18138N-18139N-18146N-19014N-18157N-18166N-18175N-18188N-18198N-18685N-18819N-18255N-18595N-18661N-18759N-18367N-18382N-28035N-18629N-18520N-18524N-18526N-18274

2p: Feature selection, extraction, and aggregationN-18286N-18549N-18608N-18664N-19041N-19114

1l-2: Deep neural networksN-18449N-18717N-18848N-18993N-18328N-18767

1b-1: Recurrent neural networksN-19012N-18695N-18588N-18733N-19103N-19138

Best-Stu: Students Best PapersN-18411N-18429N-18324N-18635N-18863

SS33: Neural Intelligence After TomorrowN-18248N-18525N-18786N-18433

1c-1: Self-organizing mapsN-18187N-19088N-18218N-18787N-19062N-18810

1-1: Neural Networks ModelsN-18186N-18898N-18052N-18746N-18459N-18511

Tuesday, July 101l-3: Deep neural networksN-18801N-18704N-18736N-18764N-19036N-19077


SS11-31: Special Session on Cognition & Development and Neural Models for Behavior RecognitionN-18306N-18340N-18897N-18181N-18708N-18854

8d: Biomedical engineeringN-18163N-18290N-18386N-18478N-18501N-18620

SS6: Feature Extraction and Learning on Image and Text DataN-18648N-18712N-18665N-18640

SS27: Extreme Learning MachinesN-19018N-18143N-18257N-18598N-18671N-19050

SS3: Special Session on Complex-Valued and Quaternionic Neural NetworksN-18236N-18261N-18156N-18246N-18681N-18943


1h-2: Spiking neural networksN-18911N-18370N-18953N-18089N-18273N-18814

6c-2: Neuromorphic hardwareN-18484N-19008N-18443N-18141N-18282N-18493

1n-1: Other topics in artificial neural networksN-18086N-18623N-18728N-19059N-18795N-18678

SS7: Advances in Reservoir Computing N-18481N-18912N-18948N-19019N-18884N-18471N-18091

2k-2: Mixture models, ensemble learning, and other meta-learning or committee algorithmsN-19010N-18815N-18292N-18792N-18973N-18547

1b-2: Recurrent neural networksN-28040N-19139N-18245N-19017N-18500N-18538

POS2: Poster Session 2N-18214N-18221N-18230N-18239N-18242N-18244N-18247N-18252N-18253N-18254N-18262N-18263N-18264N-18270N-18285N-18291N-18300N-18309N-18312N-18318N-18319N-18349N-18353N-18358N-18360N-18391N-18403N-18417N-18419N-18420N-18297N-18591N-18560N-28032N-18536N-18151N-18320N-18395N-18387N-18658N-18893N-18322


2g-h-l: Probabilistic methods and Gaussian processesN-18007N-18843N-18791N-18335N-18868N-18771

2b-1: Unsupervised learning and clusteringN-18402N-18860N-18212N-18496N-19005N-18225

2a-1: Supervised learningN-18578N-18737N-18044N-18497N-18613N-18689

SS4: Special Session on Deep Neural Audio ProcessingN-18064N-18203N-18276N-18470N-18686N-18162

1c-2: NEURAL NETWORK MODELSN-18298N-18556N-19051N-18913N-19032N-19100

2f-m: Online learning and Sparse codingN-19086N-18603N-18062N-18012N-18222N-18752

Wednesday, July 112e-1: Deep learningN-18516N-18922N-18055N-18895N-18348N-18878


6a-6c: NEUROENGINEERINGN-18329N-18778N-18616N-18070N-18885N-18631


SS17: Special Session on Concept drift, domain adaptation & learning in dynamic environmentsN-18115N-18351N-18398N-18415N-19021N-19084

8a-1: Applications of deep networksN-18271N-18599N-18641N-18363N-18866


2e-2: Deep learningN-18979N-18303N-18116N-18037N-18832N-18401

Cdss-06: Special Session on Interactive/Multiple Clustering using Evolutionary Computation, Fuzzy, Machine Learning and/or Neural NetworksN-18051N-18090N-18986N-18864N-18703

8a-2: Applications of deep networksN-18581N-18142N-18630N-18684N-19095N-18769


2i: Support vector machines and kernel methodsN-28049N-18652N-18855N-18436N-18919N-19046


POS3: Poster Session 3N-18439N-18441N-18452N-18454N-18455N-18456N-18457N-18465N-18509N-18531N-18535N-18567N-18570N-18586N-18592N-18602N-18604N-18605N-18606N-18611N-18614N-18615N-18617N-18621N-18628N-18637N-19031N-18643N-18655N-18707N-18723N-18725N-18729N-18730N-18732N-18743N-18780N-18784N-18788N-18790N-18268N-18405N-19061N-18108N-18269N-18201N-18099N-18461

2e-3: Deep learningN-18451N-18726N-18104N-18809N-18514N-19049

8l-2: Temporal data analysis, prediction, and forecasting; time series analysisN-18577N-18751N-18888N-18909N-19033N-19055


8n-1: Data mining and knowledge discoveryN-18065N-18168N-18173N-18259N-18305N-18316

SS2-1: Special Session on Machine Learning and Deep Learning Methods applied to Vision and Robotics (MLDLMVR)N-18908N-19044N-19056N-19108N-28028N-18768

8e-2: Data analysis and pattern recognitionN-18442N-18575N-18742N-18747N-18750N-18756

Thursday, July 128n-2: Data mining and knowledge discoveryN-18336N-18435N-18444N-18862N-18871N-18901

8o: Power system applicationsN-18029N-18073N-18074N-18083N-18553N-18573

8a-4 : Applications of deep networksN-19037N-18668N-18483N-18523N-18447N-19120

8u: Clinical applicationsN-18131N-18191N-18232N-18674N-18991N-18946

SS21: Deep Reinforcement LearningN-18426N-18479N-18240N-18200N-18397N-18929

2c-d: Reinforcement and Semi-supervised learningN-18822N-18827N-19125N-18744N-18323N-18354


8s: Manufacturing and industrial applicationsN-18125N-18311N-18408N-18564N-18715N-18887

CDSS22-1: Special Session on Blockchain Research and ApplicationsN-18350N-18380N-18407N-18544N-18760


9: CROSS-DISCIPLINARY TOPICSN-18495N-19035N-18920N-18182N-19004

SS28: Adversarial machine learning in information securityN-19101N-18489N-18491N-18656N-19034N-18765

8: ApplicationsN-18798N-18881N-18944N-18234N-18626N-19097


WT5: Workshop on Computational Energy Management in Smart Grids N-18816N-18877N-18476N-18078N-18330N-18332

POS4: Poster Session 4N-28005N-18830N-18853N-18889N-18961N-18968N-18982N-18989N-19015N-19020N-19023N-19024N-19025N-19027N-19030N-19065N-19069N-19070N-19081N-19083N-19092N-19099N-19109N-19118N-19136N-28033N-28038N-28041N-18399N-18042N-19093N-18105N-18178N-18940N-18097N-18177N-18185N-19119N-18829N-18932N-18150N-18574N-18977N-18249N-28020N-18692N-18636N-18945N-18935N-18202

CDSS-03: Special Session The Role of Computational Intelligence Technologies in Controlling BordersN-18346N-18431N-18480N-18505

CDSS22-2: Special Session on Blockchain Research and ApplicationsN-18543N-18850N-18910N-19082N-18129

8v: ApplicationsN-18783N-18313N-18345N-18818N-18287N-18283

SS20: Special Session on Neurocomputation and CognitionN-18081N-18507N-18821N-19047N-18396N-19013N-18190

8vpst: Other applicationsN-18260N-18907N-18925N-18647N-18533N-18757

SS5: Data Driven Approach for Bio-medical and HealthcareN-18445N-18697N-18900N-18585N-18905N-18256N-18289

3: NeurodynamicsN-18589N-18414N-18597N-18059N-18734

WT5-2: Workshop on Computational Energy Management in Smart GridsN-18189N-18205N-18683

Friday, July 138g: RoboticsN-18140N-18231N-18235N-18537N-18956N-18987

8l-1: Temporal data analysis, prediction, and forecasting; time series analysisN-18103N-18107N-18132N-18169N-18217N-18288

CDSS23-2: Special Session on Computational IntelligenceN-18554N-18870N-18096N-18937N-19039

8mnoq: ApplicationsN-18996N-19123N-18997N-19142N-18958

7: BIO-INSPIRED AND BIOMORPHIC SYSTEMSN-18114N-18763N-18404N-18796N-18838N-18477

5-1: Neural Models of Perception, Cognition and ActionN-18176N-18840N-18357N-18565N-18437N-18984

8e-1: Data analysis and pattern recognitionN-28050N-18120N-18133N-18265N-18275N-18384

WT2: Workshop 2N-18424

S13: Special Session on Advanced Machine Learning Methods for Large-scale Complex Data EnvironmentN-18392N-18438N-18650N-19102N-18440

CDSS15-1: Special Session on Computational Intelligence for Cognitive Robotics and Smart Grids SecurityN-18223N-18325N-18892N-18896N-18039

1l-1: Deep neural networksN-18347N-18651N-19133N-18701N-18488

S12: Special Session on Biologically Inspired Computational VisionN-18193N-18352N-18794N-18891

5-2: Neural Models of Perception, Cognition and ActionN-18412N-18226N-18972N-19137N-18192N-18963

CDSS-05: Special Session on Computational Intelligence for Bioinformatics and Computational BiologyN-18207N-18326N-18344N-18811N-19007N-18084

SS35: Evolutionary Computation for Neural NetworksN-18066N-18988N-18942N-18005N-18063

SS22: Ordinal and Monotonic ClassificationN-18159N-18506N-18875N-18659N-18880N-18206

Author Index

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/CreateJDFFile false /Description > /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ > /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ]>> setdistillerparams> setpagedevice

/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 2.00333 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.00167 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/CreateJDFFile false /Description >>> setdistillerparams> setpagedevice



































/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 2.00333 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.00167 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /P

Documents

Modeling Gene Transcriptional Regulation by Means of … · 2018-08-09 · Modeling Gene Transcriptional Regulation by Means of Hyperplanes Genetic Clustering Fabrizio Frasca , Matteo