In this paper we introduce a Web-based tool for the analysis of Genomic Expression (GE) data based in K-Formal Concept Analysis (KFCA). First we present the task of analysing GE data and then we describe the tool implementing KFCA. As a second contribution, we present a mechanism to visualise a sequence of concept lattices by fixing the intents against the concept lattice of the contranominal scale of attributes B(M, M, 6=) . Derived from this we also propose a mechanism to explore the scope of objects in such sequences.
The transcriptome of a species is the set of gene expression products, be they proteins or messenger RNA (mRNA) chains. DNA micro-arrays are a mechanism to take measures of such data in the form of an expression profile, a record of the concentration of different mRNA associated to a subset of the species genome with respect to a condition, a particular state or sequence of states undergone by the cells under study.
In this context, the concentration of the transcribed product (usually mRNA) is the (gene) expression value, and the expression values of a set of genes under the same condition, an expression profile. Therefore, given a genome —a set of genes—G = {gi}in=1 the Gene Expression (GE) data taken to analyse their functional influence consists of the expression value of every gene Rij — an expression profile—under one condition mj in a non-explicitly given set of p conditions M = {mj }j=1 . Under these premises, co-regulation refers to the increment (up-regulation) or decrement (down-regulation) of the expression value in a set of genes brought about by the change in expression value of other genes.
GE data exploration using Formal Concept Analysis includes the seminal
work for of [
In this paper we introduce WebGeneKFCA, an application supporting
Exploratory Analysis of GE data using KFCA that attempts to embody the
iterative process of exploration based on inductive databases suggested by Pensa et
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al. [
Data procurement and normalisation is described in Sec. 2.1. Our extension of the state of the art in concept lattice (CL) visualisation that provides a representation for sequences of these is described in Sec. 2.2.
Relying on this property, we present yet another new visualisation feature whereby the related concepts in different CL of the sequence can be aggregated and their scope in terms of the value of a single continuous parameter explored (Sec. 2.3). The paper closes with a summary of contributions and further work. 2
In this Section we describe the Exploratory Analysis of Gene Expression Data using the inductive databases paradigm as embodied in WebGeneKFCA 1. 2.1
Before any new data can be analysed it must be uploaded to the platform in
form of Affymetrix v4 CEL files [
Prior to data analysis, the user must choose how to normalise the data to make it suitable for K-Formal Concept Analysis. Currently we support four different types of normalisation schemes that make use of a special kind of profile called control : no normalisation, by the arithmetic mean, the geometric mean or the maximum value of the control profile. 2.2
As explained in [
Several algorithms exist for the visualisation of CL, each with its advantages
and disadvantages (see [
To ensure this property, the CL corresponding to a particular φ (ϕ) is drawn over the silhouette of the CL of a (virtual) contranominal scale involving all possible attributes, NcM = B(M, M, 6=) .
The rationale for this overlay is as follows: in the boolean lattice B(M, M, 6=),
the top is a concept with no attributes. The next level of concepts from the top
are those which only have one attribute, and so on. Call |M | = p, the number of
conditions. Clearly, the total number of levels is the number of conditions plus
one, and the number of concepts in each level l is pl , whence B(M, M, 6=) has
the maximum possible number of Formal Concepts for a given set of attributes
M , a well-known result (see [
The important fact is that any possible intent in any lattice with p attributes appears in this virtual order diagram. Thus the locations of these Formal Concepts of the most complex CL related to M can serve as locations for those Formal Concepts of any other CL with the same attribute set M . Figure 2.(a) shows an example of such an overlay of a CL with relatively few concepts, while another example is shown in Fig. 2.(b) of a CL whose set of intents approaches that of the boolean lattice (despite conspicuous absences, e.g. in the atom set).
In this visualisation scheme, the size of each concept node is directly
proportional to its extent size (but see 2.3). Making the mouse hover over each node,
a dialog box showing the attributes of that concept and its number of objects
appears. On clicking on the node, a floating window appears showing the full
extent. Besides, since these objects are genes, each of them can be selected causing
its associated information, obtained from the corresponding NetAffx Annotation
file [
An additional property of each object (gene) can be observed when clicking the button with the legend “More info...”. The new view that comes out (Fig. 3) displays the set of concepts the gene appears in through the CL full sequence. We call this the scope of the object (gene).
Against the backdrop of the boolean lattice, every concept appearing in any of the CL is rendered and a blue path connects all the concepts that the selected gene has ever belonged to. Hovering with the mouse over one of the blue dots from this path makes a tooltip appear showing the scope in ϕ (or φ) for the gene and that concept. The size of the dot is proportional to the width of the scope, the size of the ϕ interval. This information is also complemented with the data from the NetAffx Annotation file. 3
We have presented a Web-based tool to analyse GE data obtained from microarrays and to cluster the genes and test conditions by their similarity in either up- or down-regulation. The system sifts through many CL and saves its results in a database for later reading. The user can inspect through a visual, point-and-click interface the gene expression and related information in Gene Ontology-contextualised CL. Thanks to direct links, it is very easy to gather gene information from other Genomics sites.
Since the basic exploration mechanism is K-Formal Concept Analysis, the user has a wealth of CL that make it difficult to propose and validate datasuggested hypotheses. To curb this exploration complexity we have proposed a novel visualisation scheme which amounts to the visual embedding of CL in the representation of the most complex lattice pertaining to a set of attributes, viz. the contranominal scale of attributes. It is conceivable that this representation could cater to some other interval-valued parameters like intervals of temporal continua.
We have also proposed a mechanism to aggregate the visualisation mechanisms above that enables the study of the robustness of gene appearance in concepts vs. the variation of thresholds, the scope. We believe that gene scope is an important tool to ascertain the quality of the CL with respect to the “noise” in gene expression values and will explore it in further work.