User Guide

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Concept Explorer. The User Guide

September 12, 2006

Introduction

What is it?

This is a version 1.3 of "Concept Explorer"(ConExp) tool, that implements basic

functionality needed for study and research of Formal Concept Analysis(FCA).

Formal Concept Analysis is a branch of lattice theory, that was developed

starting from early 1980-ies by members of Rudolf Wille’s group in Darmstadt.

It can be used for analysis of simple attribute object tables (called context in

FCA) and exploration of diﬀerent dependencies, that exists between attributes.

For more information about Formal Concept Analysis, see http://www.math.tu-

dresden.de/~ganter/fba.html and http://www.fcahome.org.uk/

ConExp is released under BSD-style license. Please read ﬁle license.txt in

the distribution. You can read license ﬁles of libraries, that are used in ConExp,

reading ﬁle, containing "license" in its name and ﬁrst name of which corresponds

to the name of the library jar ﬁle.

If you use ConExp in scientiﬁc research, please cite the following article [1].

What can I do with it?

ConExp provides the following functionality:

•context editing

•building concept lattices from context

•ﬁnding bases of implications that are true in context

•ﬁnding bases of association rules that are true in context

•performing attribute exploration

A little bit of history

ConExp was ﬁrst developed as a part of master’s thesis under the supervision

of Prof. Dr. Tatyana Taran at the National Technical University of Ukraine

"KPI" in 2000. During the following years, it was extended and now is an open

source project on Sourceforge [5].

ConExp installation

Required software

In order to run ConExp, the Java Runtime Environment version 1.4 or higher is

required. It is usually recommended to use latest version of JRE (1.5.0 on the

moment of writing). If you don’t have it, you can get them from the following

URL: http://java.sun.com/j2se/downloads.html

Installation process

Just unpack the content of zip or tar.gz ﬁle into preferred location. Make sure,

that java can be called from this location (Just open the console in selected

directory and type java -version in order to check availability of java on your

system. If java is installed, then information about environment and version of

java software should be displayed)

Working with Concept Explorer

Starting the work

Run the appropriate start script("conexp.bat" on Windows, "conexp.sh" on

Unix). On Unix: before that set the executable attribute for "conexp.sh". If

you run it from the command line, make sure, that you are in the installation

directory.

Alternatively, on all platforms you can run "java -jar conexp.jar" from the

command line. On Windows use "javaw -jar conexp.jar" if you don’t want to

see the java console.

Concept Explorer user interface overview

ConExp user interface consists of the following parts:

Main toolbar - Contains buttons for global application operations - “Cre-

ate new document”, “Open”, “Save”, “Compute the number of concepts”,

“Compute concept lattice”, “Perform attribute exploration”, “Calculate the

Duquenne-Guigues set of implications”, “Calculate association rules” and

also a combo box, that allows to select the update mode for document

components that are computed from context - lattices, implication and

association rule sets. Currently, the two update mode are supported -

clearing of aﬀected component or recomputation of aﬀected components.

The ﬁrst mode is recommended, when user is going to make a lot of

changes in context, or the size of context is big. In this mode aﬀected

components are cleared and can be recomputed by calling compute oper-

ation for the corresponding view type. In the second mode, the aﬀected

components are recomputed after each change of context. This may lead

to big computational expenses if context is big or dense.

Main pane. Main pane includes document tree, option pane, and view pane.

Document tree displays the structure of the current document and al-

lows to navigate between diﬀerent views (i.e. context view, lattice

visualization view(s), implications view and association rules view).

Option pane allows to edit diﬀerent options connected with view.

View pane contains the display for current view. For each view there is

a corresponding toolbar with view-speciﬁc operations .

Status bar

Creating the new document

Usually, the new document is created on the start of work with ConExp. Alter-

natively, one can create a new document by pressing “New context” button on

main toolbar or selecting “New” menu item in “Files” menu.

If there was a previously opened and modiﬁed document, user will be prompted

to save it (or cancel creating new document) before the creation of a new doc-

ument.

Opening existing documents

ConExp allows to work with several diﬀerent data formats. It is possible to

work with contexts, that were created using ConImp [3] .

Currently the following formats are supported:

cex - ConExp native format. This is XML-based format. Stores information

about context and lattice line diagram, and also, whether implications

and/or associative rules were calculated. It is recommended to use this

format for work.

cxt - ConImp context data. Only context can be stored in such format.

csv - Comma - Separated values - For now, only import of context is supported

for this format. Actual separator is semicolon(;). It is assumed, that the

ﬁrst line of ﬁle contains attributes names, and ﬁrst cell is empty (I.e, if

one has a context with attributes attr1 and attr2, then ﬁrst line will be

the following:”;attr1;attr2”. Each next line should start from object name

and then sequence of 0 and 1. In cells, in which 1 is set, cross will be put

in imported context.

oal - Object Attribute list - For now, only import of context is supported for

this format. Each line presents information about object and then which

attributes this object possess. If object obj1 has attributes attr2 and attr3,

then line for obj1 will look as follows: “obj1:attr2;attr3”

Also it is possible to reopen document, on which you were working before, by

selecting one of the items in “Reopen” sub-menu in “Files” menu.

Saving your work

In order to save your work, use menu items “Save” and “Save as” in “Files”

menu, or “Save ﬁle” button on main toolbar. The recommended storage format

is native ConExp format

Working with context

Undo/redo support

For all operations, that are performed on context, undo/redo support is pro-

vided. One can undo the performed operations by pressing “Undo last action”

button and redo by pressing “Redo last action” button on context editor’s tool-

bar.

Changing size of context

In order to change the size of context, one should use the properties window on

the left side of window, and enter new number of objects/attributes in “object

count”/”attribute count” properties.

Also it is possible to add new object(attribute) into context by pressing “Add

object”/”Add attribute” button on context editor’s toolbar.

In order to remove some set of object/attributes, select them in context

editor and then perform “Remove object(s)”/”Remove attribute(s)” action from

context editor’s context menu.

Compressed view of context

If one want to get a better overview over the context, one can select “Com-

pressed” option on context editor’s property pane. Then the width of context’s

columns will be set just to ﬁt value of cross, and one can have a better look on

structure of context.

Arrow relation visualization

In order to visualize arrow relation, select “show arrow” in property “Show arrow

relations”. (If you don’t know, what it is, probably, you don’t need it. To learn

more about arrow relations, have a look at book [2])

Entering data into the context

Fast editing of contexts If one need to input a context of moderate size,

one can use the so-called fast context editing.

Just use keys “x” and “.” , when staying in cell in relation area, than the

cross or blank value will be entered in current cell and cursor will move to the

next cell in relation area.

Transformations on selected areas After selecting the area of cell, one

can perform transformations of content of incidence relation between objects

and attributes.

The following transformation are supported:

Fill selection - ﬁll the selected area of incidence relation with crosses.

Clear selection - clears the content of selected area of incidence relation

Inverse selection - replaces in selected area of incidence relation crosses with

one and vice-versa.

All these transformations can be performed by using appropriate command from

context menu.

Operations on contexts

Following operations can be performed on contexts:

object clariﬁcation - replacing in context objects, that have equal sets of at-

tributes, with one (ﬁrst from beginning of context) object. This operation

is invoked by pressing “Clarify objects” button on context editor’s toolbar.

attribute clariﬁcation - analogous operation, but only on attribute set. Is

invoked by pressing “Clarify attributes” button on context editor toolbar.

object set reduction - removing from object set all objects, that can be ob-

tained as a result of intersection of some other objects. In process of per-

forming reduction clariﬁcation is also performed. This operation doesn’t

change the structure of the concept lattice - concept lattice of reduced

context is isomorphic to the concept lattice of the original context. Oper-

ation is performed by pressing “Reduce objects” button on context editor’s

toolbar.

attribute set reduction - analogous operation on attribute set. Operation

is performed by pressing “Reduce attributes” button on context editor’s

toolbar.

context reduction - simultaneous application of object and attribute set re-

duction. Performed by pressing “Reduce context” button on context edi-

tor’s toolbar.

transposition - exchange of objects and attribute set and corresponding change

of relation between them. Performed by pressing “Transpose context” but-

ton on context editor’s toolbar.

Exploring the line diagram

Building the concept lattice

In order to build concept lattice, use button “Build Lattice” on the main toolbar.

After some time, that depends from complexity of lattice, the drawing of lattice

(also named line diagram) will appear. (Remark - layout of lattice is time

consuming operation, that’s why ﬁrst only drawing, consisting from one node

can appear, and then again, after some time, the layouted lattice will appear).

Interpreting the drawing

Concept lattice represents the univocal transformation of the context.

Top element of the lattice corresponds to the unit element of concept lattice.

Bottom element of concept lattice represents the zero element of concept lattice.

Each node of lattice corresponds to so called (formal) concept in Formal

Concept Analysis - a pair (O, A), where O - set of objects and A - set of

attributes, such, that A contains all attributes, that all objects from O have in

common and only this attributes, and O contains all objects from context, that

has set attributes A among their attributes. Set of objects O is called extent

of concept (O, A) and set of attributes A is called intent of set of attributes

So called reduced labeling is used in order to succinctly represent information

about intents and extents of formal context. If label of attribute A is attached

to some concept, that means, that this attribute occurs in intents of all con-

cepts, reachable by descending paths from this concept to zero concept (bottom

element) of lattice. If label of object O is attached to some concept, this means,

that object O lays in extents of all concepts, reachable by ascending paths in

lattice graph from this concept to unit concept (top element) of lattice.

If drawing of node contains blue ﬁlled upper semicircle, that means, that

there is an attribute, attached to this concept. If drawing of node contains

black ﬁlled lower semicircle, that means, that there is a object, attached to this

concept.

Sometimes node or edge in line diagrams is displayed in red color. This

means, that this edge or node are located very near or overlap with some other

node. In order to improve layout, try manual adjustment of layout or some

other layout.

Visualization modes

Basically, there is two visualization modes, that behave diﬀerently, when draw-

ing of lattice doesn’t ﬁt into the existing screen estate.

They are:

scrolling mode - when drawing of lattice doesn’t ﬁt into the screen estate,

that virtual window is enlarged and user can see only some part of lattice

drawing. This mode is activated by default.

ﬁt to screen mode - drawing of lattice is rescaled in order to ﬁt into the

available screen estate.

Switching between scrolling and ﬁt to screen mode is performed with the help of

“Scale picture to ﬁt into the image” button on lattice visualization pane toolbar.

Pressing this button toggles between ﬁrst mode and second and vice versa.

The following commands make sense only in scrolling mode:

Grab and drag - this command performs panning of the visible area. After

pressing this button, the cursor changes to cross and user can pan the

drawing. To switch oﬀ this mode, press “Grab and Drag” button one

more time.

Zoom in, Zoom out, No zoom - these commands perform actions, corre-

sponding to their names.

Changing visualization options

The following visualization options can be adjusted via in “drawing options”

properties pane on left part of the screen:

Attribs - upper label visualization mode. Possible values are “Show labels” -

show attribute’s label at corresponding concept (See also remark before

about reduced labeling).

Objects - lower label visualization mode. Possible values are

Don’t show - no labels are shown

Show labels - show object labels below the corresponding concepts

Show own objects - for concepts, that has some objects attached (has

non empty object contingent) show number and percentage of ob-

jects, that belong exactly (i.e., their attribute set is equal to intent)

to this concept

Show object count - for every node show, exactly what number (per-

centage) of object lay in extent of this node’s concept.

Stability - for every node show, what minimal number of objects should

be removed from context, that node with such intent disappeared

from concept lattice.

Draw node - this option specify, how the radius of node is calculated. The

possible values are:

~to own objects - node radius is calculated proportionally to size of

contingent (amount of objects, that match intent of this node exactly)

ﬁxed radius - all nodes has equal node radius. Actual node radius is

determined by option “Node radius”

~of object extent - node radius is calculated proportionally to size of

its extent.

stability - node radius is calculated proportionally to its stability to de-

struction (see description of Stability above).

Draw edge - speciﬁes, how exactly edge is drawn. The possible values are:

one pixel - edge width is ﬁxed

no - edge is not drawn

~object - proportionally to the number of objects, that “pass” through

this edge. Equivalent of “~of object extent” option for drawing node

~connection - edge size is proportional to ratio between extent size of

lower and upper concept, that are connected by edge. This value is

equal to conﬁdence of approximate association rule, that corresponds

to edge.

Highlight - speciﬁes, which nodes are highlighted, except for selected edges.

These options were created in order to make exploration of lattice easier.

Possible values of this option are:

Filter and ideal - nodes of ﬁlter (all nodes, that are reachable by as-

cending paths from selected node to top of lattice) and ideal ( all

nodes, that are reachable by descending paths from selected node to

bottom of lattices) are highlighted

Selected - only selected node is highlighted

Neighbors - selected node and it’s upper and lower neighbors are high-

lighted

Ideal - nodes of ideal are highlighted

Filter - nodes of ﬁlter are highlighted

No - no nodes are highlighted. This option may be useful for storing

images of lattice.

Label font size - speciﬁes the size of font, that is used for upper and lower

labels.

Grid size x - speciﬁes the preferred distance by x coordinate between diﬀerent

nodes on one level of drawing. It is used as parameter for layout and after

layout change of this value leads to rescaling of coordinates of nodes by x

scale

Grid size y -speciﬁes the preferred distance by y coordinate between nodes on

adjacent levels of drawing. It is used as parameter for layout and after

layout change of this value leads to rescaling of coordinates of nodes by y

scale.

Node radius - this parameter speciﬁes the maximal possible radius of concept

node and is used when drawing nodes.

Changing layout of lattice

If the initial drawing of lattice is not very satisfactory, than it is recommended

to try to perform several diﬀerent layouts in order to ﬁnd the best ﬁrst approx-

imation before starting to perform manual adjustment of drawing.

Warning: performing layout of lattice is irreversible operation (for now).

Don’t do it, if you have done adjustments, that you would not like to loose.

Several algorithms have diﬀerent options, that can be access through “Layout

options” tab in properties panel.

The following layout algorithms are provided:

Minimal intersections - this is adapted to lattices version of algorithm for

laying out hierarchical graphs. It tries to minimize number of intersections

between edges. It has no parameters. Usually this algorithm provides best

results, but it is pretty slow for the big lattices.

Chain decomposition - adapted version of algorithms of chain decomposi-

tion by M. Skorsky. This algorithms builds so called additive lines di-

agrams. It’s recommended to use ideal node movement strategy, when

working with such line diagrams. This algorithm produces very good

results for distributive lattices. Chain decomposition algorithms has fol-

lowing options:

Representation - what kind of representation is used for concept, when

his coordinates are calculated. Can be either attribute-based or

object-based.

Placement - determines assignment of values to set of vectors. Can take

one of three possible values - exponential,straight or angular.

Rotate left, Rotate right - performs rotation of set of attribute vectors

- is used to select the best one from several possible.

The next algorithms belongs to family of so-called “force-directed” layout algo-

rithms. They are:

Freese layout - adaptation of Ralph Freese [4] algorithm for drawing lattices.

Algorithms has following parameters:

Attraction - regulates the attraction force between nodes

Repulsion - regulates the repulsion force between nodes.

Angle - this is not actually a parameter of the algorithms. Freese algo-

rithms performs layout in 3D space, and angle parameter controls

the angle, which is used for projecting results of layout in 3D space

of 2D surface of screen

Force layout - other force directed algorithm, that diﬀers from previous one

by the way, how the forces are calculated. Parameters of this algorithm

are analogous to the parameters of the previous one.

Manually adjustment of the drawing

Unfortunately, for now no one layout algorithms, that produce good results for

all types of lattice is known. So, the last way to produce good drawing is to

perform the manual adjustment of the lattice.

Movement of lattice nodes is constrained in ConExp in order to maintain a

correct parent-child (successor-predecessor) relations between nodes.

Following tools exists in ConExp in order to help manually adjust a lattice:

Ideal node movement mode - when moving a node, the whole ideal of the

node is moved. The switch between this mode and one node movement

strategy is performed by pressing “Toggle node move mode” button.

Align nodes to grid - performs alignment of node coordinates to the invisible

grid of size 8 on 8 pixels.

Storing default lattice drawing settings

As there are a lot of options for performing layout of line diagram, it is possible

for user to store some set of settings as default. In order to do so, press “Store

preferences as default” button on lattice visualization pane toolbar. After that,

these preferences will be used as default for all newly computed concept lattices.

Storing images of drawing One of the most frequent uses of ConExp is

to produce images of lattice drawings for some future usage. This task can

be achieved by creating a good drawing of lattice and then pressing the “Save

lattice image” button on lattice visualization pane toolbar. Currently saving

image to png and jpeg is supported.

Building lattices of subcontexts

ConExp also provides the ability to build lattices, that corresponds to sub-

context of the original context. This task can be achieved by using attribute

selection and object selection pane on the right side of lattice drawing pane.

After selecting or deselecting name of object or attribute, the new lattice, that

corresponds to new selected subcontext is build. In order to include into se-

lection all objects(attributes) use “Select all objects” (“Select all attributes”)

buttons at the bottom of corresponding panes.

Warning: building lattice of subcontexts leads to destruction of information

about previous drawing. Please store the image or create a lattice snapshot, if

you obtained the useful result after some work.

Creating a lattice snapshot

If you have spent some time adjusting the layout of the lattice, it may be well

worth to create a copy of the drawing before exploring other alternative ways

to layout lattice. Also, one may want to be able to consider several drawings

of diﬀerent subcontexts or to be able to consider several alternative drawings of

lattice.

In order to create a “snapshot” of the current drawing of lattice (i.e. the

exact copy of current drawing of lattice), press “Store current lattice as a view”

button on lattice visualization pane toolbar. After that the copy of the drawing

will be created and will be shown in the document tree.

Displaying the lattice statistics

For the currently computed lattices, it is possible to display statistics about its

diﬀerent characteristics:

Concept count the number of concepts in the current lattice.

Edge count the number of edges in the current lattice.

Lattice height the length of the maximal descending path from lattice unit

element to the lattice zero element.

Lattice width estimation the lower and upper bounds of the lattice width.

The lower bound estimation is computed as a maximal count of elements

in one layer of the lattice (this value is always less or equals to the lattice

width). The estimate of the upper bound is “worse” in sense of precision,

and equals to concept count - lattice height .

Working with implication bases

Calculating Duquenne-Guigues base

In order to ﬁnd so called Duquenne-Guigues base of implications, that holds

in context, one should press button “Calculate Duquenne-Guigues base of im-

plications ” on the main toolbar. The main feature of Duquenne-Guigues base

of implications is that this base has a minimal possible number of implications

among all possible bases of implications, that holds in context.

Implications, that appears in “Implication sets” pane, has the following for-

mat:

No <Number of objects> Premise ==> Conclusion.

No simply means number of implication in list.

Number of objects shows, for how much objects implication holds.

Premise and conclusion are usually list of attribute names, that occur in

premise (conclusion). Also, premise can be “{}”, that means, that this implica-

tion has empty premise and holds for all objects from context.

Implication can be displayed in one of two colors: blue or red.

Blue colors means, that there are objects in context, that supports this rule.

Red color means, that there are no objects, that support implication, and

usually such implication mean, that set of objects, that contained in premise,

doesn’t occur together in context. Also such implication includes all attributes

from context among its attributes.

Searching for associations

Among association rules, in diﬀerence from implication, also non-strict rules are

allowed, i.e. rules, for which if premise hold, conclusion doesn’t necessarily hold

- it is true only for some percent of all objects, that are covered by premise of

rule. The base of association rules consist of two parts - that base of strict rules

(Duquenne-Guigues base) and base of approximate rules (so called Luxenburger

base).

ConExp allows to calculate base of association rules. In order to do this,

one should press “Calculate association rules” button on main toolbar.

The display format of association rule is a small modiﬁcation of the format

for implications. It is:

No <Number of objects, for which premise holds> Premise =[Rule conﬁ-

dence]=><Number of objects, for which premise and conclusion holds> Con-

clusion.

Also, in addition to red and blue colors, that are used in display of implica-

tions, green color is used for approximate, not strict rules.

Performing attribute exploration

The problem of implications, that are calculated for some context, is that they

holds only for objects from context, and don’t generally hold for all object from

domain of interest. In order to overcome this deﬁciency, attribute exploration

procedure should be used.

Attribute exploration is a interactive procedure, in which program asks ques-

tion about dependencies between diﬀerent attribute from some ﬁxed set of at-

tributes. If expert conﬁrms, that such dependency generally holds, it should

answer “yes”, if he rejects dependency, that expert should provide counterexam-

ple. If expert answered correctly on all questions, than after the end of attribute

exploration procedure he will get the set of all implications, that describes de-

pendencies between diﬀerent attributes in domain of interest.

Attribute exploration procedure can start from empty context, where only

attributes are speciﬁed, or from context, where some objects already described.

In order to start attribute exploration procedure, one should press button

“Start attribute exploration” on main toolbar.

Then the ﬁrst question is asked, and user should either conﬁrm it, either

reject it, either stop attribute exploration procedure. If user rejects question,

than other dialog would appear, that would ask to provide a counterexample.

Users mailing list

We always glad to hear your feedback about program.

The best place to give feedback and ask questions about ConExp is the

ConExp user’s mailing list: conexp-user@lists.sourceforge.net

ConExp’s team

Currently, team of developers consists of :

•Dr. Serhiy Yevtushenko - initial and chief developer

•Tim Kaiser

•Julian Tane

•Dr. Sergei Objedkov

The documentation team also includes:

•Joachim Hereth-Correia

•Heiko Reppe

If you would like to join development, you are welcome.

References

[1] Serhiy A. Yevtushenko. System of data analysis "Concept Explorer". (In

Russian). Proceedings of the 7th national conference on Artiﬁcial Intelligence

KII-2000, p. 127-134, Russia, 2000.

[2] B. Ganter and R. Wille. “Formal Concept Analysis:Mathematical Founda-

tions”, Springer-Verlag, 1999

[3] ComImp - http://www.mathematik.tu-darmstadt.de/~burmeister/

[4] http://www.math.hawaii.edu/~ralph/LatDraw/

[5] http://www.sourceforge.net

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