Incremental Graph-Based Discovery of Relational Concepts Ana Cecilia - - PowerPoint PPT Presentation

Incremental Graph-Based Discovery

• f Relational Concepts

Ana Cecilia Tenorio, Eduardo F. Morales

Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE) México

Overview

• Explore the environment and gather

information from sensors

• Use BK to identify objects and relations
• Repeated information ≈ potential concepts
• Incrementally build a graph
• Induce a new concept:
• Find frequent sub-graphs (Subdue)
• Generalize over similar sub-graphs (Progol)
• Replace the induced concept in the graph by a

new node and repeat

Experimental Setup

• Mobile robot with sensors (simulation)
• Background knowledge able to recognize

from information of sensors:

• Objects: vertical surfaces (walls, back
• f chairs), horizontal surfaces (tables,

seats), legs, …

• Relations: above, in-front, next-to, …

Incremental Graph Construction

Incremental Graph Construction

Incremental Graph Construction

Incremental Graph Construction

Incremental Graph Construction

Incremental Graph Construction

Incremental Graph Construction

Find common sub-graphs

Find common sub-graphs

• Sub-graph isomorphism (NP-complete)
• Graph discovery system - Subdue (Holder et
• al. 94)
• Heuristic beam search using MDL
• Allows small mismatches - to cope with

errors in sensors

• Fast: 100 nodes & 100 arcs in ≈ 5 sec, 4K

nodes & 4K arcs ≈ 15 sec

Group similar sub-graphs

• Each sub-graph represents a potential concept
• If a new sub-graph is similar (high proportion
• f common literals or small cost of structural

changes) to existing sub-graphs in a group

• Then adds it to the group and generalize
• Else create a new group

Induce new concepts

• Transform graphs into predicates (E+)
• Clause body = relations in sub-graph
• Clause head = new predicate symbol with

args = distinctive arguments in body

• E- = graphs from other groups +

artificially created

• Use an ILP algorithm (Progol) to learn a

new concept

Hierarchical Concepts

• Replace new concept by new node in

the original graph

• May involve instantiations and inexact

matching

• Repeat the whole process until no more

sub-graphs are found

• Can induce hierarchical concepts

Simplify

Simplify

Hierarchical Concepts

Experiments

• A simulated Pioneer 2 robot with laser

(Player/Stage)

• BK: wall/1 and touches/2

Experiments

• Polygons, BK: line/1, curve/1, angcc/2, angcx/2
• Furniture, BK: flat_board/1, leg/1, …, on/2,

next_to/2, behind/2, in_front_of/2, above/2

Experiments

Experiments

Conclusions

• Incremental discovery of new concepts
• Graph-based, common sub-graphs, ILP
• Tested on simulation and artificial domains
• Define an exploration strategy
• Incorporate actions to perform tasks
• Test on a real robot

Future Work