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Ch48-I044963.fm Page 238 Tuesday, August 1, 2006 4:04 PM
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density functions are computed using kernel smoothing. Using the gradient method, the mapping
matrices W i, which minimize R, are obtained.

Feature Extractor Selection
The set of instances U is divided into r subsets U -,j = \,...,r before performing the task (Figure l(b)).
The subsets are arranged by temporal order. The choice of r includes a trade-off between the locality
of the evaluation and the reliability of the action decision. To evaluate it, U is divided so that instances
of similar state and action are included into the same subset. The vector c" = («".,«",r" IL) is defined
from the instance u, and t/is divided by applying the ISODATA algorithm for the set {c"}. Here, L is
the time taken to accomplish the task and ris the time when the instance u is observed. The value of
each component is normalized to the range [0,1]. To avoid aliasing problems, the robot always uses
two neighbouring subsets to evaluate the effectiveness of a feature extractor.
The robot executes the following process at every interval.
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1) Selecting subsets of instances: Select subsets of instances V according to a procedure shown in the
next section, k = 0.
2) Calculating a reliability of action decision: Calculate substate s ok corresponding to the £-th
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selected feature extractors F oli and the entropy H,_ V(A \ S o) using the instances in V .
H.v(A | S o) = £ P v ( « " | S o)logP, ;(«" | S o), (2)
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where S o ={s ol,...,s ok} (S o = (j> , if k =0) and P, v denotes a probability calculated on the set V.
H, V(A\S O) means an uncertainty of the action decision. Evaluate the uncertainty using a threshold
H lk.
• If H, V(A | S o) <H IH, then go to 4.
• Otherwise, k = n and '-V = U, then go to 4.
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• Otherwise, k = n and V * \J t then go to 2 with U = U and k = 0.
• Otherwise, go to 3.
3) Selecting a feature extractor: Let the set of unselected feature extractors be T. Calculate an
expected entropy for each unselected feature extractor F, e T. The expected entropy is:

where s. is a substate corresponding to F.. Select the feature extractor F o/[+1 which has the
minimum entropy, that is, has the maximum information gain, k <— k +1. go to 2.
4) Deciding an action: Execute the action a which maximizes Pc O(a \ S o).

Selecting Subsets of Instance
The robot selects subsets of instances 9) in order to calculate a probability and an entropy according to
the states S 0(T - Y),...,S 0(T - h) observed in the past h steps. For each subset (/. the robot counts the
number of substates which satisfy P u (£„(•)) >0 in h substates. If the count C j is greater than a
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threshold C th, [/. and U j+l are added to U. If C. = 0, the robot uses all instances (TJ = U).