Improving circuit miniaturization and its efficiency using Rough Set Theory( A machine learning...
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A theoretical approach based on Rough Set Theory for Electronic Circuit miniaturization
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- 1. Improving circuit miniaturization and its efficiency using
Rough Set Theory Presented by :Sarvesh Singh Rawat
- 2. Introduction One goal of the Knowledge Discovery is extract
meaningful knowledge. Rough Sets theory was introduced by Z. Pawlak
(1982) as a mathematical tool for data analysis. Rough sets have
many applications in the field of Knowledge Discovery: feature
selection, discretization process, data imputations and create
decision Rules. Rough set have been introduced as a tool to deal
with, uncertain Knowledge in Artificial Intelligence
Application.
- 3. Equivalence Relation Let X be a set and let x, y, and z be
elements of X. An equivalence relation R on X is a Relation on X
such that: Reflexive Property: xRx for all x in X. Symmetric
Property: if xRy, then yRx. Transitive Property: if xRy and yRz,
then xRz.
- 4. Rough Sets Theory Let T (U , A, C, D), be a Decision system
data, Where: U is a non-empty, finite set called the universe , A
is a non-empty finite set of attributes, C and D are subsets of A,
Conditional and Decision attributes subsets respectively. is called
the value set of a , The elements of U are objects, cases, states,
observations. The Attributes are interpreted as features,
variables, characteristics conditions, etc. a :U Va for a A, V
a
- 5. Indiscernibility Relation The Indecernibility relation
IND(P) is an equivalence relation. Let a A , P , the
indiscernibility A relation IND(P), is defined as follows: IND( P)
{(x, y) U U : for all a P, a ( x) a( y)}
- 6. Indiscernibility Relation The indiscernibility relation
defines a partition in U. Let P A, U/IND(P) denotes a family of all
equivalence classes of the relation IND(P), called elementary sets.
Two other equivalence classes U/IND(C) and U/IND(D), called
condition and decision equivalence classes respectively, can also
be defined.
- 7. R-lower approximation Let X U and R C , R is a subset of
conditional features, then the R-lower approximation set of X, is
the set of all elements of U which can be with certainty classified
as elements of X. RX {Y U / R :Y X} R-lower approximation set of X
is a subset of X
- 8. R-upper approximation the R-upper approximation set of X, is
the set of all elements of U such that: RX {Y U / R :Y X } X is a
subset of R-upper approximation set of X. R-upper approximation
contains all data which can possibly be classified as belonging to
the set X the R-Boundary set of X is defined as: BN ( X ) RX
RX
- 9. Representation of the approximation sets If If RX RX RX RX
then, X is R-definible (the boundary set is empty) then X is Rough
with respect to R. ACCURACY := Card(Lower)/ Card (Upper)
- 10. Decision Class The decision d determines the partition
CLASS T (d ) { X 1 ,..., X r ( d ) } of the universe U. Where X k
{x U : d ( x) k} for 1 k r (d ) CLASS T (d ) will be called the
classification of objects in T determined by the decision d. The
set Xk is called the k-th decision class of T
- 11. Decision Class This system data information has 3 classes,
We represent the partition: lower approximation, upper
approximation and boundary set.
- 12. Dispensable feature Let R a family of equivalence relations
and let P R, P is dispensable in R if IND(R) = IND(R-{P}),
otherwise P is indispensable in R. CORE The set of all
indispensable relation in C will be called the core of C. CORE(C)=
RED(C), where RED(C) is the family of all reducts of C.
- 13. CASE STUDY Circuit - miniaturization In this section, a
simple structure using logic gates is shown which is the magnified
view of a portion of complicated circuit and it is further reduced
using Rough Set based on logical classifier and rules.
- 14. Information Table (I) , , { , {{ , , A set of data is
generated by each gate in binary form (either 0 or 1), and the
wires represents that attributes. The basic idea behind circuit
miniaturization is to mine te data that is obtained as a result of
each gate in a logical manner using algebraic developments so that
the final result is not altered. The example that is shown here is
a small circuit but the same technique can be implemented in bigger
circuits using the same procedure.
- 15. Information Table (II)
- 16. Approximations Let X U and R C R is a subset of conditional
, features, then the R-lower approximation RX {Y U / R :Y X} The
R-upper approximation set of X, is the set of all elements of U
such that: RX {Y U / R :Y X The accuracy of approximation is given
by | ( PX ) | p(X ) | ( PX ) | }
- 17. Approximation From our information system, we have two
classes of decision set as 0 and 1. As the data value is discrete
(either 0 or 1) so the total number of lower approximations is
equal to that of the upper approximations.
- 18. Decision rules The algorithm should minimize the number of
features included in decision rules.
- 19. Conclusions and outcomes We have reduced the number of
gates without affecting the output of the given circuit using the
mathematical model of Rough Set Theory. It saves a lot of time and
power that is wasted in switching of gates , the wiring-crises is
reduced, crosssectional area of chip is reduced, the number of
transistors that can implemented in chip is multiplied many
folds.
- 20. References Pawlak, Z. (1997). Rough set approach to
knowledge-based decision support. European journal of operational
research, 99(1), 48-57. Pawlak, Z. (1998). Rough set theory and its
applications to data analysis. Cybernetics & Systems, 29(7),
661-688. Roy, S, S. Viswanatham, V, M. Krishna, P, V. Saraf, N,
Gupta. A, and Mishra, R. (2013). Applicability of Rough Set
Technique for Data Investigation and Optimization of Intrusion
Detection System. 9th International Conference, QShine 2013, India,
January 11-12, 2013,(pp.479-484). Roy, S, S. Viswanatham, V, M.
Rawat, S, S. Shah, H. (2013). Multicriteria decision examination
for electrical power grid monitoring system. Intelligent Systems
and Control (ISCO), 2013 7th International Conference on pp.
26-30.
- 21. THANK YOU!