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Drawbacks of back-propagation algorithm The back-propagation algorithm suffers from two major drawbacks, namely network paralysis and trapping at local minima. These issues are briefly outlined below. Network paralysis: As the network receives training, the weights are adjusted to large values. This can force all or most of the neurons to operate at large Outs, i.e., in a region where F ' (Net) →0. Since the error sent back for training is proportional to F ' (Net), the training process comes to a virtual standstill. One way to solve the problem is to reduce η, which, however, increases the training time. Layer j Neuron p w p, q , k 1 Layer k ∑+ F ∑+ F w p, q , k Net j F ' Outp, j (1−Outp, j) q3 ∑ w . p , q , k δ q = q δ p, j 1 2 w , k q p, 3 q , k Fig. 14.7: The computation of δp at layer j. Neuron q1 ∑+ F Neuron q2 ∑+F Neuron q3 δ , k q 1 δ k 2 , q δ , k q 3
Trapping at local minima: Back-propagation adjusts the weights to reach the minima (vide fig. 14.8) of the error function (of weights). However, the network can be trapped in local minima. This problem, however, can be solved by adding momentum to the training rule or by statistical training methods applied over the back-propagation algorithm [26]. Weight 2 Error function of weights local minima1 Local minima2 Weight 1 Fig. 14.8:Valleys in error function cause back-propagation algorithm trapped at local minima. Adding momentum to the training rule: To eliminate the problem of trapping at local minima, recently a momentum term was added to the right hand side of the adaptation rule [17]. Formally, Wp,q,k(n+1) = Wp,q,k(n) + η δq, k Outp, j + α ∆ wp, q, k (n-1). The last term in the right hand side corresponds to momentum. The addition of the momentum term forces the system to continue moving in the same direction on the error surface, without trapping at local minima. A question may naturally arise: why call this momentum term? The answer came from the analogy of a rolling ball with high momentum passing over a narrow hole.
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Artificial Intelligence and Soft Co
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Library of Congress Cataloging-in-P
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understanding of the subject. The r
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4. Structural organization of the b
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ACKNOWLEDGMENT The author gratefull
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To my parents, Mr. Sailen Konar and
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Chapter 2: The Psychological Perspe
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5.4.2 Syntactic Methods for Theorem
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9.4.4 Realization of Fuzzy Inferenc
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Chapter 14: Machine Learning Using
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17.4.2.7 Fusing Multi-sensory Data
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22.4 Parallelism at Knowledge Repre
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1 Introduction to Artificial Intell
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instances of decision making [27],
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End. Begin state := new-states - ex
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(a) Generate and Test Approach: Thi
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this problem is useful for the foll
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disciplines. As a young discipline
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The bird and its attributes here ha
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[19] , Kosko [15] and Pedrycz [30]
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Reasoning in the presence of imprec
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where AI finds extensive applicatio
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M1 M2 M3 J2 J 1 8 5 J 2 J 1 2 8 J 2
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1.5.3 The Modern Period The modern
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A B AND C D E AND Y Fig. 1.12: A Pe
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improve reliability by realizing fr
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in AI problems, it supports massive
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[7] Dean, T., Allen, J. and Aloimon
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[34] Rajendra, C. and Chaudhury, D.
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2 The Psychological Perspective of
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The scope of realization of the pro
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2.2.3 Feature-based Approach for Pa
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From Sensory Registers Echoic Reg.
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cognitive memory and its utilizatio
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Tulving’s model bridges a potenti
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A " (a) (b) Fig. 2.6: The character
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his friend s facial image in memory
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sum need not be 180 degrees. Thus a
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same evening. Then he started medit
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construction of knowledge and its o
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saved in a magnetic media, which he
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set-point + error Controller Plant
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Cognitive science has emerged as a
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Further show that the Euclidean lea
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[4] Biswas, B., Mukherjee, A. K. an
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[28] Peterson, M. A., Kihlstrom, J.
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Production Systems, Logical Calculu
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against the data items of the WM. I
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Suppose the WM contains the data Bi
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To demonstrate the working principl
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i) Prefer rules for firing, where u
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In fig. 3.3, the antecedent clauses
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possible offspring states are gener
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Backward Reasoning: The backward re
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p q r s denotes joint premises t w
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3.11.1 Isolation of Knowledge and C
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state, as the predecessor states of
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[3] Buchanan, B. G. and Shortliffe,
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issues: first ‘what to search’
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We will now present two typical alg
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Further, the first state within the
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n1 n2 n3 n8 (a) (b) (c) (d) (e) (f
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The iterative deepening search thus
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legal next states will also lie on
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End. Then push those children into
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Procedure Best-First-Search Begin 1
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End. have multiple parents; Under t
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node. Under this circumstance, the
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6. Pn- Γ the set of paths from nod
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Therefore, f * (n’) = g* (n’) +
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0 +10 B 1+3 C +4 D +5 E F G 2+2 3+1
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The above algorithm considers two d
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Step 1: X (7) Step 2: Step 3: U X (
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(iv) If all of the nodes connected
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If the values are propagated up to
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ii) the alpha value of any MAX node
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αmin =2 βmax =1 C αmin =1 e(n) =
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eductions. Constraint satisfaction
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5 The Logic of Propositions and Pre
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5.2 Formal Definitions The followin
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Definition 5.7: A propositional for
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5.4.1 Semantic Method for Theorem P
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8. p \/ (q Λ ¬ q) ⇔ p 9. p Λ (
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) AND, OR Removal: If the L.H.S. co
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Since all the terminals of the tree
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p v q ¬ q v r p v r ¬ p v s r v s
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Let AS = {A1, A2,, …..,An} be the
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4. If P is a WFF and X is not a qua
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original expression: ( ¬ P11 ∨
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S: = S ∪ {variable or constant /
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¬ Loves (john, mary) ¬Child (X)
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which implies that if q is true the
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ii) C is a ground instance of C [9]
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) p→ (q→ r) ⇔ (p Λ q) → r
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[6] Leinweber, D., “Knowledge-bas
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of a ‘classroom scene’ interpre
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Sits-on (Y, bench, classhour), Pers
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Sits-on (mita, bench, classhour). 3
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Teacher (X) Sub-goal fails Person (
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Definition 6.5: A definite goal is
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Example 6.5, presented below, illus
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6.6.1 Risk of Using CUT It is to be
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In the SLD tree for the Taxpayer pr
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6.9 Fixed Points in Non-Horn Clause
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6.11 Conclusions The main advantage
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preferred X50 >= 2, default X100
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7.1 Introduction Predicate Logic is
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proposed this logic and called it n
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We now present a few modal properti
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Expert Reasoning System New data Dy
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PR5: ¬Visits (Wife, market, Monday
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IN (n1) + IN (n2) + (n11) retracts
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may hold (and not must hold). An ex
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The resulting stable consequences t
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In this example, we call ψ = Bird
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important factor in non-monotonic r
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a) Boy(X) ∧ ¬ L ¬ Likes (X, cho
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8 Structured Approach to Knowledge
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predicate boy (jim). This can be re
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Consequently, we represent the abov
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Is-a Is-a Is-a Protozoa Bacteria Is
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Example 8.2: This example illustrat
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A common question that may be raise
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∴ q is true. 2) Defeasible deriva
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Examination Hall Seat Arrangement I
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Petri nets [5]. It, however, does n
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Since p1 and p 2 contain tokens and
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For building dependency structures,
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The most significant drawback of CD
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Once a script structure for a given
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[6] Nilsson, N. J., Principles of A
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techniques, we first introduce the
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of precision of data and certainty
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where D and S stand for disease and
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To illustrate the reasoning process
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2. It might happen that none of the
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One interesting property of Bayesia
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We now compute the messages that no
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The main steps [8], [12] of the bel
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Updating a node X thus involves upd
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j ↓ i→ round oval-shaped and MB
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Formally, the set of all possible o
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The orthogonal summation of belief
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The orthogonal summation operations
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integers, then we can definitely sa
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where a / b in fast-runner subset r
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where the “o” denotes a fuzzy A
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This may be formally written as µ
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cumulative maximum of the two succe
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“If you can manage to evaluate th
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[7] Shenoy, P. P. and Shafer, G.,
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10.1 Introduction Databases associa
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a finite set of places, D= {d1, d2
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µfast runner(x) 0.9 0.6 0.2 0.1 5
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present in the consequent part; Aug
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Procedure Cycle-detection (P, Q, m,
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Procedure Put-transition (Newlistk,
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The trace of the algorithm cycle- d
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p1 p2 pm n1 n2 nm Fig. 10.4: A tran
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where the elements qw / ∈ {0, 1}
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Q' m and Rm matrices. It may be not
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Definition 10.9: An arc is called p
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The procedure forward reasoning is
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In the above example, A, B, and C a
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n V (q k j ∧r j k ) to be close t
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Let us assume for the sake of simpl
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It is evident from the above distri
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= R b m o ((P ' f m) T o Nf c (t+1)
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Since such choice of Rfm and Rbm sa
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one step of belief revision in the
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10.9 Conclusions The chapter presen
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References [1] Bugarin, A. J. and B
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[24] Looney, C. G., "Fuzzy Petri ne
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11 Reasoning with Space and Time Th
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The other one is an extension by ne
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touches another, the common points
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Procedure Move-optimal (R , Startin
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at Jadavpur University verified thi
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µ above(θ) =sin 2 θ , when -∏
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c c a b q r a b (b) (a) d d p q r p
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11.5 Temporal Reasoning by Situatio
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Holds( now, rain-ceased) Axiom (3)
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Interpretation I Interpretation II
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Example 11.3: Prove that Ā(p) ≡
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11.6.3 Some Elementary Proofs in PT
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The second rule is generally called
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11.9 Conclusions The chapter demons
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12 Intelligent Planning This chapte
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sets opposite to the TV. So they oc
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where On (X, Y) means the object X
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this, let us consider the last prob
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(B), we generate the old state 3, w
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12.3 Least Commitment Planning The
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To start solving the problem, we fi
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We now have three partially ordered
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12.4 Hierarchical Task Network Plan
Page 394 and 395: d=0 d=1 d=2 d=3 Fig. 12.16: A hiera
Page 396 and 397: J1 J2 M1 M2 M3 or Job schedules J2
Page 398 and 399: job k from time 0. For example, the
Page 400 and 401: 3. Design a hierarchical plan for t
Page 402 and 403: trainer, who supplies the input-out
Page 404 and 405: Definition 13.1: An object is an en
Page 406 and 407: The restriction of hypotheses can b
Page 408 and 409: Positive instances: 1. Object (larg
Page 410 and 411: To illustrate how LEX performs inte
Page 412 and 413: alive dead Z=A/W 2 1 0 0 1 2 Living
Page 414 and 415: where Pi denotes the proportion of
Page 416 and 417: 3. Apply Mapping Function: Apply th
Page 418 and 419: determine the animals because it do
Page 420 and 421: simplest form of reinforcement lear
Page 422 and 423: Let us now assume that the game is
Page 424 and 425: How can we compute the utility valu
Page 426 and 427: 13.5 Learning by Inductive Logic Pr
Page 428 and 429: know f ? These questions can be ans
Page 430 and 431: |H| (1-ε) m ≤ δ ⇒ m ≥ (1/ε
Page 432 and 433: [7] Michalski, R. S., “A theory a
Page 434 and 435: However, most biologists are of the
Page 436 and 437: The most common non-linear function
Page 438 and 439: (d) b1 a1 (e) c1 cj cq bi ah Fig.14
Page 440 and 441: transverse diameter, etc. as the in
Page 442 and 443: x 1 x 2 x n Penultimate layer ∑+F
Page 446 and 447: x1 x2 xn 14.6 Widrow-Hoff's Multi-l
Page 448 and 449: x 1 x 2 x 1 x 2 The training proces
Page 450 and 451: • If not, select another ADALINE,
Page 452 and 453: ni 1 = '1' output ( firing ). Each
Page 454 and 455: designed the weights (W) of a singl
Page 456 and 457: AND z1 s11 OR w11 w12 w 1n v 11 v12
Page 458 and 459: − ~ w X k, l ∼ = ⎡ ⎤ ⎢
Page 460 and 461: V x ∑ w O j = Sgn ( j+ ji i + A
Page 462 and 463: neural nets in the fields mentioned
Page 464 and 465: where the first summation is over a
Page 466 and 467: circuit,” IEEE Trans. on Circuits
Page 468 and 469: their joint usage in many problems,
Page 470 and 471: 1 0 1 0 11 0 1 0 1 0 1 1 0 10 1 1 1
Page 472 and 473: 15.2 Deterministic Explanation of H
Page 474 and 475: Thus, in a total of N selections wi
Page 476 and 477: and population size = 2, which mean
Page 478 and 479: The behavior of GA without mutation
Page 480 and 481: a = ∑ Lt (π 0 P n ) i i=1 n→
Page 482 and 483: Eθ GA Program Z1, Z2, Z3, Z4, X1,
Page 484 and 485: e [W1 W2 W3 W4 W5 W6] T and [ G1 G2
Page 486 and 487: function. So, GA in each evolution
Page 488 and 489: f(x) = Sin (x) + [x * x + y] 1/2 ca
Page 490 and 491: (EQ (DU(MT CS) (NOT CS)) (DU(MS NN)
Page 492 and 493: [4] Chakraborty, U. K. and Muehlenb
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16 Realizing Cognition Using Fuzzy
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Cognitive maps are generally used f
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Theorem 16.1: With initial values o
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Here W T is a transposed weight mat
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example, for moving one’s arm, th
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and the weight adaptation equation
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Xk+1 ∆Wk = α Ek οXk+1 T / ((Xk+
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d5 d9 d1 d6 d7 d8 d10 d11 d1=Front
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16.10 Conclusions and Future Direct
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[6] Kosko, B., “Fuzzy cognitive m
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however, have a narrow spectrum of
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contaminated with it. However, for
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1. Move the mask over the image, so
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∇ 2 (g * f ) = ( ∇ 2 g ) * f. W
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It may be noted that segmenting an
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machine has to narrate the game onl
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schematic diagram, briefly outlinin
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same process for all clusters, we g
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Level 1 Level 2 Level 0 Neuron Fig.
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I (u, v) YI Fig. 17.12: Camera mode
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epipolar planes meet the image plan
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(a, b, 1) Fig. 17.15: A 3-D represe
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case III: Planes not parallel to th
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yi = -fi (xi,* ai - 1*) + ( fi / a
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Sample Execution: This is a program
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U t11 t12 t13 t14 x V = t21 t22 t23
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obtained after linearizing measurem
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co-ordinate systems. The correspond
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18 Linguistic Perception Building p
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psychological aspects of understand
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S NP VP ART N VP the man VP V NP ki
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( S ( NP ( ( ART the ) (N man ) ) (
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Sentence: NP VP 1 6 NP: ART N 2 ART
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18.2.3.1 Learning For adaptation of
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context sensitive grammar is thus m
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Generally, we start the sentence S
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VP: V NP S0 S1 Tagged procedure V:=
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Laugh agent animal enjoyer entity p
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18.5 Discourse and Pragmatic Analys
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Thus the elements of communicative
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19 Problem Solving by Constraint Sa
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The recognition problem is the pres
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CSP deals with two classical proble
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= 10 10 = 10 = * Fig. 19.2 (b): Pro
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+ _ V1 R1 V 2 V3 I1 I2 I3 V R2 R3 S
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V = Now assuming the values of V, R
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On (A, Ta) ∧ On (B, Ta) ∧On (C,
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We now represent the neighboring re
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Step 1: (x
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such variable xj , xk, etc., attach
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of C3. If the constraints are liste
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The possible labels of the junction
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The main part of CSP is the formula
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20 Acquisition of Knowledge Acquisi
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invite the experts to attend a meet
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B E A= test ?, B = test results, C
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The database in fig. 20.2 is extrac
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20.5 Knowledge Refinement by Hebbia
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* * * n i ( t + 1) = n i ( t ) at t
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L(r,s) L(s,r) Y(r) Y(s) OS(r,s) n1
Page 614 and 615:
The FPN of fig. 20.5 is formed with
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L(a,l) L(l,a) Y(a) Y(l) OS(a,l) n1
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[3] Cooke, N. and Macdonald, J.,
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21 Validation, Verification and Mai
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Here the problem characteristic is
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The chapter will cover various issu
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21.2.1 Qualitative Methods for Perf
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Paired t-test: Suppose xi ∈ X and
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Ancestor P = {p1,p2} Tr = {tr1,tr2,
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21.3.2 Inconsistencies in Knowledge
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q tr1 tr2 p1 p2 …………… pn
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A rule may also include a number of
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21.4 Maintenance of Knowledge Based
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control of data and knowledge is un
Page 642 and 643:
8. Stefik, M., Introduction to Know
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are not suitable for AI application
Page 646 and 647:
Because of non-determinism in the s
Page 648 and 649:
Procedure Partial-Expansion Begin W
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Step: Fig.22.4: A tree expanded by
Page 652 and 653:
Procedure Generous-Sharing Begin Fl
Page 654 and 655:
To evaluate the performance of the
Page 656 and 657:
Definition 22.2: If the antecedents
Page 658 and 659:
a) AND -Parallelism Consider a logi
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However, given sufficient computing
Page 662 and 663:
EPN = { P, Tr, D, f, m, A, a, I, o
Page 664 and 665:
It is to be noted that if- then ope
Page 666 and 667:
After the bindings of the variables
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F(x) ← A(X) , B(Y) (1) A(1) ← (
Page 670 and 671:
the result produced by clause (2) m
Page 672 and 673:
Else Flag:= true; End; Until no-of
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transition for the PTVVM. The PTVVM
Page 676 and 677:
For the sake of convenience, the pi
Page 678 and 679:
22.6 Conclusions The chapter starte
Page 680 and 681:
Rule 3: S(X, Y) → Z (Y, X) Rule 4
Page 682 and 683:
23 Case Study I: Building a System
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features in human faces and their r
Page 686 and 687:
Definition 23.4: A linear edge segm
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lock containing edge. The productio
Page 690 and 691:
Definition 23.13: The measure of di
Page 692 and 693:
Partitioning Fe into Blocks Feature
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The fuzzy membership functions used
Page 696 and 697:
∆ • Fig. 23.4: The delta and th
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Thus we have altogether 6 different
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cross-section of the vocal tract, w
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23.4.2 Training a Multi-layered Neu
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information with their normalized v
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SR (Y, X) OR (M (X) ∧ M (Y) ∧ L
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procedure, however, no attempts hav
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23.5.5 Belief Revision and Limitcyc
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that the inferences will be minimal
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the formation of the FPN. The FPN o
Page 716 and 717:
is then initiated for detecting the
Page 718 and 719:
initial fuzzy beliefs at all places
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at all feasible x, y. Then estimate
Page 722 and 723:
[13] Malmberg, B., Manual of Phonet
Page 724 and 725:
24.1 Mobile Robots Mobile robots ar
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about its world. There exists ample
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the process, else it attempts to fi
Page 730 and 731:
Depending on the type of planning p
Page 732 and 733:
WEST NORTH SOUTH Fig. 24.5: Represe
Page 734 and 735:
NW child B NE child 'C' SW child 'D
Page 736 and 737:
As observed from the node status, t
Page 738 and 739:
In their evolutionary planner algor
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tuning of the path, such as avoidin
Page 742 and 743:
S S= starting point, G= Goal point,
Page 744 and 745:
Once the training is over, the syst
Page 746 and 747:
N o Table 24.2: Training pattern sa
Page 748 and 749:
24.9.1 Finite State Machine Finite
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occurrence of a state, but also in
Page 752 and 753:
24.10 An Application in a Soccer Pl
Page 754 and 755:
Exercises 1. Devise an algorithm fo
Page 756 and 757:
[15] Meng, H. and Picton, P. D.,
Page 758 and 759:
24 + The Expectations from the Read
Page 760 and 761:
Appendix A How to Run the Sample Pr
Page 762 and 763:
Predicate: LSR Argument1: S Argumen
Page 764 and 765:
ANTECEDENT 1: Predicate: END conclu
Page 766 and 767:
Rules properly arranged MAIN MENU:
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Level POSITION_FROM_LEFT NODE 1 1 H
Page 770 and 771:
calculating membership values enter
Page 772 and 773:
C > File currently in progress = ci
Page 774 and 775:
When the goal is within concave obs
Page 776 and 777:
path selected 160,160 and 240,240 T
Page 778 and 779:
(a) Robot entering the room (b) Aft
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where tr and Outr denote the target
Page 782 and 783:
∂E/∂Wsp = ∑r (∂E/∂Outr) (
Page 784 and 785:
Proof of theorem10.2: For an oscill
Page 786 and 787:
Thus, we get analogously , and 1 0
Page 788:
= Q 'f m T o Rf m o ( Q ' f m o I )
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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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