Hidden Markov Model (HMM) VIDEO LINK: https://youtu.be/YIGCWNG8BIA A Hidden Markov Model (HMM) is a statistical model in which the system has hidden states that cannot be directly observed, but produce observable outputs. It is based on the Markov property, meaning the next state depends only on the current state. Video Chapters: HMM in Artificial Intelligence 00:00 Introduction 00:31 Statistical Model 00:54 HMM Examples 02:30 HMM 03:10 HMM Components 05:23 Viterbi Algorithm 06:23 HMM Applications 06:38 HMM Problems 07:28 HMM in Handwriting Recognition 11:20 Conclusion HMM COMPONENTS A Hidden Markov Model (HMM) is a statistical model in which the system has hidden states that cannot be directly observed, but produce observable outputs. It is based on the Markov property, meaning the next state depends only on the current state. An HMM consists of states, observations, transition probabilities, emission probabilities, and initial probabilities. It is commonly used in a...
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Shark Smell Optimization Algorithm Numerical Example
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SHARK SMELL OPTIMIXATION ALGORITHM [ Numerical Example ]
Shark Smell Optimization Algorithm is population based Metaheuristic optimization algorithm. Shark Smell Optimization Algorithm is inspired by the Shark food foraging behavior.
Shark Smell Optimization Algorithm Steps:
Initialize Algorithm Parameters
Initialize Population for N Sharks in the search space.
Evaluate Performance.
While (current Iteration < Maximum Iteration)
Calculate Shark Velocity
Calculate Shark Position based on forward movement.
Calculate Shark Position based on rotational movement.
Identify Shark next position based on forward and rotational movements.
Evaluate Performance.
End While
Display Best Solution.
STEP 01: Initial Important Parameters.
Current_Iteration =1;
Maximum_Iteration = 10;
and other.
STEP 02: Initial Population Randomly.
Suppose, Population Size = 2;
Position(1) = -0.9891
Position(2) = -8.3236
STEP 03: Using Fitness Function Calculate Fitness Values.
Fitness(1) = 0.97845
Fitness(2) = 69.2819
Global Best = 0.97845
STEP 04: Calculate Shark's Velocity.
NOTE: At 1st Iteration, you can either neglect initial velocity or assign very small value.
For this Check IF (Current_Iteration ==1){
Initialize Velocity.}
Else{
Modify Velocity.
End
Right Now as iteration is 1.
Velocity(1) = 0;
Velocity(2) = 0;
STEP 05: Calculate Shark Movement in the search space.
Update Position for 1st Agent
a.) Calculate Shark Forward Movement for 1st Agent.
New Position (1) = Previous Position + Previous Velocity * Current Iteration
New Position (1) = (-0.9891) + 0 * 1;
New Position (1) = -0.9291
New Fitness (1) = 0.8632
b.) Calculate Shark Rotational Movement for 1st Agent.
New Position (1) = Previous Position + (Random Value * Previous Position)
New Position (1) = 0.8632 + ( 0.9189*0.8632)
New Position (1) = 1.6563
New Fitness (1) = 2.7433
Update Position for 2nd Agent
a.) Calculate Shark Forward Movement for 2nd Agent.
New Position (2) = Previous Position + Previous Velocity * Current Iteration
New Position (2) = (-8.32361) + 0 * 1;
New Position (2) = -8.3261
New Fitness (2) = 69.2823
b.) Calculate Shark Rotational Movement for 2nd Agent.
New Position (2) = Previous Position + (Random Value * Previous Position)
New Position (2) = -8.3261 + ( 0.3259*(-8.3261))
New Position (2) = 5.6126
New Fitness (2) = 31.5015
STEP 06: Update Sharks Position based on Forward and Rotational Movement.
For 1st Agent:
New Position(1) = max { 0.8632, 2.7433} //Check max value (i.e., 0.8632)
New Position (1) = 1.6563
New Fitness (1) = 2.7433
For 2nd Agent:
New Position(2) = max {69.2823, 31.5015} //Check max value (i.e., 69.2823)
New Position (2) = -8.3261
New Fitness (2) = 69.2823
STEP 07: Increment Iteration Counter.
Current_Iteration = Current_Iteration + 1;
Current_Iteration = 1+1;
Current_Iteration = 2.
NOTE: Repeat The Loop until Stopping Criteria Met.
STEP 08: Display Best Solution Found.
First Iteration, Best Solution: 69.2823
The best position of shark is the Last Iteration that has the maximum Fitness value (for Maximization problems) is considered as the the BEST SOLUTION.
PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. - PART 2 [Example 2] 1.) Initialize Population [Current Iteration (t) = 0] Population Size = 4; 𝑥𝑖 : (i = 1,2,3,4) and (t = 0) 𝑥1 =1.3; 𝑥2=4.3; 𝑥3=0.4; 𝑥4=−1.2 2.) Fitness Function u...
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Particle Swarm Optimization (PSO) is a p opulation-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. PSO is a computational method that Optimizes a problem. PSO searches for Optima by updating generations. It is popular is an intelligent metaheuristic algorithm. In Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. After a number of iterations agents / particles will find out optimal solution in the search space. Q. What is PSO? A. PSO is a computational method that Optimizes a problem. Q. How PSO will optimize? A. By Improving a Candidate Solution. Q. How PSO Solve Problems? A. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to ...
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Whale Optimization Algorithm Code Implementation Whale Optimization Algorithm Code Files function obj_fun(test_fun) switch test_fun case 'F1' x = -100:2:100; y=x; case 'F2' x = -10:2:10; y=x; end end function [LB,UB,D,FitFun]=test_fun_info(C) switch C case 'F1' FitFun = @F1; LB = -100; UB = 100; D = 30; case 'F2' FitFun = @F2; LB = -10; UB = 10; D = 30; end % F1 Test Function function r = F1(x) r = sum(x.^2); end % F2 Test Function function r = F2(x) r = sum(abs(x))+prod(abs(x)); end end function Position = initialize(Pop_Size,D,UB,LB) SS_Bo...
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