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Hidden Markov Model (HMM)

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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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PSO Python Code || Particle Swarm Optimization in Python || ~xRay Pixy

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Particle Swarm Optimization Implementation in Python Video Chapters: 00:00 Introduction 02:01 Code 05:55 Position Initialization 08:06 PSO Main Loop 08:42 Velocity Calculation 10:02 Position Update 10:36 Fitness Evaluation 13:21 Objective Function 17:44 Result 19:00 Conclusion

.....................................................SOURCE CODE.........................................................................
import random import numpy as np from tkinter import messagebox #Define Class Particles class Particle: def __init__ (self,position): self.position=position self.velocity=np.zeros_like(position) self.best_position=position self.best_fitness=float('inf') def PSO(ObjF,Pop_Size,D,MaxT): swarm_best_position=None swarm_best_fitness=float('inf') particles=[] #Posotion Initialization position=np.random.uniform(-0.5,0.5,D) particle=Particle(position) particles.append(particle) #Fitness Update fitness=ObjF(position) if fitness<swarm_best_fitness: swarm_best_fitness=fitness swarm_best_position=position particle.best_position=position particle.best_fitness=fitness #PSO Main Loop for itr in range(MaxT): for particle in particles: #Update Velocity w = 0.8 c1 = 1.2 c2 = 1.2 r1=random.random() r2=random.random() #Velocity Calculation particle.velocity =(w*particle.velocity+c1*r1*(particle.best_position-particle.position)+c2*r2+(swarm_best_position-particle.position)) #New Position particle.position += particle.velocity #Evaluate Fitness fitness = ObjF(particle.position) #Update PBest if fitness<particle.best_fitness: particle.best_fitness=fitness particle.best_position=particle.position #Update GBest if fitness<swarm_best_fitness: swarm_best_fitness=fitness swarm_best_position=particle.position return swarm_best_position,swarm_best_fitness #Define ObjFunction def F1(x): return np.sum(x**2) def F2(x): return np.max(np.abs(x)) Objective_Function ={'F1':F1,'F2':F2} #Parameters Pop_Size=100 MaxT=100 D=2 # Iterate over each objective function and run PSO for funName, ObjF in Objective_Function.items(): Output = "Running Function = " + funName + "\n" best_position,best_fitness = PSO(ObjF,Pop_Size,D,MaxT) Output += "BEST POSITION : " + str(best_position)+"\n" Output += "BEST COST : " + str(best_fitness) Output += "\n" messagebox.showinfo("PSO RUN",Output)



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