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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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GWO Python Code || Grey Wolf Optimizer in Python || ~xRay Pixy

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SOURCE CODE

import numpy as np
import tkinter as tk
import matplotlib.pyplot as plt
from tkinter import messagebox

def initialization (PopSize,D,LB,UB):
    SS_Boundary = len(LB) if isinstance(UB,(list,np.ndarray)) else 1
    if SS_Boundary ==1:
        Positions = np.random.rand(PopSize,D)*(UB-LB)+LB
    else:
        Positions = np.zeros((PopSize,D))
        for i in range(D):
            Positions[:,i]=np.random.rand(PopSize)*(UB[i]-LB[i])+LB[i]
    return Positions

def GWO(PopSize,MaxT,LB,UB,D,Fobj):
    Alpha_Pos = np.zeros(D)
    Alpha_Fit = np.inf
    Beta_Pos = np.zeros(D)
    Beta_Fit = np.inf
    Delta_Pos = np.zeros(D)
    Delta_Fit = np.inf

    Positions = initialization(PopSize,D,UB,LB)
    Convergence_curve = np.zeros(MaxT)

    l = 0
    while l<MaxT:
        for i in range (Positions.shape[0]):
            BB_UB = Positions[i,:]>UB 
            BB_LB = Positions[i,:]<LB
            Positions[i,:] = (Positions[i,:]*(~(BB_UB+BB_LB)))+UB*BB_UB+LB*BB_LB
            Fitness = Fobj(Positions[i,:])

            if Fitness<Alpha_Fit:
                Alpha_Fit=Fitness
                Alpha_Pos=Positions[i,:]

            if Fitness>Alpha_Fit and Fitness<Beta_Fit:
                Beta_Fit=Fitness
                Beta_Pos=Positions[i,:]
            
            if Fitness>Alpha_Fit and Fitness>Beta_Fit and Fitness<Delta_Fit:
                Delta_Fit=Fitness
                Delta_Pos=Positions[i,:]
        
        a = 2-1*(2/MaxT)
        for i in range (Positions.shape[0]):
            for j in range (Positions.shape[1]):
                r1=np.random.random()
                r2=np.random.random()

                A1 = 2*a*r1-a
                C1 = 2 * r2

                D_Alpha = abs(C1*Alpha_Pos[j]-Positions[i,j])
                X1 = Alpha_Pos[j]-A1*D_Alpha
                
                r1=np.random.random()
                r2=np.random.random()

                A2 = 2*a*r1-a
                C2=2*r2

                D_Beta = abs(C2*Beta_Pos[j]-Positions[i,j])
                X2 = Beta_Pos[j]-A2*D_Beta

                r1 = np.random.random()
                r2 = np.random.random()

                A3 = 2*a*r1-a
                C3 = 2*r2

                D_Delta = abs(C3 * Delta_Pos[j] - Positions[i,j])
                X3 = Delta_Pos[j] - A3 * D_Delta

                Positions[i,j] = (X1 + X2 + X3) / 3
        l += 1
        Convergence_curve[l - 1] = Alpha_Fit
    return Alpha_Fit, Alpha_Pos, Convergence_curve

if __name__ == "__main__":
    def F1(x):
        return np.sum(x ** 2)

    Fun_name = F1
    LB = -100
    UB = 100
    D = 30
    PopSize= 100
    MaxT = 100

    bestfit, bestsol, convergence_curve = GWO(PopSize,MaxT,LB,UB,D,Fun_name)
    print("Best Fitness =", bestfit)
    print("Best Solution = ",bestsol)

# Show the final result in a message box
    root = tk.Tk()
    root.withdraw()
    messagebox.showinfo("GWO Result", f"Best Fitness: {bestfit}\nBest Solution: {bestsol}")




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