Naive Bayes Classification Algorithm

//Pseudocode for Naive Bayes classification algorithm

//Training phase
1. Read the training data set into a matrix X
2. Read the corresponding class labels into a vector Y
3. Calculate the prior probabilities of each class (P(Y=y))
4. For each feature j:
  5. Compute the likelihood probabilities P(Xj=x|Y=y) for each unique value x in feature j and class y
  6. Store the likelihood probabilities in a matrix L

//Classification phase
1. Read the test data set into a matrix X_test
2. For each instance i in X_test:
  3. For each class y:
    4. Initialize the class probability P(Y=y|X_test[i]) to the prior probability P(Y=y)
    5. For each feature j:
      6. Update the class probability P(Y=y|X_test[i]) by multiplying it with the likelihood P(Xj=X_test[i][j]|Y=y)
    7. Normalize the class probabilities for instance i
  8. Assign the class with the highest probability to instance i as the predicted class label

//Utiliity functions
1. computePriorProbabilities(Y): Given a vector Y of class labels, returns a map of prior probabilities P(Y=y) for each unique class y
2. computeLikelihoodProbabilities(X, Y): Given a matrix X of feature values and a vector Y of class labels, returns a matrix L of likelihood probabilities P(Xj=x|Y=y) for each feature j, unique value x, and class y
3. normalizeProbabilities(P): Given a map P of probabilities, normalizes the probabilities so that their sum is 1

//Helper functions
1. computeUniqueValues(X, j): Given a matrix X and a feature index j, returns a vector of unique values in feature j
2. countOccurrences(X, j, value): Given a matrix X, a feature index j, and a value, returns the count of occurrences of the value in feature j of X
3. argmax(P): Given a map P of probabilities, returns the key with the highest value

Example Usage:

//Assuming the functions computePriorProbabilities, computeLikelihoodProbabilities, normalizeProbabilities, computeUniqueValues, countOccurrences and argmax are defined.

#include <iostream>
#include <vector>
#include <map>

//Function to train the Naive Bayes classifier
void trainNaiveBayes(const Matrix& X, const Vector& Y) {
    std::map<int, float> classPriorProbabilities = computePriorProbabilities(Y);
    Matrix likelihoodProbabilities = computeLikelihoodProbabilities(X, Y);
    
    // Do something with classPriorProbabilities and likelihoodProbabilities
}

//Function to classify new instances using the trained Naive Bayes classifier
Vector classifyNaiveBayes(const Matrix& X_test) {
    Vector predictedLabels;
    
    for (int i = 0; i < X_test.size(); i++) {
        std::map<int, float> classProbabilities;
        
        for (auto& classProbability : classPriorProbabilities) {
            float classProbability = classPriorProbabilities[classProbability.first];
            
            for (int j = 0; j < X_test[i].size(); j++) {
                float likelihood = likelihoodProbabilities[j][X_test[i][j]][classProbability.first];
                classProbability *= likelihood;
            }
            
            classProbabilities[classProbability.first] = classProbability;
        }
        
        normalizeProbabilities(classProbabilities);
        
        int predictedLabel = argmax(classProbabilities);
        predictedLabels.push_back(predictedLabel);
    }
    
    return predictedLabels;
}

int main() {
    //Assuming the training data set X and class labels Y are defined
    
    //Training phase
    trainNaiveBayes(X, Y);
    
    //Assuming the test data set X_test is defined
    
    //Classification phase
    Vector predictedLabels = classifyNaiveBayes(X_test);
    
    // Do something with predictedLabels
    
    return 0;
}

In the code example, Matrix and Vector represent a data structure that can hold a matrix (2D array) and a vector (1D array), respectively. The actual implementation of these data structures is omitted for brevity. The functions computePriorProbabilities, computeLikelihoodProbabilities, normalizeProbabilities, computeUniqueValues, countOccurrences, and argmax are assumed to be implemented elsewhere in the code.