e_step.py

      def _e_step(self, X, pi, mu, sigma):
        """Performs E-step on GMM model

        Parameters:
        ------------
        X: (N x d), data points, m: no of features
        pi: (C), weights of mixture components
        mu: (C x d), mixture component means
        sigma: (C x d x d), mixture component covariance matrices

        Returns:
        ----------
        gamma: (N x C), probabilities of clusters for objects
        """
        N = X.shape[0] 
        self.gamma = np.zeros((N, self.C))

        const_c = np.zeros(self.C)
        
        
        self.mu = self.mu if self._initial_means is None else self._initial_means
        self.pi = self.pi if self._initial_pi is None else self._initial_pi
        self.sigma = self.sigma if self._initial_cov is None else self._initial_cov

        for c in range(self.C):
            # Posterior Distribution using Bayes Rule
            self.gamma[:,c] = self.pi[c] * mvn.pdf(X, self.mu[c,:], self.sigma[c])

        # normalize across columns to make a valid probability
        gamma_norm = np.sum(self.gamma, axis=1)[:,np.newaxis]
        self.gamma /= gamma_norm

        return self.gamma