Generate new components in data

[wangjiusi]

Hi, I am bothering you again.

I have encountered some difficulties in understanding the initialization of new categories based on the selected data set (Kmeans++).
More specifically, the code in DiagGaussObsModel.py

` def calcSmoothedMu(self, X, W=None):
''' Compute smoothed estimate of mean of statistic xxT.

    Args
    ----
    X : 2D array, size N x D

    Returns
    -------
    Mu_1 : 2D array, size D
        Expected value of Var[ X[n,d] ]
    Mu_2 : 1D array, size D
        Expected value of Mean[ X[n] ]
    '''
    if X is None:
        Mu1 = self.Prior.beta / self.Prior.nu
        Mu2 = self.Prior.m
        return Mu1, Mu2

    if X.ndim == 1:
        X = X[np.newaxis,:]
    N, D = X.shape
    # Compute suff stats
    if W is None:
        sum_wxx = np.sum(np.square(X), axis=0)
        sum_wx = np.sum(X, axis=0)
        sum_w = X.shape[0]
    else:
        W = as1D(W)
        sum_wxx = np.dot(W, np.square(X))
        sum_wx = np.dot(W, X)
        sum_w = np.sum(W)

    post_kappa = self.Prior.kappa + sum_w
    post_m = (self.Prior.m * self.Prior.kappa + sum_wx) / post_kappa
    Mu_2 = post_m

    prior_kmm = self.Prior.kappa * (self.Prior.m * self.Prior.m)
    post_kmm = post_kappa * (post_m * post_m)
    post_beta = sum_wxx + self.Prior.beta + prior_kmm - post_kmm
    Mu_1 = post_beta / (self.Prior.nu + sum_w)

    assert Mu_1.ndim == 1
    assert Mu_1.shape == (D,)
    assert Mu_2.shape == (D,)
    return Mu_1, Mu_2`

I know that it is calculating the center of the initial category, but I can't understand the rules of this calculation. Can you give me some advice?

Similarly, the code in ZeroMeanGaussObsModel.py

` def calcSmoothedMu(self, X, W=None):
Compute smoothed estimate of mean of statistic xxT.

    Args
    ----
    X : 2D array, size N x D

    Returns
    -------
    Mu : 2D array, size D x D
    '''
    Prior_nu = self.Prior.nu - self.D - 1
    # Prior_nu = self.Prior.nu

    if X is None:
        Mu = self.Prior.B / (Prior_nu)
        return Mu
    if X.ndim == 1:
        X = X[np.newaxis,:]
    N, D = X.shape
    # Compute suff stats
    if W is None:
        sum_wxxT = np.dot(X.T, X)
        sum_w = X.shape[0]
    else:
        W = as1D(W)
        wX = np.sqrt(W)[:,np.newaxis] * X
        sum_wxxT = np.dot(wX.T, wX)
        sum_w = np.sum(W)
    Mu = (self.Prior.B + sum_wxxT) / (Prior_nu + sum_w)
    assert Mu.ndim == 2
    assert Mu.shape == (D, D,)
    return Mu`