pyACA.ToolGmm Namespace Reference

Classes
class	CGmmState

Functions
	ToolGmm (V, K, numMaxIter=1000, prevState=None)
	helper function: gaussian mixture model
	updateGaussians_I (V, p, state)
	computeProb_I (V, state)
	initState_I (V, K)

Function Documentation

computeProb_I()

computeProb_I	(		V,
			state )

Definition at line 72 of file ToolGmm.py.

def computeProb_I(V, state):
 
    K = state.mu.shape[1]
    p = np.zeros([V.shape[1], K])
    
    # for each cluster
    for k in range(K):
        # subtract mean
        Vm = V - state.mu[:, [k]]
 
        # weighted gaussian
        p[:, k] = 1 / np.sqrt((2*np.pi)**Vm.shape[0] * np.linalg.det(state.sigma[k, :, :])) * np.exp(-.5 * np.sum(np.multiply(Vm, np.matmul(np.linalg.inv(state.sigma[k, :, :]), Vm)), axis=0).T)
        p[:, k] = state.prior[k] * p[:, k]
 
    # norm over clusters
    p = p / np.tile(np.sum(p, axis=1, keepdims=True), (1, K))
 
    return p
 
 

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initState_I()

initState_I	(		V,
			K )

Definition at line 92 of file ToolGmm.py.

def initState_I(V, K):
 
    prior = np.ones(K) / K
 
    # pick random points as cluster means
    mIdx = np.round(np.random.rand(K) * (V.shape[1]-1)).astype(int)
 
    # assign means etc.
    mu = V[:, mIdx]
    s = np.cov(V)
    sigma = np.zeros([K, V.shape[0], V.shape[0]])
    for k in range(K):
        sigma[k, :, :] = s
 
    # write initial state
    state = CGmmState(mu, sigma, prior)
 
    return state

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ToolGmm()

ToolGmm	(		V,
			K,
			numMaxIter = 1000,
			prevState = None )

helper function: gaussian mixture model

Parameters

V	features for all train observations (dimension iNumFeatures x iNumObservations)
K	number of gaussians
numMaxIter	maximum number of iterations (stop if not converged before, default: 1000)
prevState	internal state that can be stored to continue clustering later

Returns

mu: means (iNumFeatures x K)

sigma: standard deviations (K x iNumFeatures X iNumFeatures)

state: result containing internal state (if needed)

Definition at line 23 of file ToolGmm.py.

def ToolGmm(V, K, numMaxIter=1000, prevState=None):
 
    # init
    if prevState is None:
        state = initState_I(V, K)
    else:
        state = CGmmState(prevState.mu.copy(), prevState.sigma.copy(), prevState.prior.copy())
 
    for j in range(numMaxIter):
        prevState = CGmmState(state.mu.copy(), state.sigma.copy(), state.prior.copy())
 
        # compute weighted gaussian
        p = computeProb_I(V, state)
 
        # update clusters
        state = updateGaussians_I(V, p, state)
   
        # if converged, break
        if np.max(np.sum(np.abs(state.mu-prevState.mu))) <= 1e-20:
            break
 
    return state.mu, state.sigma, state
 
 

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updateGaussians_I()

updateGaussians_I	(		V,
			p,
			state )

Definition at line 47 of file ToolGmm.py.

def updateGaussians_I(V, p, state):
 
    # number of clusters
    K = state.mu.shape[1]
 
    # update priors
    state.prior = np.mean(p, axis=0)
 
    for k in range(K):
        s = 0
 
        # update means
        state.mu[:, k] = np.matmul(V, p[:, k]) / np.sum(p[:, k])
        
        # subtract mean
        Vm = V - state.mu[:, [k]]
        
        for n in range(V.shape[1]):
            s = s + p[n, k] * np.matmul(Vm[:, [n]], Vm[:, [n]].T)
 
        state.sigma[k, :, :] = s / np.sum(p[:, k])
    
    return state
 
 

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