如何解决手写数字数据集的高斯混合实现和光学识别
尝试使用手写数字数据集的光学识别在 python 中实现高斯混合模型，该数据集包含 10 个大小为 [100x64] 的训练折叠，以及每个大小为 [100x1] 的 10 个训练标签。该数据集还有一个测试数据集和大小为 $\left[110x64\right]$ 和 [110x1] 的标签集。只有两个班级 5 和 6。 我在类条件密度方法上收到以下错误：
ValueError: operands could not be broadcast together with shapes (64,64) (100,64)
鉴于此数据集配置，不知道我是否正确估计了最佳参数。 根据 Bishop（模式识别和机器学习 2006）。我首先必须通过 MLE 估计最佳参数。所以对于每一次折叠，我都在估计最佳参数，但我不知道如何计算后验概率。
我什至不知道我的方法是否正确。我在 GitHub 和 medium 上搜索过类似的例子。任何帮助或指导将不胜感激。
我的代码实现：
#----------------------------------------------------------
# Assigning parameters
#----------------------------------------------------------
#--------------------------------------------------------
# Initial guess
#----------------------------------------------------------
# Total Folds
folds = 10
#Define the number of classes
num_classes = 2
n,m = total_trainf[0].shape
means = np.zeros((num_classes,n))
phi = np.zeros((num_classes,1))
shared_cov_matrix = np.cov(np.transpose(np.concatenate(total_trainf,axis=0)),bias=True)
#posterior_prob_est = pp(w0,w,np.concatenate(total_trainf,axis=1))
c= 1
f= 0
acc_arry = []
# calculate the maximum likelihood of each observation xi
likelihood = []
means_array = np.zeros([num_classes,total_trainf[0].shape[1]])
cond_class_prob = np.zeros([num_classes,1])
# Expectation step
means = np.zeros([folds,total_trainf[0].shape[1]])
while f < folds:
uclasses = np.unique(total_trainl[f])
mu_arr,pi,sigma = get_params(total_trainf[f],total_trainl[f],means_array,phi,uclasses)
#means[f,:] = mu_arr
cov = get_cov(total_trainl[f],shared_cov_matrix,sigma)
class_prob = ccd(total_trainf[f],mu_arr,shared_cov_matrix )
f+=1
means_array[c-1] = np.mean(means,axis=0)
def get_params(data,label,means,class_type):
mean_array = np.zeros([1,data.shape[1]])
num_classes = len(class_type)
sigma = 0
col = 0
for i in range(num_classes):
ind = np.flatnonzero(label == class_type[i])
pi[i] = len(ind)/label.shape[0]
means[i] = np.mean(data[ind],axis = 0)
sigma += np.cov(data[ind].T)*(len(ind) - 1)
sigma = sigma/label.shape[0]
return means,sigma
#Covariance per fold
def get_cov(data,cov,S):
res = np.log(np.linalg.det(cov))+np.trace(np.linalg.inv(cov)*S)
return -(data.shape[0]/2)*res
#Class conditional density
def ccd(data,means: np.array,pi: np.array,cov_matrix: np.array):
inv_cov = np.linalg.inv(cov_matrix)
mu_1 = means[0]
mu_2 = means[1]
pi_1 = pi[0]
pi_2 = pi[1]
W = inv_cov*(mu_1 - mu_2)
ft = -0.5*(mu_1.T*inv_cov*mu_1)
st = 0.5*(mu_2.T*inv_cov*mu_2)
tt = np.log(pi_1/pi_2)
W_0 = ft + st + tt
return pp(W,W_0,data)
#--------------------------------------------------------
# Initial guess
#----------------------------------------------------------
# Total Folds
folds = 10
#Define the number of classes
num_classes = 2
n,n))
#Covariance matrix
cov_matrix = np.cov(np.transpose(np.concatenate(total_trainf,bias=True)
c= 1
f= 0
means_array = np.zeros([num_classes,1])
# Expectation step
while c <= num_classes:
means = np.zeros([folds,total_trainf[0].shape[1]])
while f < folds:
uclasses = np.unique(total_trainl[f])
mu_arr,pi = get_params(total_trainf[f],uclasses[c-1])
means[f,:] = mu_arr
cond_class_prob[c-1] *= ccd(total_trainf[f],cov_matrix)
f+=1
means_array[c-1] = np.mean(means,axis=0)
c += 1
参数函数
def get_params(data,class_type):
accum = 0
accum_array = np.zeros([1,data.shape[1]])
class_index = np.flatnonzero(label == class_type)
phi = len(class_index)/data.shape[0]
row = 0
col = 0
while col < data.shape[1]:
accum_array[0,col] = np.mean(data[col],axis = 0)
col += 1
return accum_array,phi
#Class conditional density
def ccd(data,mean: np.array,cov_matrix: np.array):
cond_prob = 0
for row in range(data.shape[0]):
s1 = 1/np.sqrt(((2*np.pi)**data.shape[1])*np.linalg.det(cov_matrix))
arr_dot_1 = np.dot(data[row,:] - mean,np.linalg.inv(cov_matrix))
arr_dot_2 = np.dot(arr_dot_1,(np.transpose(data[row,:] - mean)))
s2 = np.exp(-0.5*(data[row,:] - mean)*arr_dot_2)
cond_prob *= (s1 * s2[0,0])
return cond_prob
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