def find_closest(x_mat: ndarray, centroids_mat: ndarray):
"""
k均值算法中，对每个样本找到其对应最接近的聚类中心的下标。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:param centroids_mat: 聚类中心
:return: 样本对应聚类中心下标行向量
"""
x_mat = __t.r2m(x_mat)
centroids_mat = __t.r2m(centroids_mat)
k = centroids_mat.shape[0]
m = x_mat.shape[0]
idx = np.empty((m, ), dtype=int)
for i in range(m):
min_j = 0
min_dist = np.sum((x_mat[i, :] - centroids_mat[0, :])**2)
for j in range(1, k):
dist = np.sum((x_mat[i, :] - centroids_mat[j, :])**2)
if dist < min_dist:
min_dist = dist
min_j = j
idx[i] = min_j
return idx
def compute_centroids(x_mat: ndarray, idx_vec: ndarray):
"""
根据之前的聚类中心下标和样本，计算移动后的平均聚类中心值。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:param idx_vec: 聚类中心下标
:return: 新的聚类中心
"""
x_mat = __t.r2m(x_mat)
idx_vec = __t.c2r(idx_vec)
m, n = x_mat.shape
k = np.max(idx_vec) + 1
centroids = np.zeros((k, n))
cen_num = np.zeros((k, ))
for i in range(m):
centroids[idx_vec[i], :] = centroids[idx_vec[i], :] + x_mat[i, :]
cen_num[idx_vec[i]] = cen_num[idx_vec[i]] + 1
for i in range(k):
if cen_num[i] > 0:
centroids[i, :] = centroids[i, :] / cen_num[i]
return centroids
def predict(self, x_mat: ndarray) -> Union[ndarray, int]:
"""
返回预测值，是对应于 x_mat 的标记。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:return: 预测标记
"""
if not self._trained:
raise StateError('not trained yet')
x_mat = _t.r2m(x_mat)
pred = self.__predict(x_mat)
if self.strategy == 'ovr':
return _t.ret(pred)
else:
m = x_mat.shape[0]
result = np.empty((m, ))
for i in range(m):
r = pred[:, i]
result[i] = sorted([(np.sum(r == label), label)
for label in set(r)])[-1][1]
return _t.ret(result)
def map_features(x_mat: ndarray,
*,
degrees: int = 3,
variables: int = 2) -> ndarray:
"""
将 x_mat 中的一次特征映射成多次特征。可以用在线性回归、逻辑回归中。
注意不能包含截距列。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:param degrees: 最大次方数，也就是被选取特征次方之和最大值，取值需要大于等于 2
:param variables: 最大乘项数，即每个乘项最多有多少个特征相乘。这个值不会大于 degree，也不会大于特征数。当它等于 1 时，就只取次方项
:return: 映射完成的特征向量组
"""
x_mat = __t.r2m(x_mat)
m = x_mat.shape[0]
n = x_mat.shape[1]
if variables > degrees:
variables = degrees
if variables > n:
variables = n
out = np.ones((m, 1))
if variables == 1:
out = np.hstack((out, x_mat))
for d in range(2, degrees + 1):
for i in range(n):
out = np.hstack((out, x_mat[:, i:i + 1]**d))
else:
idx = list(range(n))
degree_coms = []
# 次方从 1 到 degree
out = np.hstack((out, x_mat))
for degree in range(2, degrees + 1):
# 从 n 个特征中选出 x1,x2,...,x_variables
for features_idx in list(combinations(idx, variables)):
# 转置是因为在循环中，ndarray 是按行取值的。
features = x_mat[:, features_idx].T
# 获取次方数的组合
degree_com = list(repeat(0, variables))
__degree_combinations(degree, variables, degree_com,
degree_coms)
for degree_c in degree_coms:
val = 1
for f, dc in zip(features, degree_c):
val *= 1 if dc == 0 else f**dc
out = np.hstack((out, val.reshape((val.shape[0], 1))))
degree_coms.clear()
return out
def predict(self, x_mat: ndarray) -> Union[ndarray, int]:
"""
对新的数据进行预测。当 x_mat 中只有一个样本时返回一个数字，否则返回一个行向量。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:return: 预测值或向量
"""
if self._root is None:
raise StateError('not trained yet')
x_mat = _t.r2m(x_mat)
if x_mat.shape[1] != len(self.pvs):
raise DataNotMatchError('feature quantity mismatch')
return self.__predict(self._root, x_mat)
def __match_theta_x(self, x_mat: ndarray) -> ndarray:
"""
检查输入是否和参数匹配。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:return:
"""
if self._theta is None:
raise StateError('not trained yet')
x_mat = _t.r2m(x_mat)
if x_mat.shape[1] != self._theta.shape[0]:
raise DataNotMatchError('feature quantity mismatch')
return x_mat
def train(x_mat: ndarray,
k: int,
*,
max_iters: int = 10,
initial_centroids: Iterable = None,
history: bool = False):
"""
进行k均值训练
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:param k: 聚类数目
:param max_iters: 最大迭代次数
:param initial_centroids: 初始聚类中心，不提供别的话将随机挑选聚类中心
:param history: 是否返回历史信息
:return: 计算好的聚类中心；包含每个样本所属聚类中心下标的行向量；包含每一次迭代计算的聚类中心列表（history为True的话）
"""
x_mat = __t.r2m(x_mat)
m, n = x_mat.shape
if initial_centroids is None:
rand_indices = np.arange(0, m)
np.random.shuffle(rand_indices)
initial_centroids = x_mat[rand_indices[:k], :]
if not isinstance(initial_centroids, ndarray):
initial_centroids = np.asarray(initial_centroids)
idx = None
centroids_history = None
if history:
centroids_history = [initial_centroids]
for i in range(max_iters):
idx = find_closest(x_mat, initial_centroids)
initial_centroids = compute_centroids(x_mat, idx)
if history:
centroids_history.append(initial_centroids)
if history:
return initial_centroids, idx, centroids_history
else:
return initial_centroids, idx
def __evaluation(self, x_mat: ndarray,
eval: Callable[[IProbabilityLearner], ndarray]):
if not self._trained:
raise StateError('not trained yet')
x_mat = _t.r2m(x_mat)
m = x_mat.shape[0]
n = len(self._labels)
evaluation = np.zeros((m, n), dtype=float)
if self.strategy == 'ovr':
for i, learner in enumerate(self._learners.values()):
evaluation[:, i] = eval(learner)
else:
for i, positive in enumerate(self.labels):
for negative in self.labels:
if positive == negative:
continue
evaluation[:, i] = evaluation[:, i] + eval(
self._learners[(positive, negative)])
evaluation[:, i] = evaluation[:, i] / (n - 1)
return evaluation
def predict(self, x_mat: ndarray):
"""
返回预测值，是对应于 x_mat 的标记。
:param x_mat: 特征向量组，行数 m 表示样本数，列数 n 表示特征数
:return: 预测标记
"""
if self._theta is None:
raise StateError('not trained yet')
x_mat = _t.r2m(x_mat)
if x_mat.shape[1] != self._theta.shape[0]:
raise DataNotMatchError('feature quantity mismatch')
if self.kernel == 'linear':
pred = x_mat @ self._theta + self._b
elif self.kernel == 'gauss':
m = x_mat.shape[0]
pred = np.empty((m, ))
for i in range(m):
for j in range(self._x_mat.shape[0]):
pred[i] = pred[i] + self._alphas[
j] * self._y_row[j] * gaussian_kernel(
x_mat[i], self._x_mat[j], self.gamma)
pred[i] = pred[i] + self._b
else:
m = x_mat.shape[0]
pred = np.empty((m, ))
for i in range(m):
for j in range(self._x_mat.shape[0]):
pred[i] = pred[i] + self._alphas[j] * self._y_row[
j] * self.kernel(x_mat[i], self._x_mat[j])
pred[i] = pred[i] + self._b
return _t.ret(
_t.convert_y(self.labels, (pred >= 0).astype(dtype=np.int16),
to=False))
def x_cv(self, value: Optional[ndarray]):
if value is not None:
self._x_cv = _t.r2m(value)
else:
self._x_cv = None