def call(self, inputs):
# TODO: implement mahalanobis distance to compare results
inputs = tf.dtypes.cast(inputs, tf.float32)
# import ipdb; ipdb.set_trace()
inputs = K.transpose(K.expand_dims(inputs, 1))
# with norm:
# rho = K.exp(- self.beta * K.pow(tf.norm(inputs - self.mu, ord = 'euclidean', axis = 0),2))
# same as with norm but less comp cost:
if self.dist == "mahalanobis":
if self.same_smooth_fac:
rho = K.exp(-self.beta *
K.sum(K.pow(inputs - self.mu, 2), axis=0))
else:
rho = K.exp(-tf.math.abs(self.beta) *
K.sum(K.pow(inputs - self.mu, 2),
axis=0)) # beta has to be positive
else:
if self.same_smooth_fac:
rho = K.exp(-self.beta *
K.sum(K.pow(inputs - self.mu, 2), axis=0))
else:
rho = K.exp(-tf.math.abs(self.beta) *
K.sum(K.pow(inputs - self.mu, 2),
axis=0)) # beta has to be positive
if self.normalization:
return K.transpose(rho / (K.sum(rho, axis=0) + 10e-6))
else:
return K.transpose(rho)
def _partial_powers(one_hot_encoded_row, Aadj_T, num_powers):
"""
This function computes the first num_powers powers of the adjacency matrix
for the row specified in one_hot_encoded_row
Args:
one_hot_encoded_row: one-hot-encoded row
Aadj_T: the transpose of the adjacency matrix
num_powers (int): the adjacency number of powers to compute
returns:
A matrix of the shape (num_powers, Aadj_T.shape[1]) of
the specified row of the first num_powers of the adjacency matrix.
"""
# make sure the transpose of the adjacency is used
# tensorflow requires that the sparse matrix is the first operand
partial_power = tf.reshape(
tf.sparse.to_dense(one_hot_encoded_row), shape=(1, Aadj_T.shape[1])
)
partial_powers_list = []
for i in range(num_powers):
partial_power = K.transpose(K.dot(Aadj_T, K.transpose(partial_power)))
partial_powers_list.append(partial_power)
return K.squeeze(tf.stack(partial_powers_list, axis=1), axis=0)
def _zoh(self):
M = K.concatenate([K.concatenate([K.transpose(self.AT),
K.transpose(self.B[0])], axis=1),
self.zero_padding], axis=0)
eM = K.tf.linalg.expm(self.dt * M)
return (K.transpose(eM[:self.order, :self.order]),
K.reshape(eM[:self.order, self.order:], self.B.shape))
def calculate_alphas(conv_layer,
binary_weights,
M,
num_epoc=500,
learning_rate=0.01):
'''
calculate alpha based on OLS
'''
flat_conv_layer = BK.reshape(conv_layer,
shape=(np.prod(conv_layer.get_shape()), 1))
flat_binary_weights = BK.reshape(binary_weights, shape=(M, -1))
alphas = BK.random_normal(shape=(M, 1))
flat_approx_layer = BK.dot(BK.transpose(flat_binary_weights), alphas)
loss = []
for _ in range(num_epoc):
flat_approx_layer = BK.dot(BK.transpose(flat_binary_weights), alphas)
curr_loss = BK.mean(BK.square(flat_approx_layer - flat_conv_layer),
axis=0) #tf.reduce_mean, is that correct
loss.append(curr_loss)
grad = BK.dot(
flat_binary_weights,
(flat_approx_layer - flat_conv_layer)) / flat_conv_layer.shape[0]
alphas = alphas - learning_rate * grad
return alphas, loss
def cell_offset_table(scale_size):
# Dynamic implementation of conv dims for fully convolutional model.
# In YOLO the height index is the inner most iteration.
conv_height_index = K.arange(0, stop=scale_size)
conv_width_index = K.arange(0, stop=scale_size)
conv_height_index = K.tile(conv_height_index, [scale_size]) # 늘어놓는 함수 tile -> 같은걸 N번 반복함
# 결과 -> 0~12, 0~12, ...., 0~12
# TODO: Repeat_elements and tf.split doesn't support dynamic splits.
# conv_width_index = K.repeat_elements(conv_width_index, conv_dims[1], axis=0)
conv_width_index = K.tile(
K.expand_dims(conv_width_index, 0), [scale_size, 1]) # tile을 [n, m] 쓰면 dims 2로 만들어줌
# 결과 -> [0~12], [0~12], [0~12], ...
conv_width_index = K.flatten(K.transpose(conv_width_index))
# 결과 -> 0, 0, 0, 0, 0, 0, 0 (13개), 1, 1, 1, 1, 1, 1, 1 (13개), ...
conv_index = K.transpose(K.stack([conv_height_index, conv_width_index]))
# 결과 -> [0, 0], [1, 0], [2, 0], ..., [11, 12], [12, 12]
conv_index = K.reshape(conv_index, [1, scale_size, scale_size, 1, 2])
# 결과 -> 1 * 13 * 13 에 있는 [1 * 2]의 conv index item이 만들어짐
# 각각 [1 * 2]의 값은 [0, 0], [1, 0], [2, 0], ..., [11, 12], [12, 12]
# 이런 식으로 이루어져 있음 -> Mask를 만들기 위한 과정
# 결과 shape -> 1, 13, 13, 1, 2
conv_index = K.cast(conv_index, tf.float32)
diff = (1 / scale_size * 416)
conv_index = conv_index * diff
return conv_index
def pairwise_distances(X, y=None):
'''
Input: x is a Nxd matrix
y is an optional Mxd matirx
Output: dist is a NxM matrix where dist[i,j] is the square norm between x[i,:] and y[j,:]
if y is not given then use 'y=x'.
i.e. dist[i,j] = ||x[i,:]-y[j,:]||^2
y for us is ALWAYS None
'''
###
x = X[..., 0:1]
y = X[..., 1:2]
###
x = K.cast(x, dtype=FLOAT_TYPE)
x_norm = K.reshape(K.sum((x**2), axis=1), shape=(-1, 1))
if y is not None:
y = K.cast(y, dtype=FLOAT_TYPE)
y_t = K.transpose(y)
y_norm = K.reshape(K.sum((y**2), axis=1), shape=(1, -1))
else:
y_t = K.transpose(x)
y_norm = K.reshape(x_norm, shape=(1, -1))
dist = x_norm + y_norm - 2.0 * tf.matmul(x, y_t)
return K.clip(dist, 0.0, float('inf'))
def Kget_dists(X):
"""Keras code to compute the pairwise distance matrix for a set of
vectors specifie by the matrix X.
"""
x2 = K.expand_dims(K.sum(K.square(X), axis=1), 1)
dists = x2 + K.transpose(x2) - 2 * K.dot(X, K.transpose(X))
return dists
def angular_loss_2(y_true, y_pred):
y_pred = K.clip(y_pred, _EPSILON, 1.0 - _EPSILON)
loss = tf.convert_to_tensor(0, dtype=tf.float32)
g = tf.constant(1.0, shape=[1], dtype=tf.float32)
c = tf.constant(4.0, shape=[1], dtype=tf.float32)
d = tf.constant(2.0, shape=[1], dtype=tf.float32)
alpha = tf.constant(45.0, shape=[1], dtype=tf.float32)
losses = []
losses2 = []
for i in range(0, batch_size, 3):
try:
xa = y_pred[i + 0]
xp = y_pred[i + 1]
xn = y_pred[i + 2]
fapn = c * (tf.tan(alpha * K.transpose(xa + xp) * xn)**
2) - d * (g +
tf.tan(alpha)**2) * K.transpose(xa) * xp
losses.append(fapn)
losses2.append(K.transpose(xa) * xn - K.transpose(xa) * xp)
loss = (loss + g + _loss)
except:
continue
loss = K.sum(K.log(1 + 2 * K.sum([K.exp(v) for v in losses])))
loss2 = K.sum(K.log(1 + 2 * K.sum([K.exp(v) for v in losses2])))
loss = loss + 2 * loss2
loss = loss / (batch_size / 3)
zero = tf.constant(0.0, shape=[1], dtype=tf.float32)
return tf.maximum(loss, zero)
def call(self, inputs, **kwargs): # to calculate soft labels we use T-distribution q = 1.0 / (1.0 + (K.sum( K.square(K.expand_dims(inputs, axis=1) - self.clusters), axis=2) / self.alpha)) q **= (self.alpha + 1.0) / 2.0 # with parameter alpha q = K.transpose(K.transpose(q) / K.sum(q, axis=1)) # normalize the probabilities return q # return the resulting soft labels as an output
def call(self, inputs):
if self.trainable_kernel:
output = K.dot(K.dot(inputs, self.kernel), K.transpose(inputs))
else:
output = K.dot(inputs, K.transpose(inputs))
if self.activation is not None:
output = self.activation(output)
return output
def cosine_similarity(self, x, y):
x = K.reshape(x, (K.shape(x)[0], -1))
y = K.reshape(y, (K.shape(y)[0], -1))
abs_x = K.sqrt(K.sum(K.square(x), axis=1, keepdims=True))
abs_y = K.sqrt(K.sum(K.square(y), axis=1, keepdims=True))
up = K.dot(x, K.transpose(y))
down = K.dot(abs_x, K.transpose(abs_y))
return up / down
def call(self, x_input):
X = kb.transpose(x_input)
linWX = kb.dot(self.W, X)
F = self.softabsolute(linWX)
Fsquish = self.l2row(F)
Fhat = self.l2row(kb.transpose(Fsquish))
return Fhat
def call(self, inputs, **kwargs):
'''
t分布により一番近いクラスタを判断する
ベクトル - クラスタ中心がt分布に従うと仮定
'''
q = 1.0 / (1.0 + (K.sum(
K.square(K.expand_dims(inputs, axis=1) - self.clusters), axis=2)))
q = K.transpose(K.transpose(q) / K.sum(q, axis=1))
return q
def tf_sample_gibbs(A, b, beta, N):
"""Naive sampling from p(x) = 1/Z*exp(-beta*(x^T*A*x + b*x)"""
xs = K.constant(list(itertools.product([-1,1], repeat=N))) # 2^N x N tensor
quad = -beta * K.sum(tf.tensordot(xs, A, axes=[[1],[0]]) * xs[:,:,None,None], axis=1)
quad = quad - K.max(quad, axis=[0])[None,:,:] # Put the highest quad logits around 0 to ensure precision when we add biases
logits = quad - beta*tf.tensordot(xs, b, axes=[[1],[0]])
logits = logits - K.max(logits, axis=[0]) # Same, tensorflow doesn't seem to work well with high logits
rows = tf.random.categorical(K.transpose(K.reshape(logits, (2**N,-1))), 1)[:,0]
slices = tf.gather(xs, rows, axis=0)
return K.reshape(K.transpose(slices), K.shape(b))
def spectral_norm(self, w, r=5):
w_shape = K.int_shape(w)
in_dim = np.prod(w_shape[:-1]).astype(int)
out_dim = w_shape[-1]
w = K.reshape(w, (in_dim, out_dim))
u = K.ones((1, in_dim))
for i in range(r):
v = K.l2_normalize(K.dot(u, w))
u = K.l2_normalize(K.dot(v, K.transpose(w)))
return K.sum(K.dot(K.dot(u, w), K.transpose(v)))
def call(self, x):
x = K.dot(self.pca_matrix, (K.transpose(x) - self.pca_means))
x = K.transpose(x)
x = tf.clip_by_value(x, params.QUANTIZE_MIN_VAL,
params.QUANTIZE_MAX_VAL)
x = ((x - params.QUANTIZE_MIN_VAL) *
(255.0 / (params.QUANTIZE_MAX_VAL - params.QUANTIZE_MIN_VAL)))
return K.cast(x, 'uint8')
def yolo_head(feats, anchors, num_classes):
"""Convert final layer features to bounding box parameters.
Parameters
----------
feats : tensor
Final convolutional layer features.
anchors : array-like
Anchor box widths and heights.
num_classes : int
Number of target classes.
Returns
-------
box_xy : tensor
x, y box predictions adjusted by spatial location in conv layer.
box_wh : tensor
w, h box predictions adjusted by anchors and conv spatial resolution.
box_conf : tensor
Probability estimate for whether each box contains any object.
box_class_pred : tensor
Probability distribution estimate for each box over class labels.
"""
num_anchors = len(anchors)
# Reshape to batch, height, width, num_anchors, box_params.
anchors_tensor = K.reshape(K.variable(anchors), [1, 1, 1, num_anchors, 2])
# Dynamic implementation of conv dims for fully convolutional model.
conv_dims = K.shape(feats)[1:3] # assuming channels last
# In YOLO the height index is the inner most iteration.
conv_height_index = K.arange(0, stop=conv_dims[0])
conv_width_index = K.arange(0, stop=conv_dims[1])
conv_height_index = K.tile(conv_height_index, [conv_dims[1]])
conv_width_index = K.tile(K.expand_dims(conv_width_index, 0),
[conv_dims[0], 1])
conv_width_index = K.flatten(K.transpose(conv_width_index))
conv_index = K.transpose(K.stack([conv_height_index, conv_width_index]))
conv_index = K.reshape(conv_index, [1, conv_dims[0], conv_dims[1], 1, 2])
conv_index = K.cast(conv_index, K.dtype(feats))
feats = K.reshape(
feats, [-1, conv_dims[0], conv_dims[1], num_anchors, num_classes + 5])
conv_dims = K.cast(K.reshape(conv_dims, [1, 1, 1, 1, 2]), K.dtype(feats))
box_confidence = K.sigmoid(feats[..., 4:5])
box_xy = K.sigmoid(feats[..., :2])
box_wh = K.exp(feats[..., 2:4])
box_class_probs = K.softmax(feats[..., 5:])
# Adjust preditions to each spatial grid point and anchor size.
# Note: YOLO iterates over height index before width index.
box_xy = (box_xy + conv_index) / conv_dims
box_wh = box_wh * anchors_tensor / conv_dims
return box_confidence, box_xy, box_wh, box_class_probs
def call(self, inputs, **kwargs):
embeddings = inputs[1:1 + (self.cluster_num + 1)]
projections = inputs[1 + (self.cluster_num + 1):]
inputs = inputs[0]
if self.div_val == 1:
if self.embed_dim != self.input_dim or self.force_projection:
projection = self.projections
if projection is None:
projection = projections[0]
inputs = K.dot(inputs, K.transpose(projection))
embedding = self.embeddings
if embedding is None:
embedding = embeddings[0]
out = K.dot(inputs, K.transpose(embedding))
if self.use_bias:
out = K.bias_add(out, self.biases)
out = keras.activations.softmax(out, axis=-1)
else:
cluster_probs = None
outputs = []
for i in range(len(self.cutoffs) - 1):
embed_dim = self.embed_dim // (self.div_val**i)
if embed_dim != self.input_dim or self.force_projection:
projection = self.projections[i]
if projection is None:
projection = projections[i]
cluster_input = K.dot(inputs, K.transpose(projection))
else:
cluster_input = inputs
embedding = self.embeddings[i]
if embedding is None:
embedding = embeddings[i]
cluster_output = K.dot(cluster_input, K.transpose(embedding))
if self.use_bias:
cluster_output = K.bias_add(cluster_output, self.biases[i])
if cluster_probs is None:
cluster_probs = K.dot(cluster_input, self.kernel_cluster)
if self.use_bias:
cluster_probs = K.bias_add(cluster_probs,
self.bias_cluster)
cluster_output = K.concatenate(
[cluster_output, cluster_probs], axis=-1)
cluster_output = keras.activations.softmax(cluster_output,
axis=-1)
cluster_probs = cluster_output[..., -self.cluster_num:]
cluster_output = cluster_output[..., :-self.cluster_num]
else:
cluster_output = keras.activations.softmax(cluster_output,
axis=-1)
cluster_output = cluster_output * K.expand_dims(
cluster_probs[..., i - 1])
outputs.append(cluster_output)
out = K.concatenate(outputs, axis=-1)
return out
def call(self, inputs, mask=None):
# Uses Student t-distribution (same as t-SNE)
# inputs are the variable containing the data, shape=(number_of_samples, number_of_features)
q = 1.0 / (
1.0 +
(K.sum(K.square(K.expand_dims(inputs, axis=1) - self.clusters),
axis=2) / self.alpha))
q **= ((self.alpha + 1.0) / 2.0)
q = K.transpose(K.transpose(q) / K.sum(q, axis=1))
return (q)
def call(self, inputs, **kwargs):
"""
RBF activation function
φ = exp[-β * ||x-μ||^2]
:param inputs:
:param kwargs:
:return:
"""
centers = K.expand_dims(self.centers)
h = K.transpose(centers - K.transpose(inputs))
return K.exp(-self.betas * K.sum(h**2, axis=1))
def sWasserstein(P, Q, theta, nclass, Cp=None, Cq=None):
lambda_ = 10.0
p = K.dot(P, K.transpose(theta))
q = K.dot(Q, K.transpose(theta))
sw = lambda_ * K.mean(oneDWassersteinV3(p, q))
if (Cp is not None) and (Cq is not None):
for i in range(nclass):
pi = tf.gather(p, tf.squeeze(tf.where(tf.not_equal(Cp[:, i], 0))))
qi = tf.gather(q, tf.squeeze(tf.where(tf.not_equal(Cq[:, i], 0))))
sw = sw + 100. * K.mean(oneDWassersteinV3(pi, qi))
return sw
def call(self, input):
for i in range(self.num_layer):
if i == 0:
cross = L.Lambda(lambda x: K.batch_dot(
K.dot(x, K.transpose(self.W[i])), x) + self.bias[i] + x)(
input)
else:
cross = L.Lambda(
lambda x: K.batch_dot(K.dot(x, K.transpose(self.W[i])),
input) + self.bias[i] + x)(cross)
return L.Flatten()(cross)
def call(self, inputs):
v_dim = K.int_shape(inputs)[-1]
if self.idxs == None:
self.idxs = list(range(v_dim))
if self.mode == 'reverse':
self.idxs = self.idxs[::-1]
elif self.mode == 'random':
np.random.shuffle(self.idxs)
inputs = K.transpose(inputs)
outputs = K.gather(inputs, self.idxs)
outputs = K.transpose(outputs)
return outputs
def call(self, inputs, **kwargs):
""" student t-distribution, as same as used in t-SNE algorithm.
q_ij = 1/(1+dist(x_i, u_j)^2), then normalize it.
Arguments:
inputs: the variable containing data, shape=(n_samples, n_features)
Return:
q: student's t-distribution with degree alpha, or soft labels for each sample. shape=(n_samples, n_clusters)
"""
q = 1.0 / (1.0 + (K.sum(K.square(K.expand_dims(inputs, axis=1) - self.clusters), axis=2) / self.alpha))
q **= (self.alpha + 1.0) / 2.0
q = K.transpose(K.transpose(q) / K.sum(q, axis=1))
return q
def call(self, inputs, **kwargs):
"""
Student t-distribution kernel, probability of assigning encoded sequence i to cluster k.
q_{ik} = (1 + dist(z_i, m_k)^2)^{-1} / normalization.
Arguments:
inputs: encoded input sequences, shape=(n_samples, timesteps, n_features)
Return:
q: soft labels for each sample. shape=(n_samples, n_clusters)
"""
if self.dist_metric == 'eucl':
distance = K.sum(K.sqrt(
K.sum(K.square(K.expand_dims(inputs, axis=1) - self.clusters),
axis=2)),
axis=-1)
elif self.dist_metric == 'cid':
ce_x = K.sqrt(
K.sum(K.square(inputs[:, 1:, :] - inputs[:, :-1, :]),
axis=1)) # shape (n_samples, n_features)
ce_w = K.sqrt(
K.sum(K.square(self.clusters[:, 1:, :] -
self.clusters[:, :-1, :]),
axis=1)) # shape (n_clusters, n_features)
ce = K.maximum(K.expand_dims(ce_x, axis=1), ce_w) / K.minimum(
K.expand_dims(ce_x, axis=1),
ce_w) # shape (n_samples, n_clusters, n_features)
ed = K.sqrt(
K.sum(K.square(K.expand_dims(inputs, axis=1) - self.clusters),
axis=2)) # shape (n_samples, n_clusters, n_features)
distance = K.sum(ed * ce, axis=-1) # shape (n_samples, n_clusters)
elif self.dist_metric == 'cor':
inputs_norm = (inputs - K.expand_dims(
K.mean(inputs, axis=1), axis=1)) / K.expand_dims(
K.std(inputs, axis=1),
axis=1) # shape (n_samples, timesteps, n_features)
clusters_norm = (self.clusters - K.expand_dims(
K.mean(self.clusters, axis=1), axis=1)) / K.expand_dims(
K.std(self.clusters, axis=1),
axis=1) # shape (n_clusters, timesteps, n_features)
pcc = K.mean(K.expand_dims(inputs_norm, axis=1) * clusters_norm,
axis=2) # Pearson correlation coefficients
distance = K.sum(
K.sqrt(2.0 * (1.0 - pcc)), axis=-1
) # correlation-based similarities, shape (n_samples, n_clusters)
elif self.dist_metric == 'acf':
raise NotImplementedError
else:
raise ValueError('Available distances are eucl, cid, cor and acf!')
q = 1.0 / (1.0 + K.square(distance) / self.alpha)
q **= (self.alpha + 1.0) / 2.0
q = K.transpose(K.transpose(q) / K.sum(q, axis=1))
return q
def _pairwise_distances(self, inputs: List[Tensor]) -> Tensor:
emb_c, emb_r = inputs
bs = K.shape(emb_c)[0]
embeddings = K.concatenate([emb_c, emb_r], 0)
dot_product = K.dot(embeddings, K.transpose(embeddings))
square_norm = K.batch_dot(embeddings, embeddings, axes=1)
distances = K.transpose(square_norm) - 2.0 * dot_product + square_norm
distances = distances[0:bs, bs:bs+bs]
distances = K.clip(distances, 0.0, None)
mask = K.cast(K.equal(distances, 0.0), K.dtype(distances))
distances = distances + mask * 1e-16
distances = K.sqrt(distances)
distances = distances * (1.0 - mask)
return distances
def mutual_information(tensor_a, tensor_b, bins=256):
channel = tensor_a.shape[-1].value
_a, _ = discretize_with_histogram(K.transpose(tensor_a)[i], bins=bins)
_b, _ = discretize_with_histogram(K.transpose(tensor_b)[i], bins=bins)
ab = K.stack([K.flatten(_a), K.flatten(_b)])
joint_hist = K.cast(joint_histogram(ab, bins=bins), dtype=K.floatx())
joint_proba = joint_hist / K.sum(joint_hist)
joint_proba = K.clip(joint_proba, 1e-7, 1)
a_proba = K.sum(joint_proba, axis=1)
b_proba = K.sum(joint_proba, axis=0)
a_proba = K.expand_dims(a_proba, axis=-1)
mui = K.sum(joint_hist * joint_proba * K.log(joint_proba /
(a_proba * b_proba)))
return mui
def call(self, inputs):
theta_b_output, theta_f_output = super(TrendBlock, self).call(inputs)
t = K.cast(K.arange(-self.fdw, self.fw, 1) / self.fdw, tf.float32)
t = K.transpose(
K.stack([t**i for i in range(self.theta_units)], axis=0))
t_b = t[:self.fdw]
t_f = t[self.fdw:]
backcast = K.dot(theta_b_output, K.transpose(t_b))
forecast = K.dot(theta_f_output, K.transpose(t_f))
return backcast, forecast
def shift(shape, stride, anchors):
"""Produce shifted anchors based on shape of the map and stride size.
Args:
shape (tuple): Shape to shift the anchors over.
stride (int): Stride to shift the anchors with over the shape.
anchors (numpy.array): The anchors to apply at each location.
Returns:
numpy.array: shifted anchors
"""
shift_x = (K.arange(0, shape[1], dtype=K.floatx()) +
K.constant(0.5, dtype=K.floatx())) * stride
shift_y = (K.arange(0, shape[0], dtype=K.floatx()) +
K.constant(0.5, dtype=K.floatx())) * stride
shift_x, shift_y = tf.meshgrid(shift_x, shift_y)
shift_x = K.reshape(shift_x, [-1])
shift_y = K.reshape(shift_y, [-1])
shifts = K.stack([shift_x, shift_y, shift_x, shift_y], axis=0)
shifts = K.transpose(shifts)
number_of_anchors = K.shape(anchors)[0]
k = K.shape(shifts)[0] # number of base points = feat_h * feat_w
shifts = K.cast(K.reshape(shifts, [k, 1, 4]), K.floatx())
shifted_anchors = K.reshape(anchors, [1, number_of_anchors, 4]) + shifts
shifted_anchors = K.reshape(shifted_anchors, [k * number_of_anchors, 4])
return shifted_anchors
def gramMatrix(x):
if K.image_data_format() == "channels_first":
features = K.flatten(x)
else:
features = K.batch_flatten(K.permute_dimensions(x, (2, 0, 1)))
gram = K.dot(features, K.transpose(features))
return gram
