def fit_shape(y):
mean_y = np.mean(y)
if len(y) < 5:
return np.ones(len(y)) * np.mean(y), 0, shape_lib_len, "flat"
# load or build shape series with the same length as y
n = len(y)
if n in shape_cache:
shapes = shape_cache[n]
else:
x = np.linspace(0, 1, n)
shapes = np.empty([shape_lib_len, n])
# iterate the shape library
for i in range(shape_lib_len):
shapeFun = shape_lib[i]
shapes[i] = shapeFun(x)
# store
shape_cache[n] = shapes
# normalize y, pay attention that standard deviation could be very small
std_y = publib.std(y)
if std_y < 1e-10:
std_y = 1
normal_y = (y - mean_y) / std_y
# Linear least square estimation
numerator = np.dot(shapes, normal_y)
# TRICK: we do not calculate norm(shape.^2, 2), save computation time
# denominator = np.sum(shapes * shapes, axis=1)
denominator = np.ones(shape_lib_len) * len(y)
theta = numerator / denominator
# maximum likelihood estimation:
# Calculate the error with standard shapes, The matlab code is below:
# err = sum((MB.shapes.*repmat(theta,1,length(yy))- repmat(yyn,size(MB.shapes,1), 1)).^2,2);
err = np.sum(np.power((shapes.T * theta).T - normal_y, 2), axis=1)
# find the minimum one
likelihood, shape_ind = -1 * err.min(), err.argmin()
# TRICK: flat shape is judged by |\theta|, see the paper
if abs(theta[shape_ind]) < thresh_flat:
shape_ind = shape_lib_len
shape_dir = 'flat'
fit_y = np.zeros(len(y))
likelihood = -1 * np.var(y)
elif theta[shape_ind] < 0:
shape_dir = 'dec'
fit_y = theta[shape_ind] * shapes[shape_ind]
else:
shape_dir = 'inc'
fit_y = theta[shape_ind] * shapes[shape_ind]
fit_y = fit_y * std_y + mean_y
return fit_y, likelihood, shape_ind, shape_dir
def gap_uniform(lenTS, minSize = None, num_round = None):
if minSize is None:
minSize = 2
# See paper: we estimate error of segmentation by taking the mean of 10 uniformly randomly time series
if num_round is None:
num_round = 10
random.seed(time.time())
# estimate error from uniform random time series
mat = np.array([])
for i in range(num_round):
# generate uniform time series in the range of [0,1]
uniformTS = np.array([random.uniform(0,1) for _ in range(lenTS)])
# bottomUp: use initSize=2 and k=1 to iterate every possible number of segments
_, uniformSegCost, _ = bottomup_seg(ts=uniformTS, max_err=sys.float_info.max, k=1, init_size=minSize)
# the testing K must be in [1, len(uniformTS) // 2]
# assert len(uniformSegCost) == (len(uniformTS) // minSize - 1)
if not( len(uniformSegCost) == (len(uniformTS) // minSize - 1)):
print len(uniformSegCost), (len(uniformTS) // minSize - 1)
# the length of uniformSegCost
mat = mat.reshape(i, len(uniformSegCost))
mat = np.vstack([mat, np.array(uniformSegCost)])
pass
# calculate the weighted GAP and get smoothing factor GAP
mat = np.log(mat)
sk = (num_round - 1) * publib.std(mat,axis=0) / num_round * np.sqrt(1 + 1/num_round)
weightGAP = np.mean(mat, axis=0) - sk
# return num_round uniform random experiments
return weightGAP