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quant.py
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quant.py
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# Angus Dempster, Daniel F Schmidt, Geoffrey I Webb
# QUANT: A Minimalist Interval Method for Time Series Classification
# https://arxiv.org/abs/2308.00928
import numpy as np
import torch, torch.nn.functional as F
# == generate intervals ========================================================
def make_intervals(input_length, depth):
exponent = \
min(
depth,
int(np.log2(input_length)) + 1
)
intervals = []
for n in 2 ** torch.arange(exponent):
indices = torch.linspace(0, input_length, n + 1).long()
intervals_n = torch.stack((indices[:-1], indices[1:]), 1)
intervals.append(intervals_n)
if n > 1 and intervals_n.diff().median() > 1:
shift = int(np.ceil(input_length / n / 2))
intervals.append((intervals_n[:-1] + shift))
return torch.cat(intervals)
# == quantile function =========================================================
def f_quantile(X, div = 4):
n = X.shape[-1]
if n == 1:
return X
else:
num_quantiles = 1 + (n - 1) // div
if num_quantiles == 1:
return X.quantile(torch.tensor([0.5]), dim = -1).permute(1, 2, 0)
else:
quantiles = X.quantile(torch.linspace(0, 1, num_quantiles), dim = -1).permute(1, 2, 0)
quantiles[..., 1::2] = quantiles[..., 1::2] - X.mean(-1, keepdims = True)
return quantiles
# == interval model (per representation) =======================================
class IntervalModel():
def __init__(self, input_length, depth = 6, div = 4):
assert div >= 1
assert depth >= 1
self.div = div
self.intervals = \
make_intervals(
input_length = input_length,
depth = depth,
)
def fit(self, X, Y):
pass
def transform(self, X):
features = []
for a, b in self.intervals:
features.append(
f_quantile(X[..., a:b], div = self.div).squeeze(1)
)
return torch.cat(features, -1)
def fit_transform(self, X, Y):
self.fit(X, Y)
return self.transform(X)
# == quant =====================================================================
class Quant():
def __init__(self, depth = 6, div = 4):
assert depth >= 1
assert div >= 1
self.depth = depth
self.div = div
self.representation_functions = \
(
lambda X : X,
lambda X : F.avg_pool1d(F.pad(X.diff(), (2, 2), "replicate"), 5, 1),
lambda X : X.diff(n = 2),
lambda X : torch.fft.rfft(X).abs(),
)
self.models = {}
self.fitted = False
def transform(self, X):
assert self.fitted, "not fitted"
features = []
for index, function in enumerate(self.representation_functions):
Z = function(X)
features.append(
self.models[index].transform(Z)
)
return torch.cat(features, -1)
def fit_transform(self, X, Y):
features = []
for index, function in enumerate(self.representation_functions):
Z = function(X)
self.models[index] = \
IntervalModel(
input_length = Z.shape[-1],
depth = self.depth,
div = self.div
)
features.append(
self.models[index].fit_transform(Z, Y)
)
self.fitted = True
return torch.cat(features, -1)