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[Feature] Add membership function options for fuzzy entropy #1051

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[Feature] Add membership function options for fuzzy entropy #1051

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5bca26b
Membership functions for fuzzy entropy
DongCheninmuenster Nov 18, 2024
0ac19ea
[Feature] Membership functions for fuzzy entropy
DongCheninmuenster Nov 18, 2024
5766ce2
Update entropy_fuzzy.py
DongCheninmuenster Nov 18, 2024
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22 changes: 18 additions & 4 deletions neurokit2/complexity/entropy_fuzzy.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,7 +3,7 @@
from .entropy_sample import entropy_sample


def entropy_fuzzy(signal, delay=1, dimension=2, tolerance="sd", approximate=False, **kwargs):
def entropy_fuzzy(signal, delay=1, dimension=2, tolerance="sd", approximate=False, func_name="exp", **kwargs):
"""**Fuzzy Entropy (FuzzyEn)**

Fuzzy entropy (FuzzyEn) of a signal stems from the combination between information theory and
Expand All @@ -24,12 +24,25 @@ def entropy_fuzzy(signal, delay=1, dimension=2, tolerance="sd", approximate=Fals
dimension : int
Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See
:func:`complexity_dimension` to estimate the optimal value for this parameter.
tolerance : float
Tolerance (often denoted as *r*), distance to consider two data points as similar. If
``"sd"`` (default), will be set to :math:`0.2 * SD_{signal}`. See
tolerance : scalar and two-element vector
Tolerance (often denoted as *rn*), refers to a threshold or threshold and power respectively.
distance to consider two data points as similar.See
:func:`complexity_tolerance` to estimate the optimal value for this parameter.
approximate : bool
If ``True``, will compute the fuzzy approximate entropy (FuzzyApEn).
func_name: string
The name of membership functions. Choose in
exp : exponential
gauss : gaussian
cgauss : constgaussian
bell : bell
z : z
trapez : trapezoidal
tri : triangular
sig : sigmoid



**kwargs
Other arguments.

Expand Down Expand Up @@ -78,6 +91,7 @@ def entropy_fuzzy(signal, delay=1, dimension=2, tolerance="sd", approximate=Fals
dimension=dimension,
tolerance=tolerance,
fuzzy=True,
func_name=func_name,
**kwargs,
)
else:
Expand Down
17 changes: 13 additions & 4 deletions neurokit2/complexity/entropy_sample.py
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@
from .utils_entropy import _phi, _phi_divide


def entropy_sample(signal, delay=1, dimension=2, tolerance="sd", **kwargs):
def entropy_sample(signal, delay=1, dimension=2, tolerance="sd", func_name="exp", **kwargs):
"""**Sample Entropy (SampEn)**

Compute the sample entropy (SampEn) of a signal. SampEn is a modification
Expand All @@ -30,6 +30,16 @@ def entropy_sample(signal, delay=1, dimension=2, tolerance="sd", **kwargs):
Tolerance (often denoted as *r*), distance to consider two data points as similar. If
``"sd"`` (default), will be set to :math:`0.2 * SD_{signal}`. See
:func:`complexity_tolerance` to estimate the optimal value for this parameter.
func_name: string
The name of membership functions. Choose in
exp : exponential
gauss : gaussian
cgauss : constgaussian
bell : bell
z : z
trapez : trapezoidal
tri : triangular
sig : sigmoid
**kwargs : optional
Other arguments.

Expand Down Expand Up @@ -64,9 +74,7 @@ def entropy_sample(signal, delay=1, dimension=2, tolerance="sd", **kwargs):
"""
# Sanity checks
if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1:
raise ValueError(
"Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet."
)
raise ValueError("Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet.")

# Store parameters
info = {
Expand All @@ -87,6 +95,7 @@ def entropy_sample(signal, delay=1, dimension=2, tolerance="sd", **kwargs):
dimension=dimension,
tolerance=info["Tolerance"],
approximate=False,
func_name=func_name,
**kwargs
)

Expand Down
175 changes: 78 additions & 97 deletions neurokit2/complexity/optim_complexity_tolerance.py
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Original file line number Diff line number Diff line change
Expand Up @@ -10,9 +10,7 @@
from .utils_entropy import _entropy_apen


def complexity_tolerance(
signal, method="maxApEn", r_range=None, delay=None, dimension=None, show=False
):
def complexity_tolerance(signal, method="maxApEn", r_range=None, delay=None, dimension=None, show=False):
"""**Automated selection of tolerance (r)**

Estimate and select the optimal tolerance (*r*) parameter used by other entropy and other
Expand Down Expand Up @@ -210,97 +208,87 @@ def complexity_tolerance(
54(5), 723-732.

"""
if not isinstance(method, str):
return method, {"Method": "None"}

# Method
method = method.lower()
if method in ["traditional", "sd", "std", "default"]:
r = 0.2 * np.std(signal, ddof=1)
info = {"Method": "20% SD"}

elif method in ["adjusted_sd", "nolds"] and (
isinstance(dimension, (int, float)) or dimension is None
):
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'nolds' method.")
r = (
0.11604738531196232
* np.std(signal, ddof=1)
* (0.5627 * np.log(dimension) + 1.3334)
)
info = {"Method": "Adjusted 20% SD"}

elif method in ["chon", "chon2009"] and (
isinstance(dimension, (int, float)) or dimension is None
):
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'chon2009' method.")
sd1 = np.std(np.diff(signal), ddof=1) # short-term variability
sd2 = np.std(signal, ddof=1) # long-term variability of the signal

# Here are the 3 formulas from Chon (2009):
# For m=2: r =(−0.036 + 0.26 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=3: r =(−0.08 + 0.46 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=4: r =(−0.12 + 0.62 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=5: r =(−0.16 + 0.78 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=6: r =(−0.19 + 0.91 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=7: r =(−0.2 + 1 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
if dimension <= 2 and dimension <= 7:
x = [-0.036, -0.08, -0.12, -0.16, -0.19, -0.2][dimension - 2]
y = [0.26, 0.46, 0.62, 0.78, 0.91, 1][dimension - 2]
else:
# We need to extrapolate the 2 first numbers, x and y
# np.polyfit(np.log([2,3,4, 5, 6, 7]), [-0.036, -0.08, -0.12, -0.16, -0.19, -0.2], 1)
# np.polyfit([2,3,4, 5, 6, 7], [0.26, 0.46, 0.62, 0.78, 0.91, 1], 1)
x = -0.034 * dimension + 0.022
y = 0.14885714 * dimension - 0.00180952

r = (x + y * np.sqrt(sd1 / sd2)) / (len(signal) / 1000) ** 1 / 4
info = {"Method": "Chon (2009)"}

elif method in ["neurokit", "makowski"] and (
isinstance(dimension, (int, float)) or dimension is None
):
# Method described in
# https://github.com/DominiqueMakowski/ComplexityTolerance
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'makowski' method.")
n = len(signal)
r = np.std(signal, ddof=1) * (
0.2811 * (dimension - 1)
+ 0.0049 * np.log(n)
- 0.02 * ((dimension - 1) * np.log(n))
)
if isinstance(method, str):

# Method for str.
method = method.lower()
if method in ["traditional", "sd", "std", "default"]:
r = 0.2 * np.std(signal, ddof=1)
info = {"Method": "20% SD"}

elif method in ["adjusted_sd", "nolds"] and (isinstance(dimension, (int, float)) or dimension is None):
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'nolds' method.")
r = 0.11604738531196232 * np.std(signal, ddof=1) * (0.5627 * np.log(dimension) + 1.3334)
info = {"Method": "Adjusted 20% SD"}

elif method in ["chon", "chon2009"] and (isinstance(dimension, (int, float)) or dimension is None):
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'chon2009' method.")
sd1 = np.std(np.diff(signal), ddof=1) # short-term variability
sd2 = np.std(signal, ddof=1) # long-term variability of the signal

# Here are the 3 formulas from Chon (2009):
# For m=2: r =(−0.036 + 0.26 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=3: r =(−0.08 + 0.46 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=4: r =(−0.12 + 0.62 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=5: r =(−0.16 + 0.78 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=6: r =(−0.19 + 0.91 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
# For m=7: r =(−0.2 + 1 * sqrt(sd1/sd2)) / (len(signal) / 1000)**1/4
if dimension <= 2 and dimension <= 7:
x = [-0.036, -0.08, -0.12, -0.16, -0.19, -0.2][dimension - 2]
y = [0.26, 0.46, 0.62, 0.78, 0.91, 1][dimension - 2]
else:
# We need to extrapolate the 2 first numbers, x and y
# np.polyfit(np.log([2,3,4, 5, 6, 7]), [-0.036, -0.08, -0.12, -0.16, -0.19, -0.2], 1)
# np.polyfit([2,3,4, 5, 6, 7], [0.26, 0.46, 0.62, 0.78, 0.91, 1], 1)
x = -0.034 * dimension + 0.022
y = 0.14885714 * dimension - 0.00180952

r = (x + y * np.sqrt(sd1 / sd2)) / (len(signal) / 1000) ** 1 / 4
info = {"Method": "Chon (2009)"}

elif method in ["neurokit", "makowski"] and (isinstance(dimension, (int, float)) or dimension is None):
# Method described in
# https://github.com/DominiqueMakowski/ComplexityTolerance
if dimension is None:
raise ValueError("'dimension' cannot be empty for the 'makowski' method.")
n = len(signal)
r = np.std(signal, ddof=1) * (
0.2811 * (dimension - 1) + 0.0049 * np.log(n) - 0.02 * ((dimension - 1) * np.log(n))
)

info = {"Method": "Makowski"}
info = {"Method": "Makowski"}

elif method in ["maxapen", "optimize"]:
r, info = _optimize_tolerance_maxapen(
signal, r_range=r_range, delay=delay, dimension=dimension
)
info.update({"Method": "Max ApEn"})
elif method in ["maxapen", "optimize"]:
r, info = _optimize_tolerance_maxapen(signal, r_range=r_range, delay=delay, dimension=dimension)
info.update({"Method": "Max ApEn"})

elif method in ["recurrence", "rqa"]:
r, info = _optimize_tolerance_recurrence(
signal, r_range=r_range, delay=delay, dimension=dimension
)
info.update({"Method": "1% Recurrence Rate"})
elif method in ["recurrence", "rqa"]:
r, info = _optimize_tolerance_recurrence(signal, r_range=r_range, delay=delay, dimension=dimension)
info.update({"Method": "1% Recurrence Rate"})

elif method in ["neighbours", "neighbors", "nn"]:
r, info = _optimize_tolerance_neighbours(
signal, r_range=r_range, delay=delay, dimension=dimension
)
info.update({"Method": "2% Neighbours"})
elif method in ["neighbours", "neighbors", "nn"]:
r, info = _optimize_tolerance_neighbours(signal, r_range=r_range, delay=delay, dimension=dimension)
info.update({"Method": "2% Neighbours"})

elif method in ["bin", "bins", "singh", "singh2016"]:
r, info = _optimize_tolerance_bin(signal, delay=delay, dimension=dimension)
info.update({"Method": "bin"})
elif method in ["bin", "bins", "singh", "singh2016"]:
r, info = _optimize_tolerance_bin(signal, delay=delay, dimension=dimension)
info.update({"Method": "bin"})

else:
raise ValueError("NeuroKit error: complexity_tolerance(): 'method' not recognized.")

elif np.isscalar(method):
r = [method * np.std(signal, ddof=1)]
info = {"fuzzy_entropy"}

elif isinstance(method, (list, np.ndarray)) and len(method) == 2:
r = [method[0] * np.std(signal, ddof=1), method[1]]
info = {"fuzzy_entropy"}

else:
raise ValueError(
"NeuroKit error: complexity_tolerance(): 'method' not recognized."
)
raise ValueError("Invalid type for method")

if show is True:
_optimize_tolerance_plot(r, info, method=method, signal=signal)
Expand All @@ -315,9 +303,7 @@ def complexity_tolerance(
def _optimize_tolerance_recurrence(signal, r_range=None, delay=None, dimension=None):
# Optimize missing parameters
if delay is None or dimension is None:
raise ValueError(
"If method='recurrence', both delay and dimension must be specified."
)
raise ValueError("If method='recurrence', both delay and dimension must be specified.")

# Compute distance matrix
emb = complexity_embedding(signal, delay=delay, dimension=dimension)
Expand All @@ -343,9 +329,7 @@ def _optimize_tolerance_recurrence(signal, r_range=None, delay=None, dimension=N
def _optimize_tolerance_maxapen(signal, r_range=None, delay=None, dimension=None):
# Optimize missing parameters
if delay is None or dimension is None:
raise ValueError(
"If method='maxApEn', both delay and dimension must be specified."
)
raise ValueError("If method='maxApEn', both delay and dimension must be specified.")

if r_range is None:
r_range = 40
Expand Down Expand Up @@ -383,10 +367,7 @@ def _optimize_tolerance_neighbours(signal, r_range=None, delay=None, dimension=N
kdtree = sklearn.neighbors.KDTree(embedded, metric="chebyshev")
counts = np.array(
[
np.mean(
kdtree.query_radius(embedded, r, count_only=True).astype(np.float64)
/ embedded.shape[0]
)
np.mean(kdtree.query_radius(embedded, r, count_only=True).astype(np.float64) / embedded.shape[0])
for r in r_range
]
)
Expand Down
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