"""
A module of classification schemes for choropleth mapping.
"""
import copy
import functools
import warnings
import numpy as np
import scipy.stats as stats
from sklearn.cluster import KMeans
__author__ = "Sergio J. Rey"
__all__ = [
"MapClassifier",
"quantile",
"BoxPlot",
"EqualInterval",
"FisherJenks",
"FisherJenksSampled",
"JenksCaspall",
"JenksCaspallForced",
"JenksCaspallSampled",
"HeadTailBreaks",
"MaxP",
"MaximumBreaks",
"NaturalBreaks",
"Quantiles",
"Percentiles",
"PrettyBreaks",
"StdMean",
"UserDefined",
"gadf",
"KClassifiers",
"CLASSIFIERS",
]
CLASSIFIERS = (
"BoxPlot",
"EqualInterval",
"FisherJenks",
"FisherJenksSampled",
"HeadTailBreaks",
"JenksCaspall",
"JenksCaspallForced",
"JenksCaspallSampled",
"MaxP",
"MaximumBreaks",
"NaturalBreaks",
"Quantiles",
"Percentiles",
"PrettyBreaks",
"StdMean",
"UserDefined",
)
K = 5 # default number of classes in any map scheme with this as an argument
SEEDRANGE = 1000000 # range for drawing random ints from for Natural Breaks
FMT = "{:.2f}"
try:
from numba import njit
HAS_NUMBA = True
except ImportError:
HAS_NUMBA = False
def njit(_type): # noqa ARG001
def decorator_njit(func):
@functools.wraps(func)
def wrapper_decorator(*args, **kwargs):
return func(*args, **kwargs)
return wrapper_decorator
return decorator_njit
def _format_intervals(mc, fmt="{:.0f}"):
"""
Helper methods to format legend intervals.
Parameters
----------
mc: MapClassifier
fmt: str (default '{:.0f}')
Specification of formatting for legend.
Returns
-------
tuple:
edges : list
:math:`k` strings for class intervals.
max_width : int
Length of largest interval string.
lower_open : bool
True: lower bound of first interval is open.
False: lower bound of first interval is closed.
Notes
-----
For some classifiers, it is possible that the upper bound of the first
interval is less than the minimum value of the attribute that is being
classified. In these cases ``lower_open=True`` and the lower bound of the
interval is set to ``numpy.NINF``.
"""
lowest = mc.y.min()
if hasattr(mc, "lowest") and mc.lowest is not None:
lowest = mc.lowest
lower_open = False
if lowest > mc.bins[0]:
lowest = -np.inf
lower_open = True
edges = [lowest]
edges.extend(mc.bins)
edges = [fmt.format(edge) for edge in edges]
max_width = max([len(edge) for edge in edges])
return edges, max_width, lower_open
def _get_mpl_labels(mc, fmt="{:.1f}"):
"""
Helper method to format legend intervals for matplotlib (and geopandas).
Parameters
----------
mc : MapClassifier
fmt : str (default '{:.1f}')
Specification of formatting for legend.
Returns
-------
intervals : list
:math:`k` strings for class intervals.
"""
edges, max_width, lower_open = _format_intervals(mc, fmt)
k = len(edges) - 1
left = ["["]
if lower_open:
left = ["("]
left.extend("(" * k)
right = "]" * (k + 1)
lower = ["{:>{width}}".format(edges[i], width=max_width) for i in range(k)]
upper = ["{:>{width}}".format(edges[i], width=max_width) for i in range(1, k + 1)]
lower = [_l + r for _l, r in zip(left, lower)]
upper = [_l + r for _l, r in zip(upper, right)]
intervals = [_l + ", " + r for _l, r in zip(lower, upper)]
return intervals
def _get_table(mc, fmt="{:.2f}"):
"""
Helper function to generate tabular classification report.
Parameters
----------
mc: MapClassifier
fmt: str (default '{:.2f}')
specification of formatting for legend.
Returns
-------
table : str
Formatted table of classification results.
"""
intervals = _get_mpl_labels(mc, fmt)
interval_width = len(intervals[0])
counts = list(map(str, mc.counts))
count_width = max([len(count) for count in counts])
count_width = max(count_width, len("count"))
interval_width = max(interval_width, len("interval"))
header = f"{'Interval' : ^{interval_width}}"
header += " " * 3 + f"{'Count' : >{count_width}}"
title = mc.name
header += "\n" + "-" * len(header)
table = [title, "", header]
for i, interval in enumerate(intervals):
row = f"{interval} | {counts[i] : >{count_width}}"
table.append(row)
return "\n".join(table)
def head_tail_breaks(values, cuts):
"""Head tail breaks helper function."""
values = np.array(values)
mean = np.mean(values)
if len(cuts) > 0 and cuts[-1] == mean: # this fixes floating point from GH#117
return cuts
cuts.append(mean)
if len(set(values)) > 1:
return head_tail_breaks(values[values > mean], cuts)
return cuts
def quantile(y, k=4):
"""
Calculates the quantiles for an array.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 4)
Number of quantiles.
Returns
-------
q : numpy.array
:math:`(n,1)`, quantile values.
Notes
-----
If there are enough ties that the quantile values repeat, we collapse to
pseudo quantiles in which case the number of classes will be less than ``k``.
Examples
--------
>>> import mapclassify
>>> import numpy
>>> x = numpy.arange(1000)
>>> mapclassify.classifiers.quantile(x)
array([249.75, 499.5 , 749.25, 999. ])
>>> mapclassify.classifiers.quantile(x, k=3)
array([333., 666., 999.])
"""
w = 100.0 / k
p = np.arange(w, 100 + w, w)
if p[-1] > 100.0:
p[-1] = 100.0
q = np.array([stats.scoreatpercentile(y, pct) for pct in p])
q = np.unique(q)
k_q = len(q)
if k_q < k:
warnings.warn(
f"Not enough unique values in array to form {k} classes. "
f"Setting k to {k_q}.",
UserWarning,
stacklevel=2,
)
return q
def binC(y, bins): # noqa N802
"""
Bin categorical/qualitative data.
Parameters
----------
y : numpy.array
:math:`(n,q)`, categorical values.
bins : numpy.array
:math:`(k,1)`, unique values associated with each bin.
Return
------
b : numpy.array
:math:`(n,q)` bin membership, values between ``0`` and ``k-1``.
Examples
--------
>>> import numpy
>>> import mapclassify
>>> numpy.random.seed(1)
>>> x = numpy.random.randint(2, 8, (10, 3))
>>> bins = list(range(2, 8))
>>> x
array([[7, 5, 6],
[2, 3, 5],
[7, 2, 2],
[3, 6, 7],
[6, 3, 4],
[6, 7, 4],
[6, 5, 6],
[4, 6, 7],
[4, 6, 3],
[3, 2, 7]])
>>> y = mapclassify.classifiers.binC(x, bins)
>>> y
array([[5, 3, 4],
[0, 1, 3],
[5, 0, 0],
[1, 4, 5],
[4, 1, 2],
[4, 5, 2],
[4, 3, 4],
[2, 4, 5],
[2, 4, 1],
[1, 0, 5]])
"""
# TODO: consider renaming ``binC`` to ``bin_c`` to resolve N802 (gh#185)
if np.ndim(y) == 1:
k = 1
n = np.shape(y)[0]
else:
n, k = np.shape(y)
b = np.zeros((n, k), dtype="int")
for i, _bin in enumerate(bins):
b[np.nonzero(y == _bin)] = i
# check for non-binned items and warn if needed
vals = set(y.flatten())
for val in vals:
if val not in bins:
warnings.warn(
f"\nValue not in bin: {val}\nBins: {bins}", UserWarning, stacklevel=2
)
return b
def bin(y, bins): # noqa A001
"""
Bin interval/ratio data.
Parameters
----------
y : numpy.array
:math:`(n,q)`, values to bin.
bins : numpy.array
:math:`(k,1)`, upper bounds of each bin (monotonic).
Returns
-------
b : numpy.array
:math:`(n,q)`, values of values between ``0`` and ``k-1``.
Examples
--------
>>> import numpy
>>> import mapclassify
>>> numpy.random.seed(1)
>>> x = numpy.random.randint(2, 20, (10, 3))
>>> bins = [10, 15, 20]
>>> b = mapclassify.classifiers.bin(x, bins)
>>> x
array([[ 7, 13, 14],
[10, 11, 13],
[ 7, 17, 2],
[18, 3, 14],
[ 9, 15, 8],
[ 7, 13, 12],
[16, 6, 11],
[19, 2, 15],
[11, 11, 9],
[ 3, 2, 19]])
>>> b
array([[0, 1, 1],
[0, 1, 1],
[0, 2, 0],
[2, 0, 1],
[0, 1, 0],
[0, 1, 1],
[2, 0, 1],
[2, 0, 1],
[1, 1, 0],
[0, 0, 2]])
"""
# TODO: consider renaming ``bin`` to ``bin_int`` to resolve A001 (gh#185)
if np.ndim(y) == 1:
k = 1
n = np.shape(y)[0]
else:
n, k = np.shape(y)
b = np.zeros((n, k), dtype="int")
i = len(bins)
if not isinstance(bins, list):
bins = bins.tolist()
binsc = copy.copy(bins)
while binsc:
i -= 1
c = binsc.pop(-1)
b[np.nonzero(y <= c)] = i
return b
def bin1d(x, bins):
"""
Place values of a 1-d array into bins and determine
counts of values in each bin.
Parameters
----------
x : numpy.array
:math:`(n, 1)`, values to bin.
bins : numpy.array
:math:`(k,1)`, upper bounds of each bin (monotonic).
Returns
-------
binIds : numpy.array
1-d array of integer bin IDs.
counts : int
Number of elements of ``x`` falling in each bin.
Examples
--------
>>> import numpy
>>> import mapclassify
>>> x = numpy.arange(100, dtype = "float")
>>> bins = [25, 74, 100]
>>> binIds, counts = mapclassify.classifiers.bin1d(x, bins)
>>> binIds
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])
>>> counts.tolist()
[26, 49, 25]
"""
left = [-float("inf")]
left.extend(bins[0:-1])
right = bins
cuts = list(zip(left, right))
k = len(bins)
binIds = np.zeros(x.shape, dtype="int")
while cuts:
k -= 1
_l, r = cuts.pop(-1)
binIds += (x > _l) * (x <= r) * k
counts = np.bincount(binIds, minlength=len(bins))
return (binIds, counts)
def _pretty_number(x, rounded=True):
exp = np.floor(np.log10(x))
f = x / 10**exp
if rounded:
if f < 1.5:
nf = 1.0
elif f < 3.0:
nf = 2.0
elif f < 7.0:
nf = 5.0
else:
nf = 10.0
else:
if f <= 1.0:
nf = 1.0
elif f <= 2.0:
nf = 2.0
elif f <= 5.0:
nf = 5.0
else:
nf = 10.0
return nf * 10.0**exp
def _pretty(y, k=5):
low = y.min()
high = y.max()
rg = _pretty_number(high - low, False)
d = _pretty_number(rg / (k - 1), True)
miny = np.floor(low / d) * d
maxy = np.ceil(high / d) * d
return np.arange(miny, maxy + 0.5 * d, d)
def load_example():
"""
Helper function for doc tests
"""
from .datasets import calemp
return calemp.load()
def _kmeans(y, k=5, n_init=10):
"""
Helper function to do k-means in one dimension.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int, (default 5)
Number of classes to form.
n_init : int, (default 10)
Number of initial solutions. Best of initial results is returned.
"""
y = y * 1.0 # sklearn.cluster.KMeans needs float or double dtype
y.shape = (-1, 1)
result = KMeans(n_clusters=k, init="k-means++", n_init=n_init).fit(y)
class_ids = result.labels_
centroids = result.cluster_centers_
binning = []
for c in range(k):
values = y[class_ids == c]
binning.append([values.max(), len(values)])
binning = np.array(binning)
binning = binning[binning[:, 0].argsort()]
cuts = binning[:, 0]
y_cent = np.zeros_like(y)
for c in range(k):
y_cent[class_ids == c] = centroids[c]
diffs = y - y_cent
diffs *= diffs
return class_ids, cuts, diffs.sum(), centroids
def natural_breaks(values, k=5, init=10):
"""
Natural breaks helper function. Jenks natural breaks is k-means in one dimension.
Parameters
----------
values : numpy.array
:math:`(n, 1)` values to bin.
k : int, (default 5)
Number of classes.
init: int, (default 10)
Number of different solutions to obtain using different centroids.
Best solution is returned.
"""
values = np.array(values)
uv = np.unique(values)
uvk = len(uv)
if uvk < k:
warnings.warn(
f"Not enough unique values in array to form {k} classes. "
f"Setting k to {uvk}.",
UserWarning,
stacklevel=2,
)
k = uvk
kres = _kmeans(values, k, n_init=init)
sids = kres[-1] # centroids
fit = kres[-2]
class_ids = kres[0]
cuts = kres[1]
return (sids, class_ids, fit, cuts)
@njit("f8[:](f8[:], u2)")
def _fisher_jenks_means(values, classes=5):
"""
Jenks Optimal (Natural Breaks) algorithm implemented in Python.
Notes
-----
The original Python code comes from here:
http://danieljlewis.org/2010/06/07/jenks-natural-breaks-algorithm-in-python/
and is based on a JAVA and Fortran code available here:
https://stat.ethz.ch/pipermail/r-sig-geo/2006-March/000811.html
Returns class breaks such that classes are internally homogeneous while
assuring heterogeneity among classes.
"""
n_data = len(values)
mat1 = np.zeros((n_data + 1, classes + 1), dtype=np.int32)
mat2 = np.zeros((n_data + 1, classes + 1), dtype=np.float32)
mat1[1, 1:] = 1
mat2[2:, 1:] = np.inf
v = np.float32(0)
for _l in range(2, len(values) + 1):
s1 = np.float32(0)
s2 = np.float32(0)
w = np.float32(0)
for m in range(1, _l + 1):
i3 = _l - m + 1
val = np.float32(values[i3 - 1])
s2 += val * val
s1 += val
w += np.float32(1)
v = s2 - (s1 * s1) / w
i4 = i3 - 1
if i4 != 0:
for j in range(2, classes + 1):
if mat2[_l, j] >= (v + mat2[i4, j - 1]):
mat1[_l, j] = i3
mat2[_l, j] = v + mat2[i4, j - 1]
mat1[_l, 1] = 1
mat2[_l, 1] = v
k = len(values)
kclass = np.zeros(classes + 1, dtype=values.dtype)
kclass[classes] = values[len(values) - 1]
kclass[0] = values[0]
for countNum in range(classes, 1, -1):
pivot = mat1[k, countNum]
_id = int(pivot - 2)
kclass[countNum - 1] = values[_id]
k = int(pivot - 1)
return np.delete(kclass, 0)
class MapClassifier:
r"""
Abstract class for all map classifications :cite:`Slocum_2009`
For an array :math:`y` of :math:`n` values, a map classifier places each
value :math:`y_i` into one of :math:`k` mutually exclusive and exhaustive
classes. Each classifer defines the classes based on different criteria,
but in all cases the following hold for the classifiers in PySAL:
.. math:: C_j^l < y_i \le C_j^u \ \forall i \in C_j
where :math:`C_j` denotes class :math:`j` which has lower bound
:math:`C_j^l` and upper bound :math:`C_j^u`.
Map Classifiers Supported
* :class:`mapclassify.classifiers.BoxPlot`
* :class:`mapclassify.classifiers.EqualInterval`
* :class:`mapclassify.classifiers.FisherJenks`
* :class:`mapclassify.classifiers.FisherJenksSampled`
* :class:`mapclassify.classifiers.HeadTailBreaks`
* :class:`mapclassify.classifiers.JenksCaspall`
* :class:`mapclassify.classifiers.JenksCaspallForced`
* :class:`mapclassify.classifiers.JenksCaspallSampled`
* :class:`mapclassify.classifiers.MaxP`
* :class:`mapclassify.classifiers.MaximumBreaks`
* :class:`mapclassify.classifiers.NaturalBreaks`
* :class:`mapclassify.classifiers.Quantiles`
* :class:`mapclassify.classifiers.Percentiles`
* :class:`mapclassify.classifiers.StdMean`
* :class:`mapclassify.classifiers.UserDefined`
In addition to the classifiers, there are several utility functions that
can be used to evaluate the properties of a specific classifier,
or for automatic selection of a classifier and number of classes.
* :func:`mapclassify.classifiers.gadf`
* :class:`mapclassify.classifiers.K_classifiers`
"""
def __init__(self, y):
y = np.asarray(y).flatten()
self.name = "Map Classifier"
self.fmt = FMT
self.y = y
self._classify()
self._summary()
def get_fmt(self):
return self._fmt
def set_fmt(self, fmt):
self._fmt = fmt
fmt = property(get_fmt, set_fmt)
def _summary(self):
yb = self.yb
self.classes = [np.nonzero(yb == c)[0].tolist() for c in range(self.k)]
self.tss = self.get_tss()
self.adcm = self.get_adcm()
self.gadf = self.get_gadf()
def _classify(self):
self._set_bins()
self.yb, self.counts = bin1d(self.y, self.bins)
def _update(self, data, *args, **kwargs):
"""
The only thing that *should* happen in this function is
1. input sanitization for pandas
2. classification/reclassification.
Using their ``__init__`` methods, all classifiers can re-classify given
different input parameters or additional data.
If you've got a cleverer updating equation other than the intial estimation
equation, remove the call to ``self.__init__`` below and replace it with
the updating function.
"""
if data is not None:
data = np.asarray(data).flatten()
data = np.append(data.flatten(), self.y)
else:
data = self.y
self.__init__(data, *args, **kwargs)
@classmethod
def make(cls, *args, **kwargs):
"""
Configure and create a classifier that will consume data and produce
classifications, given the configuration options specified by this
function.
Note that this implements a *partial application* of the relevant class
constructor. ``make`` creates a function that returns classifications; it
does not actually do the classification.
If you want to classify data directly, use the appropriate class
constructor, like ``Quantiles``, ``Max_Breaks``, etc.
If you *have* a classifier object, but want to find which bins new data
falls into, use ``find_bin``.
Parameters
----------
*args : required positional arguments
All positional arguments required by the classifier,
**excluding** the input data.
rolling : bool
A boolean configuring the outputted classifier to use
a rolling classifier rather than a new classifier for
each input. If ``rolling``, this adds the current data to
all of the previous data in the classifier, and
rebalances the bins, like a running median computation.
return_object : bool
Return the classifier object (or not).
return_bins : bool
Return the bins/breaks (or not).
return_counts : bool
Return the histogram of objects falling into each bin (or not).
Returns
-------
A function that consumes data and returns their bins (and object,
bins/breaks, or counts, if requested).
Notes
-----
This is most useful when you want to run a classifier many times
with a given configuration, such as when classifying many columns of an
array or dataframe using the same configuration.
Examples
--------
>>> import libpysal
>>> import mapclassify
>>> import geopandas
>>> import numpy
>>> import pandas
>>> df = geopandas.read_file(libpysal.examples.get_path("columbus.dbf"))
>>> classifier = mapclassify.Quantiles.make(k=9)
>>> cl = df[["HOVAL", "CRIME", "INC"]].apply(classifier)
>>> cl["HOVAL"].values[:10]
array([8, 7, 2, 4, 1, 3, 8, 5, 7, 8])
>>> cl["CRIME"].values[:10]
array([0, 1, 3, 4, 6, 2, 0, 5, 3, 4])
>>> cl["INC"].values[:10]
array([7, 8, 5, 0, 3, 5, 0, 3, 6, 4])
>>> data = [
... numpy.linspace(3,8,num=10),
... numpy.linspace(10, 0, num=10),
... numpy.linspace(-5, 15, num=10)
... ]
>>> data = pandas.DataFrame(data).T
>>> data
0 1 2
0 3.000000 10.000000 -5.000000
1 3.555556 8.888889 -2.777778
2 4.111111 7.777778 -0.555556
3 4.666667 6.666667 1.666667
4 5.222222 5.555556 3.888889
5 5.777778 4.444444 6.111111
6 6.333333 3.333333 8.333333
7 6.888889 2.222222 10.555556
8 7.444444 1.111111 12.777778
9 8.000000 0.000000 15.000000
>>> data.apply(mapclassify.Quantiles.make(rolling=True))
0 1 2
0 0 4 0
1 0 4 0
2 1 4 0
3 1 3 0
4 2 2 1
5 2 1 2
6 3 1 4
7 3 0 4
8 4 0 4
9 4 0 4
>>> dbf = libpysal.io.open(libpysal.examples.get_path("baltim.dbf"))
>>> data = dbf.by_col_array("PRICE", "LOTSZ", "SQFT")
>>> my_bins = [1, 10, 20, 40, 80]
>>> cl = [mapclassify.UserDefined.make(bins=my_bins)(a) for a in data.T]
>>> len(cl)
3
>>> cl[0][:10]
array([4, 5, 5, 5, 4, 4, 5, 4, 4, 5])
"""
# only flag overrides return flag
to_annotate = copy.deepcopy(kwargs)
return_object = kwargs.pop("return_object", False)
return_bins = kwargs.pop("return_bins", False)
return_counts = kwargs.pop("return_counts", False)
rolling = kwargs.pop("rolling", False)
if rolling:
# just initialize a fake classifier
data = list(range(10))
cls_instance = cls(data, *args, **kwargs)
# and empty it, since we'll be using the update
cls_instance.y = np.array([])
else:
cls_instance = None
# wrap init in a closure to make a consumer.
# Qc Na: "Objects/Closures are poor man's Closures/Objects"
def classifier(data, cls_instance=cls_instance):
if rolling:
cls_instance.update(data, inplace=True, **kwargs)
yb = cls_instance.find_bin(data)
else:
cls_instance = cls(data, *args, **kwargs)
yb = cls_instance.yb
outs = [yb, None, None, None]
outs[1] = cls_instance if return_object else None
outs[2] = cls_instance.bins if return_bins else None
outs[3] = cls_instance.counts if return_counts else None
outs = [a for a in outs if a is not None]
if len(outs) == 1:
return outs[0]
else:
return outs
# for debugging/jic, keep around the kwargs.
# in future, we might want to make this a thin class, so that we can
# set a custom repr. Call the class `Binner` or something, that's a
# pre-configured Classifier that just consumes data, bins it, &
# possibly updates the bins.
classifier._options = to_annotate
return classifier
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"k": kwargs.pop("k", self.k)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
def __str__(self):
return self.table()
def __repr__(self):
return self.table()
def table(self):
fmt = self.fmt
return _get_table(self, fmt=fmt)
def __call__(self, *args):
"""
This will allow the classifier to be called like it's a function.
Whether or not we want to make this be ``find_bin`` or ``update`` is a
design decision.
I like this as ``find_bin``, since a classifier's job should be to classify
the data given to it using the rules estimated from the ``_classify()``.
function.
"""
return self.find_bin(*args)
def get_tss(self):
"""Returns sum of squares over all class means."""
tss = 0
for class_def in self.classes:
if len(class_def) > 0:
yc = self.y[class_def]
css = yc - yc.mean()
css *= css
tss += sum(css)
return tss
def _set_bins(self):
pass
def get_adcm(self):
"""
Absolute deviation around class median (*ADCM*).
Calculates the absolute deviations of each observation about its class
median as a measure of fit for the classification method.
Returns sum of *ADCM* over all classes.
"""
adcm = 0
for class_def in self.classes:
if len(class_def) > 0:
yc = self.y[class_def]
yc_med = np.median(yc)
ycd = np.abs(yc - yc_med)
adcm += sum(ycd)
return adcm
def get_gadf(self):
"""Goodness of absolute deviation of fit."""
adam = (np.abs(self.y - np.median(self.y))).sum()
# return 1 if array is invariant
gadf = 1 if adam == 0 else 1 - self.adcm / adam
return gadf
def find_bin(self, x):
"""
Sort input or inputs according to the current bin estimate.
Parameters
----------
x : numpy.array, int, float
A value or array of values to fit within the estimated bins.
Returns
-------
right : numpy.array, int
A bin index or array of bin indices that classify the
input into one of the classifiers' bins.
Notes
-----
This differs from similar functionality in
``numpy.digitize(x, classi.bins, right=True)``.
This will always provide the closest bin, so data "outside" the classifier,
above and below the max/min breaks, will be classified into the nearest bin.
``numpy.digitize`` returns :math:`k+1` for data greater than the greatest bin,
but retains 0 for data below the lowest bin.
"""
x = np.asarray(x).flatten()
right = np.digitize(x, self.bins, right=True)
if right.max() == len(self.bins):
right[right == len(self.bins)] = len(self.bins) - 1
return right
def get_legend_classes(self, fmt=FMT):
"""
Format the strings for the classes on the legend.
Parameters
----------
fmt : str (default '{:.2f}')
Formatting specification.
Returns
-------
classes : list
:math:`k` strings with class interval definitions.
"""
return _get_mpl_labels(self, fmt)
def plot(
self,
gdf,
border_color="lightgray",
border_width=0.10,
title=None,
legend=False,
cmap="YlGnBu",
axis_on=True,
legend_kwds={"loc": "lower right", "fmt": FMT},
file_name=None,
dpi=600,
ax=None,
):
"""
Plot a mapclassifier object.
Parameters
----------
gdf : geopandas.GeoDataFrame
Contains the geometry column for the choropleth map.
border_color : str (default 'lightgray')
Matplotlib color string to use for polygon border.
border_width : float (default 0.10)
Width of polygon border.
title : str (default None)
Title of map.
cmap : str (default 'YlGnBu')
Matplotlib color string for color map to fill polygons.
axis_on : bool (default True)
Show coordinate axes.
legend_kwds : dict (default {'loc': 'lower right', 'fmt':FMT})
Options for ``ax.legend()``.
file_name : str (default None)
Name of file to save figure to.
dpi : int (default 600)
Dots per inch for saved figure.
ax : matplotlib.Axis (default None)
Axis on which to plot the choropleth.
Default is ``None``, which plots on the current figure.
Returns
-------
f, ax : tuple
Matplotlib figure and axis on which the plot is made.
Examples
--------
>>> import libpysal
>>> import geopandas
>>> import mapclassify
>>> gdf = geopandas.read_file(libpysal.examples.get_path("columbus.shp"))
>>> q5 = mapclassify.Quantiles(gdf.CRIME)
>>> q5.plot(gdf) # doctest: +SKIP
Notes
-----
Requires ``matplotlib``, and implicitly requires a
``geopandas.GeoDataFrame`` as input.
"""
try:
import matplotlib.pyplot as plt
except ImportError:
raise ImportError(
"Mapclassify.plot depends on matplotlib.pyplot, and this was"
"not able to be imported. \nInstall matplotlib to"
"plot spatial classifier."
) from None
if ax is None:
f = plt.figure()
ax = plt.gca()
else:
f = plt.gcf()
ax = gdf.assign(_cl=self.y).plot(
column="_cl",
ax=ax,
cmap=cmap,
edgecolor=border_color,
linewidth=border_width,
scheme=self.name,
legend=legend,
legend_kwds=legend_kwds,
)
if not axis_on:
ax.axis("off")
if title:
f.suptitle(title)
if file_name:
plt.savefig(file_name, dpi=dpi)
return f, ax
[docs]
class HeadTailBreaks(MapClassifier):
"""
Head/tail Breaks Map Classification for Heavy-tailed Distributions.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> import numpy
>>> numpy.random.seed(10)
>>> cal = mapclassify.load_example()
>>> htb = mapclassify.HeadTailBreaks(cal)
>>> htb.k
3
>>> htb.counts.tolist()
[50, 7, 1]
>>> htb.bins
array([ 125.92810345, 811.26 , 4111.45 ])
>>> numpy.random.seed(123456)
>>> x = numpy.random.lognormal(3, 1, 1000)
>>> htb = mapclassify.HeadTailBreaks(x)
>>> htb.bins
array([ 32.26204423, 72.50205622, 128.07150107, 190.2899093 ,
264.82847377, 457.88157946, 576.76046949])
>>> htb.counts.tolist()
[695, 209, 62, 22, 10, 1, 1]
Notes
-----
Head/tail Breaks is a relatively new classification method developed
for data with a heavy-tailed distribution.
Implementation based on contributions by
Alessandra Sozzi <alessandra.sozzi@gmail.com>.
For theoretical details see :cite:`Jiang_2013`.
"""
[docs]
def __init__(self, y):
MapClassifier.__init__(self, y)
self.name = "HeadTailBreaks"
def _set_bins(self):
x = self.y.copy()
bins = []
bins = head_tail_breaks(x, bins)
self.bins = np.array(bins)
self.k = len(self.bins)
[docs]
class EqualInterval(MapClassifier):
"""
Equal Interval Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations. Each value is the ID of the class
the observation belongs to
:math:`yb[i] = j` for :math:`j>=1` if :math:`bins[j-1] < y[i] <= bins[j]`,
otherwise :math:`yb[i] = 0`.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> ei = mapclassify.EqualInterval(cal, k=5)
>>> ei.k
5
>>> ei.counts.tolist()
[57, 0, 0, 0, 1]
>>> ei.bins
array([ 822.394, 1644.658, 2466.922, 3289.186, 4111.45 ])
Notes
-----
Intervals defined to have equal width:
.. math::
bins_j = min(y)+w*(j+1)
with :math:`w=\\frac{max(y)-min(j)}{k}`
"""
[docs]
def __init__(self, y, k=K):
"""
see class docstring
"""
if min(y) == max(y):
raise ValueError(
f"Not enough unique values in array to form {k} classes. "
"All values in `y` are equal."
)
self.k = k
MapClassifier.__init__(self, y)
self.name = "EqualInterval"
def _set_bins(self):
y = self.y
k = self.k
max_y = max(y)
min_y = min(y)
rg = max_y - min_y
width = rg * 1.0 / k
cuts = np.arange(min_y + width, max_y + width, width)
if len(cuts) > self.k: # handle overshooting
cuts = cuts[0:k]
cuts[-1] = max_y
bins = cuts.copy()
self.bins = bins
[docs]
class Percentiles(MapClassifier):
"""
Percentiles Map Classification
Parameters
----------
y : numpy.array
Attribute to classify.
pct : numpy.array (default [1, 10, 50, 90, 99, 100])
Percentiles.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> p = mapclassify.Percentiles(cal)
>>> p.bins
array([1.357000e-01, 5.530000e-01, 9.365000e+00, 2.139140e+02,
2.179948e+03, 4.111450e+03])
>>> p.counts.tolist()
[1, 5, 23, 23, 5, 1]
>>> p2 = mapclassify.Percentiles(cal, pct = [50, 100])
>>> p2.bins
array([ 9.365, 4111.45 ])
>>> p2.counts.tolist()
[29, 29]
>>> p2.k
2
"""
[docs]
def __init__(self, y, pct=[1, 10, 50, 90, 99, 100]):
self.pct = pct
MapClassifier.__init__(self, y)
self.name = "Percentiles"
def _set_bins(self):
y = self.y
pct = self.pct
self.bins = np.array([stats.scoreatpercentile(y, p) for p in pct])
self.k = len(self.bins)
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"pct": kwargs.pop("pct", self.pct)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class PrettyBreaks(MapClassifier):
[docs]
def __init__(self, y, k=5):
"""
Pretty breakpoints
Computes breaks that are equally spaced round values which
cover the range of values in `y`. The breaks are chosen so that
they are 1, 2, or 5 times a power of 10.
Parameters
----------
y : array (n,1)
attribute to classify
k : int
The number of desired classes
Notes
-----
The number of classes may be different from the specified `k`,
as the rounding of the upper bounds takes precedent.
The lower bound of the first interval will be equal to the
minimum of the data.
"""
self.k = k
MapClassifier.__init__(self, y)
self.name = "Pretty"
def _set_bins(self):
bins = _pretty(self.y, self.k)
self.bins = bins[1:]
[docs]
class BoxPlot(MapClassifier):
"""
BoxPlot Map Classification.
Parameters
----------
y : numpy.array
Attribute to classify
hinge : float (default 1.5)
Multiplier for *IQR*.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin ids for observations.
bins : array
:math:`(n,1)`, the upper bounds of each class (monotonic).
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
low_outlier_ids : numpy.array
Indices of observations that are low outliers.
high_outlier_ids : numpy.array
Indices of observations that are high outliers.
Notes
-----
The bins are set as follows::
bins[0] = q[0]-hinge*IQR
bins[1] = q[0]
bins[2] = q[1]
bins[3] = q[2]
bins[4] = q[2]+hinge*IQR
bins[5] = inf (see Notes)
where :math:`q` is an array of the first three quartiles of :math:`y` and
:math:`IQR=q[2]-q[0]`.
If :math:`q[2]+hinge*IQR > max(y)` there will only be 5 classes and no high
outliers, otherwise, there will be 6 classes and at least one high
outlier.
Examples
--------
>>> import mapclassify
>>> import numpy
>>> cal = mapclassify.load_example()
>>> bp = mapclassify.BoxPlot(cal)
>>> bp.bins
array([-5.287625e+01, 2.567500e+00, 9.365000e+00, 3.953000e+01,
9.497375e+01, 4.111450e+03])
>>> bp.counts.tolist()
[0, 15, 14, 14, 6, 9]
>>> bp.high_outlier_ids.tolist()
[0, 6, 18, 29, 33, 36, 37, 40, 42]
>>> cal[bp.high_outlier_ids].values
array([ 329.92, 181.27, 370.5 , 722.85, 192.05, 110.74, 4111.45,
317.11, 264.93])
>>> bx = mapclassify.BoxPlot(numpy.arange(100))
>>> bx.bins
array([-49.5 , 24.75, 49.5 , 74.25, 148.5 ])
"""
[docs]
def __init__(self, y, hinge=1.5):
"""
Parameters
----------
y : numpy.array
:math:`(n,1)`, attribute to classify
hinge : float (default 1.5)
Multiple of inter-quartile range.
"""
self.hinge = hinge
MapClassifier.__init__(self, y)
self.name = "BoxPlot"
def _set_bins(self):
y = self.y
pct = [25, 50, 75, 100]
bins = [stats.scoreatpercentile(y, p) for p in pct]
iqr = bins[-2] - bins[0]
self.iqr = iqr
pivot = self.hinge * iqr
left_fence = bins[0] - pivot
right_fence = bins[-2] + pivot
if right_fence < bins[-1]:
bins.insert(-1, right_fence)
else:
bins[-1] = right_fence
bins.insert(0, left_fence)
self.bins = np.array(bins)
self.k = len(bins)
def _classify(self):
MapClassifier._classify(self)
self.low_outlier_ids = np.nonzero(self.yb == 0)[0]
self.high_outlier_ids = np.nonzero(self.yb == 5)[0]
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"hinge": kwargs.pop("hinge", self.hinge)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class Quantiles(MapClassifier):
"""
Quantile Map Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations. Each value is the ID of the class
the observation belongs to
:math:`yb[i] = j` for :math:`j>=1` if :math:`bins[j-1] < y[i] <= bins[j]`,
otherwise :math:`yb[i] = 0`.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> q = mapclassify.Quantiles(cal, k=5)
>>> q.bins
array([1.46400e+00, 5.79800e+00, 1.32780e+01, 5.46160e+01, 4.11145e+03])
>>> q.counts.tolist()
[12, 11, 12, 11, 12]
"""
[docs]
def __init__(self, y, k=K):
self.k = k
MapClassifier.__init__(self, y)
self.name = "Quantiles"
def _set_bins(self):
y = self.y
k = self.k
self.bins = quantile(y, k=k)
[docs]
class StdMean(MapClassifier):
"""
Standard Deviation and Mean Map Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify
multiples : numpy.array (default [-2, -1, 1, 2])
The multiples of the standard deviation to add/subtract from
the sample mean to define the bins.
anchor : bool (default False)
Anchor upper bound of one class to the sample mean.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Notes
-----
If anchor is True, one of the intervals will have its closed upper bound
equal to the mean of y. Intermediate intervals will have widths equal to
the standard deviation of y. The first interval will be closed on the
minimum value of y, and the last interval will be closed on the maximum of
y. The first and last intervals may have widths different from the
intermediate intervals.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> st = mapclassify.StdMean(cal)
>>> st.k
5
>>> st.bins
array([-967.36235382, -420.71712519, 672.57333208, 1219.21856072,
4111.45 ])
>>> st.counts.tolist()
[0, 0, 56, 1, 1]
>>> st3 = mapclassify.StdMean(cal, multiples = [-3, -1.5, 1.5, 3])
>>> st3.bins
array([-1514.00758246, -694.03973951, 945.8959464 , 1765.86378936,
4111.45 ])
>>> st3.counts.tolist()
[0, 0, 57, 0, 1]
>>> stda = mapclassify.StdMean(cal, anchor=True)
>>> stda.k
9
>>> stda.bins
array([ 125.92810345, 672.57333208, 1219.21856072, 1765.86378936,
2312.50901799, 2859.15424663, 3405.79947527, 3952.4447039 ,
4111.45 ])
>>> float(cal.mean()), float(cal.std()), float(cal.min()), float(cal.max())
(125.92810344827588, 546.6452286365233, 0.13, 4111.45)
"""
[docs]
def __init__(self, y, multiples=[-2, -1, 1, 2], anchor=False):
self.multiples = multiples
self.anchor = anchor
MapClassifier.__init__(self, y)
self.name = "StdMean"
def _set_bins(self):
y = self.y
s = y.std(ddof=1)
m = y.mean()
if self.anchor:
min_z = int((y.min() - m) / s)
max_z = int((y.max() - m) / s) + 1
self.multiples = list(range(min_z, max_z))
cuts = [m + s * w for w in self.multiples]
y_max = y.max()
if cuts[-1] < y_max:
cuts.append(y_max)
self.bins = np.array(cuts)
self.k = len(cuts)
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"multiples": kwargs.pop("multiples", self.multiples)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class MaximumBreaks(MapClassifier):
"""
Maximum Breaks Map Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
mindiff : float (default 0)
The minimum difference between class breaks.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> mb = mapclassify.MaximumBreaks(cal, k=5)
>>> mb.k
5
>>> mb.bins
array([ 146.005, 228.49 , 546.675, 2417.15 , 4111.45 ])
>>> mb.counts.tolist()
[50, 2, 4, 1, 1]
"""
[docs]
def __init__(self, y, k=5, mindiff=0):
if min(y) == max(y):
raise ValueError(
f"Not enough unique values in array to form {k} classes. "
"All values in `y` are equal."
)
self.k = k
self.mindiff = mindiff
MapClassifier.__init__(self, y)
self.name = "MaximumBreaks"
def _set_bins(self):
xs = self.y.copy()
k = self.k
xs.sort()
diffs = xs[1:] - xs[:-1]
idxs = np.argsort(diffs)
k1 = k - 1
ud = np.unique(diffs)
if len(ud) < k1:
warnings.warn(
"Insufficient number of unique diffs. Breaks are random.",
UserWarning,
stacklevel=3,
)
mp = []
for c in range(1, k):
idx = idxs[-c]
cp = (xs[idx] + xs[idx + 1]) / 2.0
mp.append(cp)
mp.append(xs[-1])
mp.sort()
self.bins = np.array(mp)
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"k": kwargs.pop("k", self.k)})
kwargs.update({"mindiff": kwargs.pop("mindiff", self.mindiff)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class NaturalBreaks(MapClassifier):
"""
Natural Breaks Map Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
initial : int (default 10)
The number of initial solutions generated with different centroids.
The best of initial results are returned.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> import numpy
>>> numpy.random.seed(123456)
>>> cal = mapclassify.load_example()
>>> nb = mapclassify.NaturalBreaks(cal, k=5)
>>> nb.k
5
>>> nb.counts.tolist()
[49, 3, 4, 1, 1]
>>> nb.bins
array([ 75.29, 192.05, 370.5 , 722.85, 4111.45])
"""
[docs]
def __init__(self, y, k=K, initial=10):
self.k = k
self.init = initial
MapClassifier.__init__(self, y)
self.name = "NaturalBreaks"
def _set_bins(self):
x = self.y.copy()
k = self.k
values = np.array(x)
uv = np.unique(values)
uvk = len(uv)
if uvk < k:
warnings.warn(
f"Not enough unique values in array to form {k} classes. "
f"Setting k to {uvk}.",
UserWarning,
stacklevel=3,
)
k = uvk
uv.sort()
# we set the bins equal to the sorted unique values and ramp k
# downwards. no need to call kmeans.
self.bins = uv
self.k = k
else:
res0 = natural_breaks(x, k, init=self.init)
self.bins = np.array(res0[-1])
self.k = len(self.bins)
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"k": kwargs.pop("k", self.k)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class FisherJenks(MapClassifier):
"""
Fisher Jenks optimal classifier - mean based.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> fj = mapclassify.FisherJenks(cal)
>>> float(fj.adcm)
799.24
>>> fj.bins.tolist()
[75.29, 192.05, 370.5, 722.85, 4111.45]
>>> fj.counts.tolist()
[49, 3, 4, 1, 1]
"""
[docs]
def __init__(self, y, k=K):
if not HAS_NUMBA:
warnings.warn(
"Numba not installed. Using slow pure python version.",
UserWarning,
stacklevel=3,
)
nu = len(np.unique(y))
if nu < k:
raise ValueError(
f"Fewer unique values ({nu}) than specified classes ({k})."
)
self.k = k
MapClassifier.__init__(self, y)
self.name = "FisherJenks"
def _set_bins(self):
x = np.sort(self.y).astype("f8")
self.bins = _fisher_jenks_means(x, classes=self.k)
[docs]
class FisherJenksSampled(MapClassifier):
"""
Fisher Jenks optimal classifier - mean based using random sample.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
pct : float (default 0.10)
The percentage of :math:`n` that should form the sample.
If ``pct`` is specified such that :math:`n*pct > 1000`, then
:math:`pct = 1000./n`, unless truncate is ``False``.
truncate : bool (default True)
Truncate ``pct`` in cases where :math:`pct * n > 1000.`.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Notes
-----
For theoretical details see :cite:`Rey_2016`.
"""
[docs]
def __init__(self, y, k=K, pct=0.10, truncate=True):
self.k = k
n = y.size
if (pct * n > 1000) and truncate:
pct = 1000.0 / n
ids = np.random.randint(0, n, int(n * pct))
y = np.asarray(y)
yr = y[ids]
yr[-1] = max(y) # make sure we have the upper bound
yr[0] = min(y) # make sure we have the min
self.original_y = y
self.pct = pct
self._truncated = truncate
self.yr = yr
self.yr_n = yr.size
MapClassifier.__init__(self, yr)
self.yb, self.counts = bin1d(y, self.bins)
self.name = "FisherJenksSampled"
self.y = y
self._summary() # have to recalculate summary stats
def _set_bins(self):
fj = FisherJenks(self.y, self.k)
self.bins = fj.bins
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"k": kwargs.pop("k", self.k)})
kwargs.update({"pct": kwargs.pop("pct", self.pct)})
kwargs.update({"truncate": kwargs.pop("truncate", self._truncated)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class JenksCaspall(MapClassifier):
"""
Jenks Caspall Map Classification.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> jc = mapclassify.JenksCaspall(cal, k=5)
>>> jc.bins
array([1.81000e+00, 7.60000e+00, 2.98200e+01, 1.81270e+02, 4.11145e+03])
>>> jc.counts.tolist()
[14, 13, 14, 10, 7]
"""
[docs]
def __init__(self, y, k=K):
self.k = k
MapClassifier.__init__(self, y)
self.name = "JenksCaspall"
def _set_bins(self):
x = self.y.copy()
k = self.k
# start with quantiles
q = quantile(x, k)
solving = True
xb, cnts = bin1d(x, q)
# class means
if x.ndim == 1:
x.shape = (x.size, 1)
n, k = x.shape
xm = [np.median(x[xb == i]) for i in np.unique(xb)]
xb0 = xb.copy()
q = xm
it = 0
rk = list(range(self.k))
while solving:
xb = np.zeros(xb0.shape, int)
d = abs(x - q)
xb = d.argmin(axis=1)
if (xb0 == xb).all():
solving = False
else:
xb0 = xb
it += 1
q = np.array([np.median(x[xb == i]) for i in rk])
cuts = np.array([max(x[xb == i]) for i in np.unique(xb)])
cuts.shape = (len(cuts),)
self.bins = cuts
self.iterations = it
[docs]
class JenksCaspallSampled(MapClassifier):
"""
Jenks Caspall Map Classification using a random sample.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
pct : float (default 0.10)
The percentage of :math:`n` that should form the sample.
If ``pct`` is specified such that :math:`n*pct > 1000`, then
:math:`pct = 1000./n`.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> import numpy
>>> cal = mapclassify.load_example()
>>> numpy.random.seed(0)
>>> x = numpy.random.random(100000)
>>> jc = mapclassify.JenksCaspall(x)
>>> jcs = mapclassify.JenksCaspallSampled(x)
>>> jc.bins
array([0.20108144, 0.4025151 , 0.60396127, 0.80302249, 0.99997795])
>>> jcs.bins
array([0.19978245, 0.40793025, 0.59253555, 0.78241472, 0.99997795])
>>> jc.counts.tolist()
[20286, 19951, 20310, 19708, 19745]
>>> jcs.counts.tolist()
[20147, 20633, 18591, 18857, 21772]
# not for testing since we get different times on different hardware
# just included for documentation of likely speed gains
#>>> t1 = time.time(); jc = Jenks_Caspall(x); t2 = time.time()
#>>> t1s = time.time(); jcs = Jenks_Caspall_Sampled(x); t2s = time.time()
#>>> t2 - t1; t2s - t1s
#1.8292930126190186
#0.061631917953491211
Notes
-----
This is intended for large :math:`n` problems. The logic is to apply
``Jenks_Caspall`` to a random subset of the :math:`y` space and then bin the
complete vector :math:`y` on the bins obtained from the subset. This would
trade off some "accuracy" for a gain in speed.
"""
[docs]
def __init__(self, y, k=K, pct=0.10):
self.k = k
n = y.size
if pct * n > 1000:
pct = 1000.0 / n
ids = np.random.randint(0, n, int(n * pct))
y = np.asarray(y)
yr = y[ids]
yr[0] = max(y) # make sure we have the upper bound
self.original_y = y
self.pct = pct
self.yr = yr
self.yr_n = yr.size
MapClassifier.__init__(self, yr)
self.yb, self.counts = bin1d(y, self.bins)
self.name = "JenksCaspallSampled"
self.y = y
self._summary() # have to recalculate summary stats
def _set_bins(self):
jc = JenksCaspall(self.y, self.k)
self.bins = jc.bins
self.iterations = jc.iterations
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
kwargs.update({"k": kwargs.pop("k", self.k)})
kwargs.update({"pct": kwargs.pop("pct", self.pct)})
if inplace:
self._update(y, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, **kwargs)
return new
[docs]
class JenksCaspallForced(MapClassifier):
"""
Jenks Caspall Map Classification with forced movements.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default 5)
The number of classes required.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> jcf = mapclassify.JenksCaspallForced(cal, k=5)
>>> jcf.k
5
>>> jcf.bins
array([1.34000e+00, 5.90000e+00, 1.67000e+01, 5.06500e+01, 4.11145e+03])
>>> jcf.counts.tolist()
[12, 12, 13, 9, 12]
>>> jcf4 = mapclassify.JenksCaspallForced(cal, k=4)
>>> jcf4.k
4
>>> jcf4.bins
array([2.51000e+00, 8.70000e+00, 3.66800e+01, 4.11145e+03])
>>> jcf4.counts.tolist()
[15, 14, 14, 15]
"""
[docs]
def __init__(self, y, k=K):
if min(y) == max(y):
raise ValueError(
f"Not enough unique values in array to form {k} classes. "
"All values in `y` are equal."
)
self.k = k
MapClassifier.__init__(self, y)
self.name = "JenksCaspallForced"
def _set_bins(self):
x = self.y.copy()
k = self.k
q = quantile(x, k)
solving = True
xb, cnt = bin1d(x, q)
# class means
if x.ndim == 1:
x.shape = (x.size, 1)
n, tmp = x.shape
xm = [x[xb == i].mean() for i in np.unique(xb)]
q = xm
xbar = np.array([xm[xbi] for xbi in xb])
xbar.shape = (n, 1)
ss = x - xbar
ss *= ss
ss = sum(ss)
down_moves = up_moves = 0
solving = True
it = 0
while solving:
# try upward moves first
moving_up = True
while moving_up:
class_ids = np.unique(xb)
nk = [sum(xb == j) for j in class_ids]
candidates = nk[:-1]
i = 0
up_moves = 0
while candidates:
nki = candidates.pop(0)
if nki > 1:
ids = np.nonzero(xb == class_ids[i])
mover = max(ids[0])
tmp = xb.copy()
tmp[mover] = xb[mover] + 1
tm = [x[tmp == j].mean() for j in np.unique(tmp)]
txbar = np.array([tm[xbi] for xbi in tmp])
txbar.shape = (n, 1)
tss = x - txbar
tss *= tss
tss = sum(tss)
if tss < ss:
xb = tmp
ss = tss
candidates = []
up_moves += 1
i += 1
if not up_moves:
moving_up = False
moving_down = True
while moving_down:
class_ids = np.unique(xb)
nk = [sum(xb == j) for j in class_ids]
candidates = nk[1:]
i = 1
down_moves = 0
while candidates:
nki = candidates.pop(0)
if nki > 1:
ids = np.nonzero(xb == class_ids[i])
mover = min(ids[0])
mover_class = xb[mover]
target_class = mover_class - 1
tmp = xb.copy()
tmp[mover] = target_class
tm = [x[tmp == j].mean() for j in np.unique(tmp)]
txbar = np.array([tm[xbi] for xbi in tmp])
txbar.shape = (n, 1)
tss = x - txbar
tss *= tss
tss = sum(tss)
if tss < ss:
xb = tmp
ss = tss
candidates = []
down_moves += 1
i += 1
if not down_moves:
moving_down = False
if not up_moves and not down_moves:
solving = False
it += 1
cuts = [max(x[xb == c]) for c in np.unique(xb)]
cuts = np.reshape(np.array(cuts), (k,))
self.bins = cuts
self.iterations = it
[docs]
class UserDefined(MapClassifier):
"""
User Specified Binning.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
bins : numpy.array
:math:`(k,1)`, upper bounds of classes (have to be monotically increasing).
lowest : float (default None)
Scalar minimum value of lowest class. Default is to set the minimum
to ``-inf`` if ``y.min()`` > first upper bound (which will override
the default), otherwise minimum is set to ``y.min()``.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> bins = [20, max(cal)]
>>> bins
[20, 4111.45]
>>> ud = mapclassify.UserDefined(cal, bins)
>>> ud.bins.tolist()
[20.0, 4111.45]
>>> ud.counts.tolist()
[37, 21]
>>> bins = [20, 30]
>>> ud = mapclassify.UserDefined(cal, bins)
>>> ud.bins.tolist()
[20.0, 30.0, 4111.45]
>>> ud.counts.tolist()
[37, 4, 17]
Notes
-----
If upper bound of user bins does not exceed
``max(y)`` we append an additional bin.
"""
[docs]
def __init__(self, y, bins, lowest=None):
if bins[-1] < max(y):
bins = np.append(bins, max(y))
self.lowest = lowest
self.k = len(bins)
self.bins = np.array(bins)
self.y = y
MapClassifier.__init__(self, y)
self.name = "UserDefined"
def _set_bins(self):
pass
def _update(self, y=None, bins=None):
if y is not None:
if hasattr(y, "values"):
y = y.values
y = np.append(y.flatten(), self.y)
else:
y = self.y
if bins is None:
bins = self.bins
self.__init__(y, bins)
[docs]
def update(self, y=None, inplace=False, **kwargs):
"""
Add data or change classification parameters.
Parameters
----------
y : numpy.array (default None)
:math:`(n,1)`, array of data to classify.
inplace : bool (default False)
Whether to conduct the update in place or to return a
copy estimated from the additional specifications.
**kwargs : dict
Additional parameters that are passed to the ``__init__`` function
of the class. For documentation, check the class constructor.
"""
bins = kwargs.pop("bins", self.bins)
if inplace:
self._update(y=y, bins=bins, **kwargs)
else:
new = copy.deepcopy(self)
new._update(y, bins, **kwargs)
return new
# We have to override the plot method for additional kwargs for UserDefined
[docs]
def plot(
self,
gdf,
border_color="lightgray",
border_width=0.10,
title=None,
legend=False,
cmap="YlGnBu",
axis_on=True,
legend_kwds={"loc": "lower right", "fmt": FMT},
file_name=None,
dpi=600,
ax=None,
):
try:
import matplotlib.pyplot as plt
except ImportError:
raise ImportError(
"Mapclassify.plot depends on matplotlib.pyplot, and this was"
"not able to be imported. \nInstall matplotlib to"
"plot spatial classifier."
) from None
if ax is None:
f = plt.figure()
ax = plt.gca()
else:
f = plt.gcf()
if "fmt" in legend_kwds:
legend_kwds.pop("fmt")
ax = gdf.assign(_cl=self.y).plot(
column="_cl",
ax=ax,
cmap=cmap,
edgecolor=border_color,
linewidth=border_width,
scheme=self.name,
legend=legend,
legend_kwds=legend_kwds,
classification_kwds={"bins": self.bins}, # for UserDefined
)
if not axis_on:
ax.axis("off")
if title:
f.suptitle(title)
if file_name:
plt.savefig(file_name, dpi=dpi)
return f, ax
[docs]
class MaxP(MapClassifier):
"""
MaxP Map Classification. Based on Max-p regionalization algorithm.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to classify.
k : int (default K==5)
Number of classes required.
initial : int (default 1000)
Number of initial solutions to use prior to swapping.
seed1 : int (default 0)
Random state for initial building process.
seed2 : int (default 1)
Random state for swapping process.
Attributes
----------
yb : numpy.array
:math:`(n,1)`, bin IDs for observations.
bins : numpy.array
:math:`(k,1)`, the upper bounds of each class.
k : int
The number of classes.
counts : numpy.array
:math:`(k,1)`, the number of observations falling in each class.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> mp = mapclassify.MaxP(cal)
>>> mp.bins
array([3.16000e+00, 1.26300e+01, 1.67000e+01, 2.04700e+01, 4.11145e+03])
>>> mp.counts.tolist()
[18, 16, 3, 1, 20]
"""
[docs]
def __init__(self, y, k=K, initial=1000, seed1=0, seed2=1):
if min(y) == max(y):
raise ValueError(
f"Not enough unique values in array to form {k} classes. "
"All values in `y` are equal."
)
self.k = k
self.initial = initial
self.seed1 = seed1
self.seed2 = seed2
MapClassifier.__init__(self, y)
self.name = "MaxP"
def _set_bins(self):
x = self.y.copy()
k = self.k
q = quantile(x, k)
if x.ndim == 1:
x.shape = (x.size, 1)
n, tmp = x.shape
x.sort(axis=0)
# find best of initial solutions
solution = 0
best_tss = x.var() * x.shape[0]
tss_all = np.zeros((self.initial, 1))
while solution < self.initial:
remaining = list(range(n))
seeds = [
np.nonzero(di == min(di))[0][0] for di in [np.abs(x - qi) for qi in q]
]
np.random.seed(self.seed1)
rseeds = np.random.permutation(list(range(k))).tolist()
[remaining.remove(seed) for seed in seeds]
self.classes = classes = []
[classes.append([seed]) for seed in seeds]
while rseeds:
seed_id = rseeds.pop()
current = classes[seed_id]
growing = True
while growing:
current = classes[seed_id]
low = current[0]
high = current[-1]
left = low - 1
right = high + 1
move_made = False
if left in remaining:
current.insert(0, left)
remaining.remove(left)
move_made = True
if right in remaining:
current.append(right)
remaining.remove(right)
move_made = True
if move_made:
classes[seed_id] = current
else:
growing = False
tss = _fit(self.y, classes)
tss_all[solution] = tss
if tss < best_tss:
best_solution = classes
best_it = solution
best_tss = tss
solution += 1
classes = best_solution
self.best_it = best_it
self.tss = best_tss
self.a2c = a2c = {}
self.tss_all = tss_all
for r, cl in enumerate(classes):
for a in cl:
a2c[a] = r
swapping = True
while swapping:
np.random.seed(self.seed2)
rseeds = np.random.permutation(list(range(k))).tolist()
total_moves = 0
while rseeds:
_id = rseeds.pop()
growing = True
total_moves = 0
while growing:
target = classes[_id]
left = target[0] - 1
right = target[-1] + 1
n_moves = 0
if left in a2c:
left_class = classes[a2c[left]]
if len(left_class) > 1:
a = left_class[-1]
if self._swap(left_class, target, a):
target.insert(0, a)
left_class.remove(a)
a2c[a] = _id
n_moves += 1
if right in a2c:
right_class = classes[a2c[right]]
if len(right_class) > 1:
a = right_class[0]
if self._swap(right_class, target, a):
target.append(a)
right_class.remove(a)
n_moves += 1
a2c[a] = _id
if not n_moves:
growing = False
total_moves += n_moves
if not total_moves:
swapping = False
xs = self.y.copy()
xs.sort()
self.bins = np.array([xs[cl][-1] for cl in classes])
def _ss(self, class_def):
"""Calculates sum of squares for a class."""
yc = self.y[class_def]
css = yc - yc.mean()
css *= css
return sum(css)
def _swap(self, class1, class2, a):
"""Evaluate cost of moving ``a`` from ``class1`` to ``class2``."""
ss1 = self._ss(class1)
ss2 = self._ss(class2)
tss1 = ss1 + ss2
class1c = copy.copy(class1)
class2c = copy.copy(class2)
class1c.remove(a)
class2c.append(a)
ss1 = self._ss(class1c)
ss2 = self._ss(class2c)
tss2 = ss1 + ss2
return False if tss1 < tss2 else True # noqa SIM211
def _fit(y, classes):
"""Calculate the total sum of squares for a
vector :math:`y` classified into classes.
Parameters
----------
y : numpy.array
:math:`(n,1)`, variable to be classified.
classes : array
:math:`(k,1)`, integer values denoting class membership.
"""
tss = 0
for class_def in classes:
yc = y[class_def]
css = yc - yc.mean()
css *= css
tss += sum(css)
return tss
kmethods = {}
kmethods["Quantiles"] = Quantiles
kmethods["FisherJenks"] = FisherJenks
kmethods["NaturalBreaks"] = NaturalBreaks
kmethods["MaximumBreaks"] = MaximumBreaks
[docs]
def gadf(y, method="Quantiles", maxk=15, pct=0.8):
r"""
Evaluate the Goodness of Absolute Deviation Fit (*GADF*) of a classifier and
find the minimum value of :math:`k` for which ``gadf > pct``.
Parameters
----------
y : numpy.array
:math:`(n, 1)`, values to be classified.
method : str (default 'Quantiles')
The classification method in:
``{'Quantiles', 'Fisher_Jenks', 'Maximum_Breaks', 'Natrual_Breaks'}``.
maxk : int (default 15)
Maximum value of :math:`k` to evaluate.
pct : float (default 0.8)
The percentage of *GADF* to exceed.
Returns
-------
k : int
Number of classes.
cl : object
Instance of the classifier at :math:`k`.
gadf : float
Goodness of absolute deviation fit (*GADF*).
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> qgadf = mapclassify.classifiers.gadf(cal)
>>> qgadf[0]
15
>>> float(qgadf[-1])
0.3740257590909283
Quantiles fail to exceed 0.80 before 15 classes. If we lower the bar to
0.2 we see quintiles as a result
>>> qgadf2 = mapclassify.classifiers.gadf(cal, pct = 0.2)
>>> qgadf2[0]
5
>>> float(qgadf2[-1])
0.21710231966462412
Notes
-----
The *GADF* is defined as:
.. math::
GADF = 1 - \sum_c \sum_{i \in c}
|y_i - y_{c,med}| / \sum_i |y_i - y_{med}|
where :math:`y_{med}` is the global median and :math:`y_{c,med}` is
the median for class :math:`c`.
See Also
--------
KClassifiers
"""
y = np.array(y)
adam = (np.abs(y - np.median(y))).sum()
for k in range(2, maxk + 1):
cl = kmethods[method](y, k)
gadf = 1 - cl.adcm / adam
if gadf > pct:
break
return (k, cl, gadf)
[docs]
class KClassifiers:
"""
Evaluate all :math:`k`-classifers and pick optimal based on :math:`k` and *GADF*.
Parameters
----------
y : numpy.array
:math:`(n,1)`, values to be classified.
pct : float (default 0.8)
The percentage of *GADF* to exceed.
Attributes
----------
best : MapClassifier
Instance of the optimal ``MapClassifier``.
results : dict
Keys are classifier names, values are the ``MapClassifier``
instances with the best ``pct`` for each classifier.
Examples
--------
>>> import mapclassify
>>> cal = mapclassify.load_example()
>>> ks = mapclassify.classifiers.KClassifiers(cal)
>>> ks.best.name
'FisherJenks'
>>> ks.best.k
4
>>> float(ks.best.gadf)
0.8481032719908105
Notes
-----
This can be used to suggest a classification scheme.
See Also
--------
gadf
"""
[docs]
def __init__(self, y, pct=0.8):
results = {}
best = gadf(y, "FisherJenks", maxk=len(y) - 1, pct=pct)
pct0 = best[0]
k0 = best[-1]
keys = list(kmethods.keys())
keys.remove("FisherJenks")
results["FisherJenks"] = best
for method in keys:
results[method] = gadf(y, method, maxk=len(y) - 1, pct=pct)
k1 = results[method][0]
pct1 = results[method][-1]
if (k1 < k0) or (k1 == k0 and pct0 < pct1):
best = results[method]
k0 = k1
pct0 = pct1
self.results = results
self.best = best[1]