# Source code for pysal.esda.mapclassify

"""
A module of classification schemes for choropleth mapping.
"""

__author__ = "Sergio J. Rey"

__all__ = ['Map_Classifier', 'quantile', 'Box_Plot', 'Equal_Interval',
'Fisher_Jenks', 'Fisher_Jenks_Sampled', 'Jenks_Caspall',
'Jenks_Caspall_Forced', 'Jenks_Caspall_Sampled',
'Max_P_Classifier', 'Maximum_Breaks', 'Natural_Breaks',
'Quantiles', 'Percentiles', 'Std_Mean', 'User_Defined',

CLASSIFIERS = ('Box_Plot', 'Equal_Interval', 'Fisher_Jenks',
'Jenks_Caspall_Forced', 'Jenks_Caspall_Sampled',
'Max_P_Classifier', 'Maximum_Breaks', 'Natural_Breaks',
'Quantiles', 'Percentiles', 'Std_Mean', 'User_Defined')

K = 5  # default number of classes in any map scheme with this as an argument
import numpy as np
import scipy.stats as stats
import scipy as sp
import copy
import sys
from scipy.cluster.vq import kmeans as KMEANS
from warnings import warn as Warn
try:
from numba import autojit
except ImportError:
def autojit(func):
return func

"""
"""
values = np.array(values)
mean = np.mean(values)
cuts.append(mean)
if (len(values) > 1):
return cuts

[docs]def quantile(y, k=4): """ Calculates the quantiles for an array Parameters ---------- y : array (n,1), values to classify k : int number of quantiles Returns ------- implicit : array (n,1), quantile values Examples -------- >>> x = np.arange(1000) >>> quantile(x) array([ 249.75, 499.5 , 749.25, 999. ]) >>> quantile(x, k = 3) array([ 333., 666., 999.]) >>> Note that 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 >>> x = [1.0] * 100 >>> x.extend([3.0] * 40) >>> len(x) 140 >>> y = np.array(x) >>> quantile(y) array([ 1., 3.]) """ w = 100. / 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]) return np.unique(q)
def binC(y, bins): """ Bin categorical/qualitative data Parameters ---------- y : array (n,q), categorical values bins : array (k,1), unique values associated with each bin Return ------ b : array (n,q), bin membership, values between 0 and k-1 Examples -------- >>> np.random.seed(1) >>> x = np.random.randint(2, 8, (10, 3)) >>> bins = 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 = 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]]) >>> """ 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: Warn('value not in bin: {}'.format(val), UserWarning) Warn('bins: {}'.format(bins), UserWarning) return b def bin(y, bins): """ bin interval/ratio data Parameters ---------- y : array (n,q), values to bin bins : array (k,1), upper bounds of each bin (monotonic) Returns ------- b : array (n,q), values of values between 0 and k-1 Examples -------- >>> np.random.seed(1) >>> x = np.random.randint(2, 20, (10, 3)) >>> bins = [10, 15, 20] >>> b = 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]]) >>> """ 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 type(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 : array (n, 1), values to bin bins : array (k,1), upper bounds of each bin (monotonic) Returns ------- binIds : array 1-d array of integer bin Ids counts : int number of elements of x falling in each bin Examples -------- >>> x = np.arange(100, dtype = 'float') >>> bins = [25, 74, 100] >>> binIds, counts = 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 array([26, 49, 25]) """ left = [-sys.maxint] left.extend(bins[0:-1]) right = bins cuts = 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 load_example(): """ Helper function for doc tests """ import pysal np.random.seed(10) dat = pysal.open(pysal.examples.get_path('calempdensity.csv')) cal = np.array([record[-1] for record in dat]) return cal def _kmeans(y, k=5): """ Helper function to do kmeans in one dimension """ y = y * 1. # KMEANS needs float or double dtype centroids = KMEANS(y, k)[0] centroids.sort() try: class_ids = np.abs(y - centroids).argmin(axis=1) except: class_ids = np.abs(y[:, np.newaxis] - centroids).argmin(axis=1) uc = np.unique(class_ids) cuts = np.array([y[class_ids == c].max() for c in uc]) y_cent = np.zeros_like(y) for c in uc: 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): """ natural breaks helper function Jenks natural breaks is kmeans in one dimension """ values = np.array(values) uv = np.unique(values) uvk = len(uv) if uvk < k: Warn('Warning: Not enough unique values in array to form k classes', UserWarning) Warn('Warning: setting k to %d' % uvk, UserWarning) k = uvk kres = _kmeans(values, k) sids = kres[-1] # centroids fit = kres[-2] class_ids = kres[0] cuts = kres[1] return (sids, class_ids, fit, cuts) @autojit def _fisher_jenks_means(values, classes=5, sort=True): """ Jenks Optimal (Natural Breaks) algorithm implemented in Python. 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. """ if sort: values.sort() 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 kclass
[docs]class Map_Classifier(object): """ Abstract class for all map classifications [Slocum2008]_ 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:~pysal.esda.mapclassify.Box_Plot * :class:~pysal.esda.mapclassify.Equal_Interval * :class:~pysal.esda.mapclassify.Fisher_Jenks * :class:~pysal.esda.mapclassify.Fisher_Jenks_Sampled * :class:~pysal.esda.mapclassify.HeadTail_Breaks * :class:~pysal.esda.mapclassify.Jenks_Caspall * :class:~pysal.esda.mapclassify.Jenks_Caspall_Forced * :class:~pysal.esda.mapclassify.Jenks_Caspall_Sampled * :class:~pysal.esda.mapclassify.Max_P_Classifier * :class:~pysal.esda.mapclassify.Maximum_Breaks * :class:~pysal.esda.mapclassify.Natural_Breaks * :class:~pysal.esda.mapclassify.Quantiles * :class:~pysal.esda.mapclassify.Percentiles * :class:~pysal.esda.mapclassify.Std_Mean * :class:~pysal.esda.mapclassify.User_Defined Utilities: In addition to the classifiers, there are several utility functions that can be used to evaluate the properties of a specific classifier for different parameter values, or for automatic selection of a classifier and number of classes. * :func:~pysal.esda.mapclassify.gadf * :class:~pysal.esda.mapclassify.K_classifiers """ def __init__(self, y): y = np.asarray(y).flatten() self.name = 'Map Classifier' self.y = y self._classify() self._summary() 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 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)
[docs] @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 like 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 a boolean configuring the outputted classifier to return the classifier object or not return_bins : bool a boolean configuring the outputted classifier to return the bins/breaks or not return_counts : bool a boolean configuring the outputted classifier to 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). Note ---- 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 pysal as ps >>> df = ps.pdio.read_files(ps.examples.get_path('columbus.dbf')) >>> classifier = ps.Quantiles.make(k=9) >>> classifier >>> classifications = df[['HOVAL', 'CRIME', 'INC']].apply(ps.Quantiles.make(k=9)) >>> classifications.head() HOVAL CRIME INC 0 8 0 7 1 7 1 8 2 2 3 5 3 4 4 0 4 1 6 3 >>> import pandas as pd; from numpy import linspace as lsp >>> data = [lsp(3,8,num=10), lsp(10, 0, num=10), lsp(-5, 15, num=10)] >>> data = pd.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 6.888888 2.222222 10.555556 8 7.444444 1.111111 12.777778 9 8.000000 0.000000 15.000000 >>> data.apply(ps.Quantiles.make(rolling=True)) 0 1 3 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 0 4 7 3 0 4 8 4 0 4 9 4 0 4 >>> dbf = ps.open(ps.examples.get_path('baltim.dbf')) >>> data = dbf.by_col_array('PRICE', 'LOTSZ', 'SQFT') >>> my_bins = [1, 10, 20, 40, 80] >>> classifications = [ps.User_Defined.make(bins=my_bins)(a) for a in data.T] >>> len(classifications) 3 >>> print(classifications) [array([4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 4, 1, 2, 2, 3, 4, 4, 3, 3, ... 2, 2, 2, 2])] """ # 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 = 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
[docs] def update(self, y=None, inplace=False, **kwargs): """ Add data or change classification parameters. Parameters ---------- y : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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): st = self._table_string() return st def __repr__(self): return self._table_string() def __call__(self, *args, **kwargs): """ 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)
[docs] def get_tss(self): """ Total sum of squares around class means 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
[docs] 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 _table_string(self, width=12, decimal=3): fmt = ".%df" % decimal fmt = "%" + fmt largest = max([len(fmt % i) for i in self.bins]) width = largest fmt = "%d.%df" % (width, decimal) fmt = "%" + fmt h1 = "Lower" h1 = h1.center(largest) h2 = " " h2 = h2.center(10) h3 = "Upper" h3 = h3.center(largest + 1) largest = "%d" % max(self.counts) largest = len(largest) + 15 h4 = "Count" h4 = h4.rjust(largest) table = [] header = h1 + h2 + h3 + h4 table.append(header) table.append("=" * len(header)) for i, up in enumerate(self.bins): if i == 0: left = " " * width left += " x[i] <= " else: left = fmt % self.bins[i - 1] left += " < x[i] <= " right = fmt % self.bins[i] row = left + right cnt = "%d" % self.counts[i] cnt = cnt.rjust(largest) row += cnt table.append(row) name = self.name top = name.center(len(row)) table.insert(0, top) table.insert(1, " ") table = "\n".join(table) return table
[docs] def find_bin(self, x): """ Sort input or inputs according to the current bin estimate Parameters ---------- x : array or numeric a value or array of values to fit within the estimated bins Returns ------- a bin index or array of bin indices that classify the input into one of the classifiers' bins """ x = np.asarray(x).flatten() uptos = [np.where(value < self.bins)[0] for value in x] bins = [x.min() if x.size > 0 else len(self.bins)-1 for x in uptos] #bail upwards bins = np.asarray(bins) if len(bins) == 1: return bins[0] else: return bins
[docs]class HeadTail_Breaks(Map_Classifier): """ Head/tail Breaks Map Classification for Heavy-tailed Distributions Parameters ---------- y : array (n,1), values to classify Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> import numpy as np >>> np.random.seed(10) >>> cal = load_example() >>> htb = HeadTail_Breaks(cal) >>> htb.k 3 >>> htb.counts array([50, 7, 1]) >>> htb.bins array([ 125.92810345, 811.26 , 4111.45 ]) >>> np.random.seed(123456) >>> x = np.random.lognormal(3, 1, 1000) >>> htb = HeadTail_Breaks(x) >>> htb.bins array([ 32.26204423, 72.50205622, 128.07150107, 190.2899093 , 264.82847377, 457.88157946, 576.76046949]) >>> htb.counts array([695, 209, 62, 22, 10, 1, 1]) Notes ----- Head/tail Breaks is a relatively new classification method developed and introduced by [Jiang2013]_ for data with a heavy-tailed distribution. Based on contributions by Alessandra Sozzi <alessandra.sozzi@gmail.com>. """ def __init__(self, y): Map_Classifier.__init__(self, y) self.name = 'HeadTail_Breaks' def _set_bins(self): x = self.y.copy() bins = [] bins = headTail_breaks(x, bins) self.bins = np.array(bins) self.k = len(self.bins)
[docs]class Equal_Interval(Map_Classifier): """ Equal Interval Classification Parameters ---------- y : array (n,1), values to classify k : int number of classes required Attributes ---------- yb : array (n,1), bin ids for observations, each value is the id of the class the observation belongs to yb[i] = j for j>=1 if bins[j-1] < y[i] <= bins[j], yb[i] = 0 otherwise bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> ei = Equal_Interval(cal, k = 5) >>> ei.k 5 >>> ei.counts array([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} """ def __init__(self, y, k=K): """ see class docstring """ self.k = k Map_Classifier.__init__(self, y) self.name = 'Equal Interval' 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. / 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(Map_Classifier): """ Percentiles Map Classification Parameters ---------- y : array attribute to classify pct : array percentiles default=[1,10,50,90,99,100] Attributes ---------- yb : array bin ids for observations (numpy array n x 1) bins : array the upper bounds of each class (numpy array k x 1) k : int the number of classes counts : int the number of observations falling in each class (numpy array k x 1) Examples -------- >>> cal = load_example() >>> p = Percentiles(cal) >>> p.bins array([ 1.35700000e-01, 5.53000000e-01, 9.36500000e+00, 2.13914000e+02, 2.17994800e+03, 4.11145000e+03]) >>> p.counts array([ 1, 5, 23, 23, 5, 1]) >>> p2 = Percentiles(cal, pct = [50, 100]) >>> p2.bins array([ 9.365, 4111.45 ]) >>> p2.counts array([29, 29]) >>> p2.k 2 """ def __init__(self, y, pct=[1, 10, 50, 90, 99, 100]): self.pct = pct Map_Classifier.__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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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 Box_Plot(Map_Classifier): """ Box_Plot Map Classification Parameters ---------- y : array attribute to classify hinge : float multiplier for IQR Attributes ---------- yb : array (n,1), bin ids for observations bins : array (n,1), the upper bounds of each class (monotonic) k : int the number of classes counts : array (k,1), the number of observations falling in each class low_outlier_ids : array indices of observations that are low outliers high_outlier_ids : 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 q is an array of the first three quartiles of y and IQR=q[2]-q[0] If 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 -------- >>> cal = load_example() >>> bp = Box_Plot(cal) >>> bp.bins array([ -5.28762500e+01, 2.56750000e+00, 9.36500000e+00, 3.95300000e+01, 9.49737500e+01, 4.11145000e+03]) >>> bp.counts array([ 0, 15, 14, 14, 6, 9]) >>> bp.high_outlier_ids array([ 0, 6, 18, 29, 33, 36, 37, 40, 42]) >>> cal[bp.high_outlier_ids] array([ 329.92, 181.27, 370.5 , 722.85, 192.05, 110.74, 4111.45, 317.11, 264.93]) >>> bx = Box_Plot(np.arange(100)) >>> bx.bins array([ -49.5 , 24.75, 49.5 , 74.25, 148.5 ]) """ def __init__(self, y, hinge=1.5): """ Parameters ---------- y : array (n,1) attribute to classify hinge : float multiple of inter-quartile range (default=1.5) """ self.hinge = hinge Map_Classifier.__init__(self, y) self.name = 'Box Plot' 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): Map_Classifier._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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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(Map_Classifier): """ Quantile Map Classification Parameters ---------- y : array (n,1), values to classify k : int number of classes required Attributes ---------- yb : array (n,1), bin ids for observations, each value is the id of the class the observation belongs to yb[i] = j for j>=1 if bins[j-1] < y[i] <= bins[j], yb[i] = 0 otherwise bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> q = Quantiles(cal, k = 5) >>> q.bins array([ 1.46400000e+00, 5.79800000e+00, 1.32780000e+01, 5.46160000e+01, 4.11145000e+03]) >>> q.counts array([12, 11, 12, 11, 12]) >>> """ def __init__(self, y, k=K): self.k = k Map_Classifier.__init__(self, y) self.name = 'Quantiles' def _set_bins(self): y = self.y k = self.k self.bins = quantile(y, k=k)
[docs]class Std_Mean(Map_Classifier): """ Standard Deviation and Mean Map Classification Parameters ---------- y : array (n,1), values to classify multiples : array the multiples of the standard deviation to add/subtract from the sample mean to define the bins, default=[-2,-1,1,2] Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> st = Std_Mean(cal) >>> st.k 5 >>> st.bins array([ -967.36235382, -420.71712519, 672.57333208, 1219.21856072, 4111.45 ]) >>> st.counts array([ 0, 0, 56, 1, 1]) >>> >>> st3 = Std_Mean(cal, multiples = [-3, -1.5, 1.5, 3]) >>> st3.bins array([-1514.00758246, -694.03973951, 945.8959464 , 1765.86378936, 4111.45 ]) >>> st3.counts array([ 0, 0, 57, 0, 1]) >>> """ def __init__(self, y, multiples=[-2, -1, 1, 2]): self.multiples = multiples Map_Classifier.__init__(self, y) self.name = 'Std_Mean' def _set_bins(self): y = self.y s = y.std(ddof=1) m = y.mean() 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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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 Maximum_Breaks(Map_Classifier): """ Maximum Breaks Map Classification Parameters ---------- y : array (n, 1), values to classify k : int number of classes required mindiff : float The minimum difference between class breaks Attributes ---------- yb : array (n, 1), bin ids for observations bins : array (k, 1), the upper bounds of each class k : int the number of classes counts : array (k, 1), the number of observations falling in each class (numpy array k x 1) Examples -------- >>> cal = load_example() >>> mb = Maximum_Breaks(cal, k = 5) >>> mb.k 5 >>> mb.bins array([ 146.005, 228.49 , 546.675, 2417.15 , 4111.45 ]) >>> mb.counts array([50, 2, 4, 1, 1]) >>> """ def __init__(self, y, k=5, mindiff=0): self.k = k self.mindiff = mindiff Map_Classifier.__init__(self, y) self.name = 'Maximum_Breaks' def _set_bins(self): xs = self.y.copy() k = self.k xs.sort() min_diff = self.mindiff d = xs[1:] - xs[:-1] diffs = d[np.nonzero(d > min_diff)] diffs = sp.unique(diffs) k1 = k - 1 if len(diffs) > k1: diffs = diffs[-k1:] mp = [] self.cids = [] for diff in diffs: ids = np.nonzero(d == diff) for id in ids: self.cids.append(id[0]) cp = ((xs[id] + xs[id + 1]) / 2.) mp.append(cp[0]) 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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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 Natural_Breaks(Map_Classifier): """ Natural Breaks Map Classification Parameters ---------- y : array (n,1), values to classify k : int number of classes required initial : int number of initial solutions to generate, (default=100) Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> import numpy >>> import pysal >>> numpy.random.seed(123456) >>> cal = pysal.esda.mapclassify.load_example() >>> nb = pysal.Natural_Breaks(cal, k=5) >>> nb.k 5 >>> nb.counts array([41, 9, 6, 1, 1]) >>> nb.bins array([ 29.82, 110.74, 370.5 , 722.85, 4111.45]) >>> x = numpy.array([1] * 50) >>> x[-1] = 20 >>> nb = pysal.Natural_Breaks(x, k = 5, initial = 0) Warning: Not enough unique values in array to form k classes Warning: setting k to 2 >>> nb.bins array([ 1, 20]) >>> nb.counts array([49, 1]) Notes ----- There is a tradeoff here between speed and consistency of the classification If you want more speed, set initial to a smaller value (0 would result in the best speed, if you want more consistent classes in multiple runs of Natural_Breaks on the same data, set initial to a higher value. """ def __init__(self, y, k=K, initial=100): self.k = k self.initial = initial Map_Classifier.__init__(self, y) self.name = 'Natural_Breaks' 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: Warn('Warning: Not enough unique values in array to form k classes', UserWarning) Warn("Warning: setting k to %d" % uvk, UserWarning) 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: # find an initial solution and then try to find an improvement res0 = natural_breaks(x, k) fit = res0[2] for i in xrange(self.initial): res = natural_breaks(x, k) fit_i = res[2] if fit_i < fit: res0 = res 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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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({'initial':kwargs.pop('initial', self.initial)}) if inplace: self._update(y, **kwargs) else: new = copy.deepcopy(self) new._update(y, **kwargs) return new
[docs]class Fisher_Jenks(Map_Classifier): """ Fisher Jenks optimal classifier - mean based Parameters ---------- y : array (n,1), values to classify k : int number of classes required Attributes ---------- yb : array (n,1), bin ids for observations bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> fj = Fisher_Jenks(cal) >>> fj.adcm 799.24000000000001 >>> fj.bins array([ 75.29, 192.05, 370.5 , 722.85, 4111.45]) >>> fj.counts array([49, 3, 4, 1, 1]) >>> """ def __init__(self, y, k=K): nu = len(np.unique(y)) if nu < k: raise ValueError("Fewer unique values than specified classes.") self.k = k Map_Classifier.__init__(self, y) self.name = "Fisher_Jenks" def _set_bins(self): x = self.y.copy() self.bins = np.array(_fisher_jenks_means(x, classes=self.k)[1:])
[docs]class Fisher_Jenks_Sampled(Map_Classifier): """ Fisher Jenks optimal classifier - mean based using random sample Parameters ---------- y : array (n,1), values to classify k : int number of classes required pct : float The percentage of n that should form the sample If pct is specified such that n*pct > 1000, then pct = 1000./n, unless truncate is False truncate : boolean truncate pct in cases where pct * n > 1000., (Default True) Attributes ---------- yb : array (n,1), bin ids for observations bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- (Turned off due to timing being different across hardware) """ 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. / n ids = np.random.random_integers(0, n - 1, int(n * pct)) 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 Map_Classifier.__init__(self, yr) self.yb, self.counts = bin1d(y, self.bins) self.name = "Fisher_Jenks_Sampled" self.y = y self._summary() # have to recalculate summary stats def _set_bins(self): fj = Fisher_Jenks(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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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 Jenks_Caspall(Map_Classifier): """ Jenks Caspall Map Classification Parameters ---------- y : array (n,1), values to classify k : int number of classes required Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> jc = Jenks_Caspall(cal, k = 5) >>> jc.bins array([ 1.81000000e+00, 7.60000000e+00, 2.98200000e+01, 1.81270000e+02, 4.11145000e+03]) >>> jc.counts array([14, 13, 14, 10, 7]) """ def __init__(self, y, k=K): self.k = k Map_Classifier.__init__(self, y) self.name = "Jenks_Caspall" 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 = 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 sp.unique(xb)]) cuts.shape = (len(cuts),) self.bins = cuts self.iterations = it
[docs]class Jenks_Caspall_Sampled(Map_Classifier): """ Jenks Caspall Map Classification using a random sample Parameters ---------- y : array (n,1), values to classify k : int number of classes required pct : float The percentage of n that should form the sample If pct is specified such that n*pct > 1000, then pct = 1000./n Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> x = np.random.random(100000) >>> jc = Jenks_Caspall(x) >>> jcs = Jenks_Caspall_Sampled(x) >>> jc.bins array([ 0.19770952, 0.39695769, 0.59588617, 0.79716865, 0.99999425]) >>> jcs.bins array([ 0.18877882, 0.39341638, 0.6028286 , 0.80070925, 0.99999425]) >>> jc.counts array([19804, 20005, 19925, 20178, 20088]) >>> jcs.counts array([18922, 20521, 20980, 19826, 19751]) >>> # 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 n problems. The logic is to apply Jenks_Caspall to a random subset of the y space and then bin the complete vector y on the bins obtained from the subset. This would trade off some "accuracy" for a gain in speed. """ def __init__(self, y, k=K, pct=0.10): self.k = k n = y.size if pct * n > 1000: pct = 1000. / n ids = np.random.random_integers(0, n - 1, int(n * pct)) 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 Map_Classifier.__init__(self, yr) self.yb, self.counts = bin1d(y, self.bins) self.name = "Jenks_Caspall_Sampled" self.y = y self._summary() # have to recalculate summary stats def _set_bins(self): jc = Jenks_Caspall(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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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 Jenks_Caspall_Forced(Map_Classifier): """ Jenks Caspall Map Classification with forced movements Parameters ---------- y : array (n,1), values to classify k : int number of classes required Attributes ---------- yb : array (n,1), bin ids for observations bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> jcf = Jenks_Caspall_Forced(cal, k = 5) >>> jcf.k 5 >>> jcf.bins array([[ 1.34000000e+00], [ 5.90000000e+00], [ 1.67000000e+01], [ 5.06500000e+01], [ 4.11145000e+03]]) >>> jcf.counts array([12, 12, 13, 9, 12]) >>> jcf4 = Jenks_Caspall_Forced(cal, k = 4) >>> jcf4.k 4 >>> jcf4.bins array([[ 2.51000000e+00], [ 8.70000000e+00], [ 3.66800000e+01], [ 4.11145000e+03]]) >>> jcf4.counts array([15, 14, 14, 15]) >>> """ def __init__(self, y, k=K): self.k = k Map_Classifier.__init__(self, y) self.name = "Jenks_Caspall_Forced" 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 = sp.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 sp.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 = sp.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 sp.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 sp.unique(xb)] self.bins = np.array(cuts) self.iterations = it
[docs]class User_Defined(Map_Classifier): """ User Specified Binning Parameters ---------- y : array (n,1), values to classify bins : array (k,1), upper bounds of classes (have to be monotically increasing) Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> cal = load_example() >>> bins = [20, max(cal)] >>> bins [20, 4111.4499999999998] >>> ud = User_Defined(cal, bins) >>> ud.bins array([ 20. , 4111.45]) >>> ud.counts array([37, 21]) >>> bins = [20, 30] >>> ud = User_Defined(cal, bins) >>> ud.bins array([ 20. , 30. , 4111.45]) >>> ud.counts array([37, 4, 17]) >>> Notes ----- If upper bound of user bins does not exceed max(y) we append an additional bin. """ def __init__(self, y, bins): if bins[-1] < max(y): bins.append(max(y)) self.k = len(bins) self.bins = np.array(bins) self.y = y Map_Classifier.__init__(self, y) self.name = 'User Defined' 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 : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs 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
[docs]class Max_P_Classifier(Map_Classifier): """ Max_P Map Classification Based on Max_p regionalization algorithm Parameters ---------- y : array (n,1), values to classify k : int number of classes required initial : int number of initial solutions to use prior to swapping Attributes ---------- yb : array (n,1), bin ids for observations, bins : array (k,1), the upper bounds of each class k : int the number of classes counts : array (k,1), the number of observations falling in each class Examples -------- >>> import pysal >>> cal = pysal.esda.mapclassify.load_example() >>> mp = pysal.Max_P_Classifier(cal) >>> mp.bins array([ 8.7 , 16.7 , 20.47, 66.26, 4111.45]) >>> mp.counts array([29, 8, 1, 10, 10]) """ def __init__(self, y, k=K, initial=1000): self.k = k self.initial = initial Map_Classifier.__init__(self, y) self.name = "Max_P" 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 = range(n) seeds = [np.nonzero(di == min( di))[0][0] for di in [np.abs(x - qi) for qi in q]] rseeds = np.random.permutation(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: rseeds = np.random.permutation(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 if tss1 < tss2: return False else: return True
[docs] def update(self, y=None, inplace=False, **kwargs): """ Add data or change classification parameters. Parameters ---------- y : array (n,1) array of data to classify inplace : bool whether to conduct the update in place or to return a copy estimated from the additional specifications. Additional parameters provided in **kwargs are passed to the init function of the class. For documentation, check the class constructor. """ kwargs.update({'initial':kwargs.pop('initial', self.initial)}) if inplace: self._update(y, bins, **kwargs) else: new = copy.deepcopy(self) new._update(y, bins, **kwargs) return new
def _fit(y, classes): """Calculate the total sum of squares for a vector y classified into classes Parameters ---------- y : array (n,1), variable to be classified classes : array (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["Fisher_Jenks"] = Fisher_Jenks kmethods['Natural_Breaks'] = Natural_Breaks kmethods['Maximum_Breaks'] = Maximum_Breaks
[docs]def gadf(y, method="Quantiles", maxk=15, pct=0.8): """ Evaluate the Goodness of Absolute Deviation Fit of a Classifier Finds the minimum value of k for which gadf>pct Parameters ---------- y : array (n, 1) values to be classified method : {'Quantiles, 'Fisher_Jenks', 'Maximum_Breaks', 'Natrual_Breaks'} maxk : int maximum value of k to evaluate pct : float The percentage of GADF to exceed Returns ------- k : int number of classes cl : object instance of the classifier at k gadf : float goodness of absolute deviation fit Examples -------- >>> cal = load_example() >>> qgadf = gadf(cal) >>> qgadf[0] 15 >>> qgadf[-1] 0.37402575909092828 Quantiles fail to exceed 0.80 before 15 classes. If we lower the bar to 0.2 we see quintiles as a result >>> qgadf2 = gadf(cal, pct = 0.2) >>> qgadf2[0] 5 >>> 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 -------- K_classifiers """ 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 K_classifiers(object): """ Evaluate all k-classifers and pick optimal based on k and GADF Parameters ---------- y : array (n,1), values to be classified pct : float The percentage of GADF to exceed Attributes ---------- best : object instance of the optimal Map_Classifier results : dictionary keys are classifier names, values are the Map_Classifier instances with the best pct for each classifer Examples -------- >>> cal = load_example() >>> ks = K_classifiers(cal) >>> ks.best.name 'Fisher_Jenks' >>> ks.best.k 4 >>> ks.best.gadf 0.84810327199081048 >>> Notes ----- This can be used to suggest a classification scheme. See Also -------- gadf """ def __init__(self, y, pct=0.8): results = {} best = gadf(y, "Fisher_Jenks", maxk=len(y) - 1, pct=pct) pct0 = best[0] k0 = best[-1] keys = kmethods.keys() keys.remove("Fisher_Jenks") results["Fisher_Jenks"] = 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]
def fj(x, k=5): y = x.copy() y.sort() d = {} initial = opt_part(y) # d has key = number of groups # value: list of ids, list of group tss, group size split_id = [initial[0]] tss = initial[1:] # left and right within tss sizes = [split_id - 1, len(y) - split_id] d[2] = [split_id, tss, sizes] return d def opt_part(x): """ Find optimal bi-partition of x values Parameters ----------- x : array (n,1), Array of attribute values Returns ------- opt_i : int partition index tss : float toal sum of squares left_min : float variance to the left of the break (including the break) right_min : float variance to the right of the break """ n = len(x) tss = np.inf opt_i = -999 for i in xrange(1, n): left = x[:i].var() * i right = x[i:].var() * (n - i) tss_i = left + right if tss_i < tss: opt_i = i tss = tss_i left_min = left right_min = right return (opt_i, tss, left_min, right_min)