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I have a function which returns a multidimensional array of k clusters. My algorith works for the most part, but I need it to return a categorical array instead of a multidimensional array. Here is my code:
import numpy as np
import pandas as pd
import random
from bokeh.sampledata.iris import flowers
from typing import List, Tuple
def get_closest(data_point: np.ndarray, centroids: np.ndarray):
"""
Takes a data_point and a nd.array of multiple centroids and returns the index of the centroid closest to data_point
by computing the euclidean distance for each centroid and picking the closest.
"""
N = centroids.shape[0]
dist = np.empty(N)
for i, c in enumerate(centroids):
dist[i] = np.linalg.norm(c - data_point)
index_min = np.argmin(dist)
return index_min
# Use these centroids in the first iteration of you algorithm if "Random Centroids" is set to False in the Dashboard
DEFAULT_CENTROIDS = np.array([[5.664705882352942, 3.0352941176470587, 3.3352941176470585, 1.0176470588235293],
[5.446153846153847, 3.2538461538461543, 2.9538461538461536, 0.8846153846153846],
[5.906666666666667, 2.933333333333333, 4.1000000000000005, 1.3866666666666667],
[5.992307692307692, 3.0230769230769234, 4.076923076923077, 1.3461538461538463],
[5.747619047619048, 3.0714285714285716, 3.6238095238095243, 1.1380952380952383],
[6.161538461538462, 3.030769230769231, 4.484615384615385, 1.5307692307692309],
[6.294117647058823, 2.9764705882352938, 4.494117647058823, 1.4],
[5.853846153846154, 3.215384615384615, 3.730769230769231, 1.2076923076923078],
[5.52857142857143, 3.142857142857143, 3.107142857142857, 1.007142857142857],
[5.828571428571429, 2.9357142857142855, 3.664285714285714, 1.1]])
def k_means(data_np: np.ndarray, k:int=3, n_iter:int=500, random_initialization=False) -> Tuple[np.ndarray, int]:
"""
:param data: your data, a numpy array with shape (n_entries, n_features)
:param k: The number of clusters to compute
:param n_iter: The maximal numnber of iterations
:param random_initialization: If False, DEFAULT_CENTROIDS are used as the centroids of the first iteration.
:return: A tuple (cluster_indices: A numpy array of cluster_indices,
n_iterations: the number of iterations it took until the algorithm terminated)
"""
# Initialize the algorithm by assigning random cluster labels to each entry in your dataset
k=k+1
centroids = data_np[random.sample(range(len(data_np)), k)]
labels = np.array([np.argmin([(el - c) ** 2 for c in centroids]) for el in data_np])
clustering = []
for k in range(k):
clustering.append(data_np[labels == k])
# Implement K-Means with a while loop, which terminates either if the centroids don't move anymore, or
# if the number of iterations exceeds n_iter
counter = 0
while counter < n_iter:
# Compute the new centroids, if random_initialization is false use DEFAULT_CENTROIDS in the first iteration
# if you use DEFAULT_CENTROIDS, make sure to only pick the k first entries from them.
if random_initialization is False and counter == 0:
centroids = DEFAULT_CENTROIDS[random.sample(range(len(DEFAULT_CENTROIDS)), k)]
# Update the cluster labels using get_closest
labels = np.array([get_closest(el, centroids) for el in data_np])
clustering = []
for i in range(k):
clustering.append(np.where(labels == i)[0])
counter += 1
new_centroids = np.zeros_like(centroids)
for i in range(k):
if len(clustering[i]) > 0:
new_centroids[i] = data_np[clustering[i]].mean(axis=0)
else:
new_centroids[i] = centroids[i]
# if the centroids didn't move, exit the while loop
if clustering is not None and (centroids == new_centroids).sum() == 0:
break
else:
centroids = new_centroids
pass
# return the final cluster labels and the number of iterations it took
return clustering, counter
# read and store the dataset
data: pd.DataFrame = flowers.copy(deep=True)
data = data.drop(['species'], axis=1)
data_np = np.asarray(data)
clustering, counter = k_means(data_np,4,500,False)
So clustering looks like so
clustering
[array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 57,
98], dtype=int64),
array([60, 93], dtype=int64),
array([ 50, 51, 52, 53, 54, 55, 56, 58, 61, 62, 63, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 86, 87, 89, 90, 91, 92, 94, 95, 96,
97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,
124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136,
137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149],
dtype=int64),
array([59, 64, 84, 85, 88], dtype=int64)]
However, what I'm looking for is an array like
clustering
array([1, 3, 2, ..., 4, 1, 4], dtype=int64)]
Also, the while loop is always terminating after 1 iteration which shouldn't be the case.
counter
1
EDIT1:
The code continues as follows.
def callback(attr, old, new):
# recompute the clustering and update the colors of the data points based on the result
k = slider_k.valued_throttled
init = select_init.value
clustering_new, counter_new = k_means(data_np,k,500,init)
pass
# Create the dashboard
# 1. A Select widget to choose between random initialization or using the DEFAULT_CENTROIDS on top
select_init = Select(title='Random Centroids',value='False',options=['True','False'])
# 2. A Slider to choose a k between 2 and 10 (k being the number of clusters)
slider_k = Slider(start=2,end=10,value=3,step=1,title='k')
# 4. Connect both widgets to the callback
select_init.on_change('value',callback)
slider_k.on_change('value_throttled',callback)
# 3. A ColumnDataSource to hold the data and the color of each point you need
source = ColumnDataSource(dict(petal_length=data['petal_length'],sepal_length=data['sepal_length'],petal_width=data['petal_width'],clustering=clustering))
# 4. Two plots displaying the dataset based on the following table, have a look at the images
# in the handout if this confuses you.
#
# Axis/Plot Plot1 Plot2
# X Petal length Petal width
# Y Sepal length Petal length
#
# Use a categorical color mapping, such as Spectral10, have a look at this section of the bokeh docs:
# https://docs.bokeh.org/en/latest/docs/user_guide/categorical.html#filling
plot1 = figure(plot_width=100,plot_height=100,title='Scatterplot of flowers distribution by petal length and sepal length')
plot1.yaxis.axis_label = 'Sepal length'
plot1.xaxis.axis_label = 'Petal length'
scatter1 = plot1.scatter(x='petal_length',y='sepal_length',source=source,fill_color=factor_cmap('clustering', palette=Spectral10, factors=clustering))
plot2 = figure(plot_width=100,plot_height=100,title='Scatterplot of flowers distribution by petal width and petal length')
plot2.yaxis.axis_label = 'Petal length'
plot2.xaxis.axis_label = 'Petal width'
scatter2 = plot2.scatter(x='petal_width',y='petal_length',source=source,fill_color=factor_cmap('clustering', palette=Spectral10, factors=clustering))
# 5. A Div displaying the currently number of iterations it took the algorithm to update the plot.
div = Div(text='Number of iterations: ')
Thus the end result should look like so
I'm not sure I understand what you need.
If clustering contains a list of arrays where each array represent a cluster and the ith array contains the indices of the samples that belong to the ith cluster and what you need is to convert this to a single vector of size number_of_samples that represent the cluster each sample belongs to you can do it like this:
def to_classes(clustering):
# Get number of samples (you can pass it directly to the function)
num_samples = sum(x.shape[0] for x in clustering)
indices = np.empty((num_samples,)) # An empty array with correct size
for ith, cluster in enumerate(clustering):
# use cluster indices to assign to correct the cluster index
indices[cluster] = ith
return indices
The loops exists after a single iteration because the break condition is wrong, I think what you want is actually
# note the !=
if clustering is not None and (centroids != new_centroids).sum() == 0:
break
Description: I have a sample: sample = [100, 86, 51, 100, 95, 100, 12, 61, 0, 0, 12, 86, 0, 52, 62, 76, 91, 91, 62, 91, 65, 91, 9, 83, 67, 58, 56]. I need to calculate third central moment of this sample.
My approach:
I'm making a table with top row being unique values from the sample and bottom row - frequency of each value from the top row:
table = dict(Counter(sample))
Then I'm calculating empirical k-th central moment with this formula:
def empirical_central_moment(table: dict, k):
mean = sum([value * frequency for value, frequency in table.items()]) / sum(list(table.values()))
N = sum(list(table.values()))
return sum([(value - mean)**k * frequency / N for value, frequency in table.items()])
Program:
from collections import Counter
def empirical_central_moment(table: dict, k):
mean = sum([value * frequency for value, frequency in table.items()]) / sum(list(table.values()))
N = sum(list(table.values()))
return sum([(value - mean)**k * frequency / N for value, frequency in table.items()])
sample = [100, 86, 51, 100, 95, 100, 12, 61, 0, 0, 12, 86, 0, 52, 62, 76, 91, 91, 62, 91, 65, 91, 9, 83, 67, 58, 56]
table = dict(Counter(sample))
print(empirical_central_moment(table, 3))
Problem: Instead of desired -545.33983 ... I'm getting -26721.65147589292 and I just can't wrap my head around as to why I'm gettting wrong. Will appreciate any help, thanks in advance.
Your answer is correct. Not sure what other answer you might be looking for. In general, and unless the purpose of this code is to exercise programming the logic of it, you don't need to reinvent the wheel and you'll be much faster and safer by doing something as simple as:
from scipy.stats import moment
sample = [100, 86, 51, 100, 95, 100, 12, 61, 0, 0, 12, 86, 0, 52, 62, 76, 91, 91, 62, 91, 65, 91, 9, 83, 67, 58, 56]
print(scipy.stats.moment(sample, moment=3, axis=0, nan_policy='propagate'))
I have a binary image size of NxMxK. I want to randomly pick up a non-zero pixel location in the image. However, I only can get a tupe of all non-zero pixel. How should I do it using python
I am using
location = np.where(array==True)
#Return
(array([ 66, 66, 66, ..., 133, 133, 133]), array([35, 35, 35, ..., 59, 59, 59]), array([102, 103, 104, ..., 105, 106, 107]))
My expected is that the pixel location likes (66,35,102) or (66,35,103)... because it is random
Update: This is my current solution
ln = np.random.choice (indices[0], size=1)[0]
lm = np.random.choice (indices[1], size=1)[0]
lk = np.random.choice (indices[2], size=1)[0]
Are you looking for
np.random.choice (location, size=1)
I have the two lists of arrays
splocations = [array([1,2,3]),array([4,5,6]),array([7,8,9])]
eviddisp = [array([10,11,12]), array([13,14,15])]
which I would like to multiply with each other such that I multiply each list element (which is an array) with each other list element. Here I would get a 3x2 matrix where each element is a vector. So the matrix element [0,0] would be
array([10, 22, 36]) = array([1,2,3]) * array([10,11,12])
So this matrix would be in fact a tensor of shape 3x2x3. How can I get this tensor/matrix?
I get that I need to use array(splocations) and array(eviddisp) somehow. By I realised, I am looking for a solution with numpy's tensordot, but I don't get it right. How to I proceed?
I think this is what you want, taking automatic broadcasting into account:
from numpy import array
splocations = [array([1,2,3]),array([4,5,6]),array([7,8,9])]
eviddisp = [array([10,11,12]), array([13,14,15])]
splocations = array(splocations)
viddisp = array(eviddisp)
result = splocations[:, None, :]*eviddisp
result
array([[[ 10, 22, 36],
[ 13, 28, 45]],
[[ 40, 55, 72],
[ 52, 70, 90]],
[[ 70, 88, 108],
[ 91, 112, 135]]])
I've a 2-Dim array containing the residual sum of squares of a given fit (unimportant here).
RSS[i,j] = np.sum((spectrum_theo - sp_exp_int) ** 2)
I would like to find the matrix element with the minimum value AND its position (i,j) in the matrix. Find the minimum element is OK:
RSS_min = RSS[RSS != 0].min()
but for the index, I've tried:
ij_min = np.where(RSS == RSS_min)
which gives me:
ij_min = (array([3]), array([20]))
I would like to obtain instead:
ij_min = (3,20)
If I try :
ij_min = RSS.argmin()
I obtain:
ij_min = 0,
which is a wrong result.
Does it exist a function, in Scipy or elsewhere, that can do it? I've searched on the web, but I've found answers leading only with 1-Dim arrays, not 2- or N-Dim.
Thanks!
The easiest fix based on what you have right now would just be to extract the elements from the array as a final step:
# ij_min = (array([3]), array([20]))
ij_min = np.where(RSS == RSS_min)
ij_min = tuple([i.item() for i in ij_min])
Does this work for you
import numpy as np
array = np.random.rand((1000)).reshape(10,10,10)
print np.array(np.where(array == array.min())).flatten()
in the case of multiple minimums you could try something like
import numpy as np
array = np.array([[1,1,2,3],[1,1,4,5]])
print zip(*np.where(array == array.min()))
You can combine argmin with unravel_index.
For example, here's an array RSS:
In [123]: np.random.seed(123456)
In [124]: RSS = np.random.randint(0, 99, size=(5, 8))
In [125]: RSS
Out[125]:
array([[65, 49, 56, 43, 43, 91, 32, 87],
[36, 8, 74, 10, 12, 75, 20, 47],
[50, 86, 34, 14, 70, 42, 66, 47],
[68, 94, 45, 87, 84, 84, 45, 69],
[87, 36, 75, 35, 93, 39, 16, 60]])
Use argmin (which returns an integer that is the index in the flattened array), and then pass that to unravel_index along with the shape of RSS to convert the index of the flattened array into the indices of the 2D array:
In [126]: ij_min = np.unravel_index(RSS.argmin(), RSS.shape)
In [127]: ij_min
Out[127]: (1, 1)
ij_min itself can be used as an index into RSS to get the minimum value:
In [128]: RSS_min = RSS[ij_min]
In [129]: RSS_min
Out[129]: 8