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There are three data smoothing methods:
 Binning. Binning methods smooth the sorted data values ‚Äã‚Äãby referring to their "neighborhood", that is, the values ‚Äã‚Äãaround them.
 Regression: matches function data values. Linear regression involves finding the "best‚" line to match two attributes (or variables) so that one attribute can be used to predict the other.
 Analyzing outliers : outliers can be detected by clustering, for example when similar values ‚Äã‚Äãare organized into groups or "clusters". Intuitively, values ‚Äã‚Äãthat fall outside the cluster set can be considered outliers.
Binning method for data smoothing —
Here we are dealing with Binning’s method for data smoothing. In this method, the data is first sorted and then the sorted values ‚Äã‚Äãare spread across multiple segments or cells . Since binning methods refer to a neighborhood of values, they perform local smoothing.
There are basically two types of binning —
 Binning is the same width (or distance). The simplest approach is to divide the variable range into k intervals of equal width. Spacing width — it’s just the range [A, B] of the variable divided by k,
w = (BA) / k
Thus, the interval of the i ^{ th } interval will be
[A + (i1) w, A + iw]
where i = 1, 2, 3‚Ä¶ ..k
Skewed data cannot be handled well with this method.  Binning of equal depth (or frequency): In binning of equal frequency, we divide the range [A, B] of a variable into intervals that contain (approximately) equal points; equal frequency may not be possible due to duplicate values.
How to smooth the data?
There are three approaches to performing smoothing:
 Bin smoothing mean s: when bin smoothing, each value in the bin is replaced by the bin’s mean .
 Binmean medianmodeinpythonwithoutlibraries/">median smoothing: in this method each bin value is replaced by its bin mean medianmodeinpythonwithoutlibraries/">median value.
 Bin Smoothing: When bin boundary smoothing, the minimum and maximum values ‚Äã‚Äãin a given bin are defined as bin boundaries. Each bin value is then replaced with the closest cutoff value.
Sorted data by price (in dollars): 2, 6, 7, 9, 13, 20, 21, 25, 30
Partition using equal frequency approach: Bin 1: 2, 6, 7 Bin 2: 9, 13, 20 Bin 3: 21, 24, 30 Smoothing by bin mean : Bin 1: 5, 5, 5 Bin 2: 14 , 14, 14 Bin 3: 25, 25, 25 Smoothing by bin mean medianmodeinpythonwithoutlibraries/">median: Bin 1: 6, 6, 6 Bin 2: 13, 13, 13 Bin 3: 24, 24, 24 Smoothing by bin boundary: Bin 1: 2 , 7, 7 Bin 2: 9, 9, 20 Bin 3: 21, 21, 30
Binning can also be used as a sampling method ... Here discretization refers to the process of transforming or breaking down continuous attributes, features, or variables into discrete or nominal attributes / features / variables / intervals.
For example, attribute values ‚Äã‚Äãcan be sampled by applying equal width or equal frequency binning and then replacing each bin value with the mean or mean medianmodeinpythonwithoutlibraries/">median bin, as in antialiasing by mean bin value or smoothing by bin mean medianmodeinpythonwithoutlibraries/">medians, respectively. Continuous values ‚Äã‚Äãcan then be converted to a nominal or sampled value that matches the corresponding bin value.
Below is the Python implementation:

bin_mean medianmodeinpythonwithoutlibraries/">median
import
numpy as np
from sklearn.linear_model
import
LinearRegression
from
sklearn
import
linear_model
# import statsmodels.api as sm
import
statistics
import
math
from
collections
import
OrderedDict
x
=
[]
print
(
"enter the data"
)
x
=
list
(
map
(
float
,
input
(). split ()))
print
(
" enter the number of bins "
)
bi
=
int
(
input
())
# X_dict will store data in sorted order
X_dict
=
OrderedDict ()
# x_old will store the original data
x_old
=
{}
# x_new will store data after binning
x_new
=
{}
for
i
in
range
(
len
(x)) :
X_dict [i]
=
x [i]
x_old [ i]
=
x [i]
x_dict
=
sorted
(X_dict.items (), key
=
lambda
x: x [
1
])
# list of lists (bins)
binn
=
[]
# variable to find the average of each bin
avrg
=
[]
i
=
0
k
=
0
num_of_data_in_each_bin
=
int
(math.ceil (
len
(x)
/
bi))
# executing binning
for
g, h
in
X_dict.items ():
if
(i & lt; num_of_data_in_each_bin):
avrg.append (h)
i
=
i
+
1
elif
(i
=
=
num_of_data_in_each_bin):
k
=
k
+
1
i
=
0
binn. append (statistics.mean medianmodeinpythonwithoutlibraries/">median (avrg))
avrg
=
[]
avrg.append (h)
i
=
i
+
1
binn.append (statistics.mean medianmodeinpythonwithoutlibraries/">median (avrg))
# save the new value of each of the data
i
=
0
j
=
0
for
g, h
in
X_dict.items ():
if
(i & lt; num_of_data_in_each_bin):
x_new [g]
=
round
(binn [j],
3
)
i
=
i
+
1
else
:
i
=
0
j
=
j
+
1
x_new [g]
=
round
(binn [j],
3
)
i
=
i
+
1
print
(
"number of data in each bin"
)
print
(math.ceil (
len
(x)
/
bi))
for
i
in
range (
0
,
len
(x)):
print
(
’index {2} old value {0} new value {1} ’
.
format
(x_old [i], x_new [i], i))
bin_boundary
import
numpy as np
from
sklearn.linear_model
import
LinearRegression
from
sklearn
import
linear_model
# import statsmodels.api as sm
import
statistics
import
math
from
collections
import
OrderedDict
x
=
[]
print
(
"enter the data"
)
x
=
list
(
map
(
float
,
input
(). split ()))
print
(
" enter the number of bins "
)
bi
=
int
(
input
())
# X_dict will store data in sorted order
X_dict
=
OrderedDict ()
# x_old will store the original data
x_old
=
{}
# x_new will store data after binning
x_new
= {}
for
i
in
range
(
len
( x)):
X_dict [i]
=
x [i]
x_old [i]
=
x [i]
x_dict
=
sorted
(X_dict.items (), key
=
lambda
x: x [
1
] )
# list of lists (bins)
binn
=
[]
# variable to find the average of each bin
avrg
=
[]
i
=
0
k
=
0
num_of_data_in_each_bin
=
int
(math.ceil (
len
(x)
/
bi))
for
g, h
in
X_dict.items ():
if
(i & lt; num_of_data_in_each_bin) :
avrg.append (h)
i
=
i
+
1
elif
(i
=
=
num_of_data_in_each_bin):
k
=
k
+
1
i
=
0
code class = "undefined spaces">
x_old [i]
=
x [i]
x_dict
=
sorted
(X_dict.items (), key
=
lambda
x: x [
1
])
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ML  Binning or Discretization __del__: Questions
How can I make a time delay in Python?
5 answers
I would like to know how to put a time delay in a Python script.
2973
Answer #1
import time
time.sleep(5) # Delays for 5 seconds. You can also use a float value.
Here is another example where something is run approximately once a minute:
import time
while True:
print("This prints once a minute.")
time.sleep(60) # Delay for 1 minute (60 seconds).
2973
Answer #2
You can use the sleep()
function in the time
module. It can take a float argument for subsecond resolution.
from time import sleep
sleep(0.1) # Time in seconds
ML  Binning or Discretization __del__: Questions
How to delete a file or folder in Python?
5 answers
How do I delete a file or folder in Python?
2639
Answer #1
os.remove()
removes a file.
os.rmdir()
removes an empty directory.
shutil.rmtree()
deletes a directory and all its contents.
Path
objects from the Python 3.4+ pathlib
module also expose these instance methods:
pathlib.Path.unlink()
removes a file or symbolic link.
pathlib.Path.rmdir()
removes an empty directory.
We hope this article has helped you to resolve the problem. Apart from ML  Binning or Discretization, check other __del__related topics.
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Angelo Porretti
Munchen  20230325
Maybe there are another answers? What ML  Binning or Discretization exactly means?. Will use it in my bachelor thesis
Manuel OConnell
Tallinn  20230325
Maybe there are another answers? What ML  Binning or Discretization exactly means?. I am just not quite sure it is the best method
Angelo Lehnman
Massachussetts  20230325
Simply put and clear. Thank you for sharing. ML  Binning or Discretization and other issues with StackOverflow was always my weak point 😁. Will get back tomorrow with feedback
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