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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. li>
- 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 beli>
[A + (i-1) 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 .
- Bin-mean -median-mode-in-python-without-libraries/">median smoothing: in this method each bin value is replaced by its bin mean -median-mode-in-python-without-libraries/">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 -median-mode-in-python-without-libraries/">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 -median-mode-in-python-without-libraries/">median bin, as in antialiasing by mean bin value or smoothing by bin mean -median-mode-in-python-without-libraries/">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:
ML | Binning or Discretization __del__: Questions
How can I make a time delay in Python?
I would like to know how to put a time delay in a Python script.
Here is another example where something is run approximately once a minute:
You can use the
ML | Binning or Discretization __del__: Questions
How to delete a file or folder in Python?
How do I delete a file or folder in Python?
How do I merge two dictionaries in a single expression (taking union of dictionaries)?
I have two Python dictionaries, and I want to write a single expression that returns these two dictionaries, merged (i.e. taking the union). The
How can I get that final merged dictionary in
(To be extra-clear, the last-one-wins conflict-handling of
Say you have two dictionaries and you want to merge them into a new dictionary without altering the original dictionaries:
The desired result is to get a new dictionary (
And it is indeed a single expression.
Note that we can merge in with literal notation as well:
However, since many organizations are still on Python 2, you may wish to do this in a backward-compatible way. The classically Pythonic way, available in Python 2 and Python 3.0-3.4, is to do this as a two-step process:
In both approaches,
Not yet on Python 3.5, but want a single expression
If you are not yet on Python 3.5 or need to write backward-compatible code, and you want this in a single expression, the most performant while the correct approach is to put it in a function:
and then you have a single expression:
You can also make a function to merge an arbitrary number of dictionaries, from zero to a very large number:
This function will work in Python 2 and 3 for all dictionaries. e.g. given dictionaries
and key-value pairs in
Critiques of Other Answers
Don"t use what you see in the formerly accepted answer:
In Python 2, you create two lists in memory for each dict, create a third list in memory with length equal to the length of the first two put together, and then discard all three lists to create the dict. In Python 3, this will fail because you"re adding two
and you would have to explicitly create them as lists, e.g.
Similarly, taking the union of
This example demonstrates what happens when values are unhashable:
Here"s an example where
Another hack you should not use:
This uses the
Here"s an example of the usage being remediated in django.
Dictionaries are intended to take hashable keys (e.g.
From the mailing list, Guido van Rossum, the creator of the language, wrote:
It is my understanding (as well as the understanding of the creator of the language) that the intended usage for
Response to comments
Again, it doesn"t work for 3 when keys are not strings. The implicit calling contract is that namespaces take ordinary dictionaries, while users must only pass keyword arguments that are strings. All other callables enforced it.
This inconsistency was bad given other implementations of Python (PyPy, Jython, IronPython). Thus it was fixed in Python 3, as this usage could be a breaking change.
I submit to you that it is malicious incompetence to intentionally write code that only works in one version of a language or that only works given certain arbitrary constraints.
Yes. I must refer you back to the question, which is asking for a shallow merge of two dictionaries, with the first"s values being overwritten by the second"s - in a single expression.
Assuming two dictionaries of dictionaries, one might recursively merge them in a single function, but you should be careful not to modify the dictionaries from either source, and the surest way to avoid that is to make a copy when assigning values. As keys must be hashable and are usually therefore immutable, it is pointless to copy them:
Coming up with contingencies for other value types is far beyond the scope of this question, so I will point you at my answer to the canonical question on a "Dictionaries of dictionaries merge".
Less Performant But Correct Ad-hocs
These approaches are less performant, but they will provide correct behavior.
They will be much less performant than
You can also chain the dictionaries manually inside a dict comprehension:
or in Python 2.6 (and perhaps as early as 2.4 when generator expressions were introduced):
I"m only going to do the performance analysis of the usages known to behave correctly. (Self-contained so you can copy and paste yourself.)
In Python 3.8.1, NixOS:
Resources on Dictionaries
In your case, what you can do is:
This will, as you want it, put the final dict in
If you use Python 2, you can even remove the
If you use Python version 3.9.0a4 or greater, then you can directly use: