Develop Reference

Difference between Normalizer and MinMaxScaler

I'm trying to understand the effects of applying the Normalizer or applying MinMaxScaler or applying both in my data. I've read the docs in SKlearn, and saw some examples of use. I understand that MinMaxScaler is important (is important to scale the features), but what about Normalizer?
It keeps unclear to me the practical result of using the Normamlizer in my data.
MinMaxScaler is applied column-wise, Normalizer is apllied row-wise. What does it implies? Should I use the Normalizer or just use the MinMaxScale or should use then both?

As you have said,
MinMaxScaler is applied column-wise, Normalizer is applied row-wise.
Do not confuse Normalizer with MinMaxScaler. The Normalizer class from Sklearn normalizes samples individually to unit norm. It is not column based but a row-based normalization technique. In other words, the range will be determined either by rows or columns.
So, remember that we scale features not records, because we want features to have the same scale, so the model to be trained will not give different weights to different features based on their range. If we scale the records, this will give each record its own scale, which is not what we need.
So, if features are represented by rows, then you should use the Normalizer. But in most cases, features are represented by columns, so you should use one of the scalers from Sklearn depending on the case:
MinMaxScaler transforms features by scaling each feature to a given range. It scales and translates each feature individually such that it is in the given range on the training set, e.g. between zero and one.
The transformation is given by:
X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min
where min, max = feature_range.
This transformation is often used as an alternative to zero mean, unit variance scaling.
StandardScaler standardizes features by removing the mean and scaling to unit variance. The standard score of a sample x is calculated as:
z = (x - u) / s. Use this if the data distribution is normal.
RobustScaler is robust to outliers. It removes the median and scales the data according to IQR (Interquartile Range). The IQR is the range between the 25th quantile and the 75th quantile.

Different F1 scores for different preprocessing techniques- sklearn

I am building a classification model using sklearn's GradientBoostingClassifier. For the same model, I tried different preprocessing techniques: StandarScaler, Scale, and Normalizer on the same data but I am getting different f1_scores each time. For StandardScaler, it is highest and lowest for Normalizer. Why is it so? Is there any other technique for which I can get an even higher score?

The difference lies in their respective definitions:
StandardScaler: Standardize features by removing the mean and scaling to unit variance
Normalizer: Normalize samples individually to unit norm.
Scale: Standardize a dataset along any axis. Center to the mean and component wise scale to unit variance.
The data used to fit your model will change, so will the F1 score.
Here is a useful link comparing different scalers : https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#sphx-glr-auto-examples-preprocessing-plot-all-scaling-py

How do you calculate the training error and validation error of a linear regression model?

I have a linear regression model and my cost function is a Sum of Squares Error function. I've split my full dataset into three datasets, training, validation, and test. I am not sure how to calculate the training error and validation error (and the difference between the two).
Is the training error the Residual Sum of Squares error calculated using the training dataset?
An example of what I'm asking: So if I was doing this in Python, and let's say I had 90 data-points in the training data set, then is this the correct code for the training error?
y_predicted = f(X_train, theta) #predicted y-value at point x, where y_train is the actual y-value at x
training_error = 0
for i in range(90):
out = y_predicted[i] - y_train[i]
out = out*out
training_error+=out
training_error = training_error/2
print('The training error for this regression model is:', training_error)

This is mentioned in a comment on the post but you need to divide by the total number of samples to get a number that you can compare between validation and test sets.
Simply changed the code would be:
y_predicted = f(X_train, theta) #predicted y-value at point x, where y_train is the actual y-value at x
training_error = 0
for i in range(90):
out = y_predicted[i] - y_train[i]
out = out*out
training_error+=out
#change 2 to 90
training_error = training_error/90
print('The training error for this regression model is:', training_error)
The goal of this is so you can compare two different subsets of data using the same metric. You had a divide by 2 in there which was ok as well as long as you are also dividing by the number of samples.
Another way you can do this in Python is by using the sci-kit learn library, it already has the function.
see below.
from sklearn.metrics import mean_squared_error
training_error = mean_squared_error(y_train,y_predicted)
Also generally when making calculations like this it is better and faster to use matrix multiplication instead of a for loop. In the context, of this question 90 records is quite small but when you start working with larger sample sizes you could try something like this utilizing numpy.
import numpy as np
training_error = np.mean(np.square(np.array(y_predicted)-np.array(y_train)))
All 3 ways should get you similar results.

When scale the data, why the train dataset use 'fit' and 'transform', but the test dataset only use 'transform'?

When scale the data, why the train dataset use 'fit' and 'transform', but the test dataset only use 'transform'?
SAMPLE_COUNT = 5000
TEST_COUNT = 20000
seed(0)
sample = list()
test_sample = list()
for index, line in enumerate(open('covtype.data','rb')):
if index < SAMPLE_COUNT:
sample.append(line)
else:
r = randint(0,index)
if r < SAMPLE_COUNT:
sample[r] = line
else:
k = randint(0,index)
if k < TEST_COUNT:
if len(test_sample) < TEST_COUNT:
test_sample.append(line)
else:
test_sample[k] = line
from sklearn.preprocessing import StandardScaler
for n, line in enumerate(sample):
sample[n] = map(float, line.strip().split(','))
y = np.array(sample)[:,-1]
scaling = StandardScaler()
X = scaling.fit_transform(np.array(sample)[:,:-1]) ##here use fit and transform
for n,line in enumerate(test_sample):
test_sample[n] = map(float,line.strip().split(','))
yt = np.array(test_sample)[:,-1]
Xt = scaling.transform(np.array(test_sample)[:,:-1])##why here only use transform
As the annotation says, why Xt only use transform but no fit?

We use fit_transform() on the train data so that we learn the parameters of scaling on the train data and in the same time we scale the train data.
We only use transform() on the test data because we use the scaling paramaters learned on the train data to scale the test data.
This is the standart procedure to scale. You always learn your scaling parameters on the train and then use them on the test. Here is an article that explane it very well : https://sebastianraschka.com/faq/docs/scale-training-test.html

We have two datasets : The training and the test dataset. Imagine we have just 2 features :
'x1' and 'x2'.
Now consider this (A very hypothetical example):
A sample in the training data has values: 'x1' = 100 and 'x2' = 200
When scaled, 'x1' gets a value of 0.1 and 'x2' a value of 0.1 too. The response variable value is 100 for this. These have been calculated w.r.t only the training data's mean and std.
A sample in the test data has the values : 'x1' = 50 and 'x2' = 100. When scaled according to the test data values, 'x1' = 0.1 and 'x2' = 0.1. This means that our function will predict response variable value of 100 for this sample too. But this is wrong. It shouldn't be 100. It should be predicting something else because the not-scaled values of the features of the 2 samples mentioned above are different and thus point to different response values. We will know what the correct prediction is only when we scale it according to the training data because those are the values that our linear regression function has learned.
I have tried to explain the intuition behind this logic below:
We decide to scale both the features in the training dataset before applying linear regression and fitting the linear regression function. When we scale the features of the training dataset, all 'x1' features get adjusted according to the mean and the standard deviations of the different samples w.r.t to their 'x1' feature values. Same thing happens for 'x2' feature.
This essentially means that every feature has been transformed into a new number based on just the training data. It's like Every feature has been given a relative position. Relative to the mean and std of just the training data. So every sample's new 'x1' and 'x2' values are dependent on the mean and the std of the training data only.
Now what happens when we fit the linear regression function is that it learns the parameters (i.e, learns to predict the response values) based on the scaled features of our training dataset. That means that it is learning to predict based on those particular means and standard deviations of 'x1' and 'x2' of the different samples in the training dataset. So the value of the predictions depends on the:
*learned parameters. Which in turn depend on the
*value of the features of the training data (which have been scaled).And because of the scaling the training data's features depend on the
*training data's mean and std.
If we now fit the standardscaler() to the test data, the test data's 'x1' and 'x2' will have their own mean and std. This means that the new values of both the features will in turn be relative to only the data in the test data and thus will have no connection whatsoever to the training data. It's almost like they have been subtracted by and divided by random values and have got new values now which do not convey how they are related to the training data.

Any transformation you do to the data must be done by the parameters generated by the training data.
Simply what fit() method does is create a model that extracts the various parameters from your training samples to do the neccessary transformation later on. transform() on the other hand is doing the actual transformation to the data itself returning a standardized or scaled form.
fit_transform() is just a faster way of doing the operations of fit() and transform() consequently.
Important thing here is that when you divide your dataset into train and test sets what you are trying to achieve is somewhat simulate a real world application. In a real world scenario you will only have training data and you will develop a model according to that and predict unseen instances of similar data.
If you transform the entrire data with fit_transform() and then split to train test you violate that simulation approach and do the transformation according to the unseen examples as well. Which will inevatibly result in an optimistic model as you already somewhat prepared your model by the unseen samples metrics as well.
If you split the data to train test and apply fit_transform() to both you will also be mistaken as your first transformation of train data will be done by train splits metrics only and your second will be done by test metrics only.
The right way to do these preprocessings is to train any transformer with train data only and do the transformations to the test data. Because only then you can be sure that your resulting model represents a real world solution.
Following this it actually doesnt matter if you
fit(train) then transform(train) then transform(test) OR
fit_transform(train) then transform(test)

fit() is used to compute the parameter needed for transformation and transform() is for scaling the data to convert into standard format for the model.
fit_tranform() is combination of two which is doing above work in efficiently.
Since fit_transform() is already computing and transforming the training data only transformation for testing data is left,since parameter needed for transformation is already computed and stored only transformation() of testing data is left therefor only transform() is used instead of fit_transform().

there could be two approaches:
1st approach scale with fit and transform train data, transform only test data
2nd fit and transform the whole set :train + test
if you think about: how will the model handle scaling when goes live?: When new data arrives, new data will behave just like the unseen test data in your backtest.
In the 1st case , new data will will just be scale transformed and your model backtest scaled values remain unchanged.
But in the 2nd case when new data comes then you will need to fit transform the whole dataset , that means that the backtest scaled values will no longer be the same and then you need to re-train the model..if this task can be done quickly then I guess it is ok
but the 1st case requires less work...
and if there are big differences between scaling in train and test then probably the data is non stationary and ML is probably not a good idea

fit() and transform() are the two methods used to generally account for the missing values in the dataset.The missing values can be filled either by computing the mean or the median of the data and filling that empty places with that mean or median.
fit() is used to calculate the mean or the median.
transform() is used to fill in missing values with the calculated mean or the median.
fit_tranform() performs the above 2 tasks in a single stretch.
fit_transform() is used for the training data to perform the above.When it comes to validation set only transform() is required since you dont want to change the way you handle missing values when it comes to the validation set, because by doing so you may take your model by surprise!! and hence it may fail to perform as expected.

we use fit() or fit_transform() in order to learn (to train the model) on the train data set. transform() can be used on the trained model against the test data set.

fit_transform() - learn the parameter of scaling (Train data)
transform() - Apply those learned scaling method here (Test data)
ss = StandardScaler()
X_train = ss.fit_transform(X_train) #here we need to feed this to the model to learn so it will learn the parameter of scaling
X_test = ss.transform(X_test) #It will use the learn parameter to transform

Scaling test data to 0 and 1 using MinMaxScaler

Using the MinMaxScaler from sklearn, I scale my data as below.
min_max_scaler = preprocessing.MinMaxScaler()
X_train_scaled = min_max_scaler.fit_transform(features_train)
X_test_scaled = min_max_scaler.transform(features_test)
However, when printing X_test_scaled.min(), I have some negative values (the values do not fall between 0 and 1). This is due to the fact that the lowest value in my test data was lower than the train data, of which the min max scaler was fit.
How much effect does not having exactly normalized data between 0 and 1 values have on the SVM classifier? Also, is it bad practice to concatenate the train and test data into a single matrix, perform min-max scaling to ensure values are between 0 and 1, then seperate them again?

If you can scale all your data in one shot this would be better because all your data are managed by the Scaler in a logical way (all between 0 and 1). But for the SVM algorithm, there must be no difference as the scaler will extend the scale. There's still the same difference even if it is negative.
In the documentation we can see that there are negative values so I don't think it has an impact on the result

For this scaling it probably doesn't matter much in practice, but in general you should not use your test data to estimate any parameters of the preprocessing. This can severely bias you results for more complex preprocessing steps.
There is really no reason why you would want to concatenate the data here, the SVM will deal with it.
If you would be using a model that needs positive values and your test data is not made positive, you might consider another strategy than the MinMaxScaler.