Dimensionality reduction is used to reduce the dimensions of a data set to speed up a subsequent machine learning algorithm. It removes noise and redundant features, which improves the performance of the algorithm. In this article, I will introduce you to dimensionality reduction in machine learning and its implementation using Python.

## What is Dimensionality Reduction?

In real-world problems, the datasets on which we use machine learning algorithms contain millions of samples for each feature, which makes the process of learning a model very slow and it is very difficult to find a good solution. In such situations, we have to use the concept of dimensionality reduction which means to reduce the dimensions of a dataset.

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Reducing the dimensionality of dataset results in a loss of information, so while it speeds up the process of training a machine learning model, it can worsen model performance. So if the training process is very slow, you should always try to train your model first without reducing the dimensions on the original dataset.

While in some cases, it filters out noise and other unnecessary data, resulting in better performance of your model. In addition to getting better performance and speeding up the process, dimensionality reduction is also very useful for data visualization.

## Dimensionality Reduction using Python

We have a variety of machine learning algorithms available to reduce the dimensionality of a dataset. Principal component analysis (PCA) is the most popular algorithm for reducing the dimensions of a data set. It works by identifying the hyperplane closest to the data, and then it projects the data onto it.

PCA can be used to drastically reduce the dimensionality of most datasets, even if the datasets are highly nonlinear because this algorithm can at least get rid of unnecessary dimensions. Now letâ€™s see how to implement PCA for dimensionality reduction using Python:

[[-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.62642607e+255 -6.02307143e+255] [-9.62421024e+255 -6.02303580e+255] [-1.52883585e+256 3.45985862e+257] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002625e+255 -6.02312930e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002619e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [ 5.73820464e+257 3.35548554e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255]]

### Understanding PCA:

For each principal component, the algorithm finds a unit vector-centred on zero pointing in the direction of the principal components. PCA assumes that the dataset is centred around the origin, the PCA algorithm provided by Scikit-Learn takes care of the centring of the dataset, but if you plan to implement this algorithm yourself without use Scikit-Learn, remember to centre the data first.

Hereâ€™s how you can implement PCA without using Scikit-Learn for dimensionality reduction using Python:

[[-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.62642607e+255 -6.02307143e+255] [-9.62421024e+255 -6.02303580e+255] [-1.52883585e+256 3.45985862e+257] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002625e+255 -6.02312930e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002619e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [ 5.73820464e+257 3.35548554e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255] [-9.63002624e+255 -6.02312929e+255]]

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