What is Dimensionality Reduction in Machine Learning?

Machine learning is nothing but a research field that allows computers without any specific programming to “learn” like humans. High-dimensionality statistics and dimensionality reduction techniques that have been used for data visualization. These techniques are applied in machine learning to simplify a classification or regression dataset to fit a predictive model better. In this article, we give a gentle introduction to dimensionality reduction for machine learning. Machine learning is growing at a breakneck pace. Get the best machine learning certification and become a machine learning expert in no time!


Table of contents

  • What is Dimensionality Reduction?
  • Why is Dimensionality Reduction significant in Machine Learning?
  • Dimensionality Pros and Cons
  • Dimensionality Reduction Methods
  • Conclusion


So, let’s dive into what Dimensionality Reduction is. Let’s go!


What is Dimensionality Reduction?

There are always too many variables in machine learning classification problems based on which the final classification is performed. These factors are variables called features. The greater the number of characteristics, the harder it becomes to imagine and then work on the training package. Most of these characteristics are often correlated, and thus redundant. This is where algorithms for dimensionality reduction come into play. Dimensionality reduction is the method of reducing, by having a set of key variables, the number of random variables under consideration. It can be divided into feature discovery and extraction of features.


Why is Dimensionality Reduction significant in Machine Learning?

A primary e-mail classification issue can be explored via an intuitive instance of dimensionality reduction, where we need to identify whether or not the e-mail is spam. A large variety of features may be involved, such as whether or not the e-mail has a general title, the content of the e-mail, whether or not the e-mail uses a template, etc. Some of these characteristics can, however, overlap. In another case, as both of the above are associated to a high degree, a classification problem that relies on both humidity and rainfall can be collapsed into only one underlying feature. Thus, in such problems, we can reduce the number of characteristics. It can be difficult to imagine a 3-D classification problem, while a 2-D one can be mapped to simple 2-dimensional space and a 1-D problem to a simple line.


Dimensionality Pros and Cons

Dimensionality reduction allows us to forecast outcomes, based on some predictors. But it has some advantages and disadvantages that come with it. Here are some of them.


  • This helps to compact data, and thus to reduce storage space.
  • This lowers computing time.
  • It also helps to eliminate unnecessary, if any, functionality.



  • This will contribute to a certain amount of data loss.
  • PCA appears to find linear, which is often undesirable, associations between variables.
  • In cases where the mean and covariance are not adequate to describe datasets, PCA fails.
  • We can not know how many primary components to keep-some thumb rules are enforced in practice.


Dimensionality Reduction Methods


The most popular and well-known techniques of dimensionality reduction are those that apply linear transformations, such as

  • PCA (Principal Component Analysis): PCA rotates and projects data in the direction of increasing variance, which is widely used for dimensionality reduction in continuous data. The principal components are the functions with the highest variance.
  • Factor Analysis: A tool used to minimize a large number of variables into smaller numbers of variables. To find the most significant ones, the data observed values are represented as functions of a variety of possible causes. A linear transformation of lower-dimensional latent factors and added Gaussian noise are thought to trigger the observations.
  • LDA (Linear Discriminant Analysis): It projects data in a manner that maximizes class separability. The projection closely incorporates examples from the same class—the projection positions examples from various groups far apart.


Non- linear:

Where the data does not lie on a linear subspace, non-linear transformation methods or various learning methods are used. It is based upon a manifold hypothesis, which states that the most critical knowledge is concentrated in a limited number of low dimensional manifolds in a high dimensional structure. If a linear subspace is a flat sheet of paper, then a basic example of a non-linear manifold is a paper’s rolled-up sheet. Informally, in non-linear dimensionality reduction, this is called a Swiss roll, a canonical problem. Some standard methods of multiple learning are

  1. Multidimensional scaling (MDS): A method used in geometrical spaces to evaluate data’s similarity or dissimilarity as distances. Project data to a lower dimension such that data points in the higher dimension close to each other (in Euclidean distance) are also close in the lower dimension. 
  2. Isometric Feature Mapping (Isomap): Projects data (rather than Euclidean distance as in MDS) to a lower dimension while retaining the geodesic distance. The smallest distance between two points on a curve is the geodetic distance.
  3. Locally Linear Embedding (LLE): recovers from linear fits, global non-linear structure. Each local patch of the manifold, provided enough data, can be written as a linear, weighted sum of its neighbors.
  4. Hessian Eigen Mapping (HLLE): Projects data to a smaller degree while retaining the local neighborhood such as LLE, but uses the Hessian operator to achieve this outcome and hence the term better.
  5. Spectral Embedding (Laplacian Eigenmaps): Uses spectral techniques by mapping nearby inputs to nearby outputs to minimize dimensionality. This preserves locality instead of local linearity.
  6. t-distributed Stochastic Neighbor Embedding (t-SNE): Stochastic Neighbor Embedding (t-SNE) t-distributed: Calculates the probability that pairs of data points are connected in high-dimensional space and then selects a low-dimensional embedding that generates a similar distribution.



For dimensionality reduction and no mapping of techniques to issues, there is no best technique. Machine learning experts suggest the best way is to use systematic, controlled trials to discover what techniques of dimensionality reduction result in the best results on your dataset when combined with your model of choice. Linear algebra and multiple learning strategies usually presume that all input features have the same scale or distribution. This implies that if the input variables have different scales or units, it is good practice to either normalize or standardize data before using these approaches.