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Principal Component Analysis in Data Science: Understanding The Basics of PCA

Principal Component Analysis (PCA) is a statistical technique that allows one to identify a set of representative features from a larger dataset. The original motivation for principal component analysis was the problem of robust estimation in data analysis. Today, PCA can be seen as a valuable tool for data science practitioners as it is used to address many problems in data analysis and modeling, including finding new insights into existing data sets.

 

In other words, Principal component analysis (PCA) is a statistical technique that allows you to summarize the variation in a set of observations or a data matrix.

 

In this article, we will discuss how principal component analysis works and what it can be used for. We will also demonstrate how you can apply principal component analysis in your projects.

What is Principal Component Analysis (PCA)?

Principal Component Analysis (PCA) is a method for transforming data into a new form by extracting its principal components. The principal components are linear transformations of the original variable with the largest variance-to-mean ratio. It is also known as singular value decomposition (SVD) and is one of the most famous techniques in data science.

 

For example, if we have a variable that represents the number of times a person has been to the gym in the last week, it may be helpful to understand this variable by breaking it down into two components: 

 
  • One that represents how often they went to the gym 

  • Another that represents how long they stayed at the gym. 

 

In this case, it would be helpful to see how many times they went to the gym and how many hours they spent there.

 

Detailed explanation 

Principal Component Analysis (PCA) is a technique for transforming a large set of variables into a smaller set that captures the maximum information from the original data. It is often used in data science to combine multiple variables into one 'super' variable, representing the most important concepts or variables in the dataset.

 

The goal of PCA is to find and select a single variable that explains as much of the variation in your data as possible. This enables you to use this variable to measure your dataset and extract insights from it rather than looking at all the features simultaneously.

 

In general terms, PCA tries to reduce data dimensionality by finding a low-dimensional solution to a linear system of equations. This can be achieved by transforming the original data into an orthogonal matrix whose columns are uncorrelated. In this process, each variable is given its own row vector, which is then transformed into an orthogonal matrix by applying the Gram–Schmidt procedure to find the eigenvectors of that matrix. The first principal component (PC1) accounts for up to 75% of the total variation in the original dataset, with only 16% variance remaining after PCA is applied.

 

For a detailed and technical explanation of PCA in data science, refer to the popular data science course in Bangalore, co-powered by IBM. 

 

Understanding the concept behind PCA

 

The concept behind PCA is that if you have n observations in your dataset, there are n-1 dimensions in your space. Each observation has k features (or attributes). 

The first step is finding orthogonalized subspaces containing as much information as possible while minimizing variance among each observation's features. This process is called singular value decomposition (SVD). 

 

The algorithm iterates through these steps until no more iterations are necessary or until convergence occurs—which could take quite a long time, depending on how big your dataset is!

 

Steps involved in Principal Component Analysis

 
  1. Standardizing the desired dataset 

  2. Computing the variance matrix for the features of the dataset 

  3. Calculating the covariance matrix's eigenvalues and eigenvectors

  4. Organizing the eigenvalues ​​and their corresponding eigenvectors

  5. Selecting an eigenvalue to form an eigenvector values

  6. Transforming the original matrix 

 

Applications of PCA 

 
  • Finding the inter-relation between the datasets

  • An effective way to visualize and interpret the data

  • The quantity of variables is reduced, simplifying further analysis.

  • It is frequently used to represent the genetic separation and similarity of populations.

 

Benefits of using PCA

 
  • PCA assists in accelerating the data mining process 

  • In addition to removing correlated features, it aids in data compression.

  • PCA converts high-dimensional data into low-dimensional data, which enhances data visualization. 

 

Drawbacks of using PCA

Apart from having many benefits, PCA has some negative points that can trigger the data science process. Some of them are: 

 
  • Sometimes It can lead to data loss 

  • It frequently exposes linear correlations between variables, which can be problematic.

  • It is ineffective when meaning and covariance alone are insufficient to define datasets.

 

Conclusion

Overall, PCA is fundamental to many data science applications. There are plenty of advantages to implementing PCA in your data science workflows. It can be used to speed up computation operations. It also reduces the amount of space needed for storage and can even be used to visualize the relationships between different data variables simultaneously. 

 

Principal Component Analysis is one of the first steps a data scientist will take when analyzing a new dataset. It's even something that data analysts should consider using in their work, as PCA can often reveal valuable insights about new datasets. Consider joining Learnbay's data scientist course in Bangalore if you want to upgrade your skills and work as a data scientist at tech giants. 

Publication: 29/11/2022 12:26

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