Linear Discriminant Analysis For Machine Learning: What You Need to Know?

The advancement in technology in recent years has enabled connected devices to handle massive amounts of data. However, the storage and security of data still remain big concerns when dealing with such huge amounts of data. This is why it is very important to handle data in the right manner. It can often be a time-consuming task.

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This is where data dimensionality reduction techniques, like linear discriminant analysis or LDA, come into the picture. These techniques can help you in handling datasets in a much better way while ensuring data security and privacy. Our focus in this blog will be on discussing linear discriminant analysis data dimensionality reduction technique. Let us start by talking about dimensionality reduction.

What is dimensionality reduction? 

You will be able to better understand the technique of linear discriminant analysis if you know the background of the concept it is based on. When you are dealing with multi-dimensional data, you have data that has a number of features that are correlated with each other. If we plot multi-dimensional data in two or three dimensions, we are using the dimensionality reduction technique.

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An alternative that is also quite commonly used as a substitute for dimensionality reduction is plotting of data using histograms, scatter plots, and box plots, amongst others. These graphs can be used to find patterns in a given set of raw data. However, charts don’t present data in a way that is easy to decipher for common people. Also, data with a lot of features would need several charts to identify patterns in that dataset.

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Data dimensionality reduction techniques, such as LDA, help in overcoming these concerns by using two or three dimensions for plotting data. This will allow you to be more explicit in your presentation of data, which will make sense to even those people who don’t have a technical background. 

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What is linear discriminant analysis?

It is one of the most used dimensionality reduction techniques. It is used in machine learning as well as applications that have anything to do with the classification of patterns. LDA serves a very specific purpose, which is to project features that exist in a high dimensional space onto space at a lower dimension.

This is done to do away with common dimensionality issues and bring down dimensional costs and resources. Ronald A Fisher holds the credit for the development of the original concept in 1936 –Fisher’s Discriminant Analysis or Linear Discriminant. Originally, linear discriminant was a two-class technique. The multi-class version came in later. 

Linear discriminant analysis is a supervised classification method that is used to create machine learning models. These models based on dimensionality reduction are used in the application, such as marketing predictive analysis and image recognition, amongst others. We will discuss applications a little later.

So what are we exactly looking for with LDA? There are two areas that this dimensionality reduction technique helps in discovering – The parameters that can be used to explain the relationship between a group and an object – The classification preceptor model that can help in separating the groups. This is why LDA is widely used to model varieties in different groups. So you can use this technique to use two or more than two classes for the distribution of a variable.

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Extensions to linear discriminant analysis

LDA is considered one of the simplest and most effective methods available for classification. As the method is so simple and easy to understand, we have a few variations as well as extensions available for it. Some of these include:

1. Regularized discriminant analysis or RDA

RDA is used for bringing regularization into variance or covariance estimation. This is done to moderate the impact that variables have on LDA.

2. Quadratic discriminant analysis or QDA

In QDA, different classes use their own variance estimate. In case the number of the input variable is more than usual, every class uses its covariance estimate.  

3. Flexible discriminant analysis or FDA

FDA makes use of inputs with non-linear combinations. Splines are a good example.

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Common LDA applications

LDA finds its use in several applications. It can be used in any problem that can be turned into a classification problem. Common examples include speed recognition, face recognition, chemistry, microarray data classification, image retrieval, biometrics, and bioinformatics to name a few. Let’s discuss a few of these.

1. Face recognition

In computer vision, face recognition is considered one of the most popular applications. Face recognition is carried out by representing faces using large amounts of pixel values. LDA is used to trim down the number of features to prepare grounds for using the classification method. The new dimensions are combinations of pixel values that are used to create a template. 

2. Customer identification

If you want to identify customers on the basis of the likelihood that they will buy a product, you can use LDA to collect customer features. You can identify and choose those features that describe the group of customers that are showing higher chances of buying a product.

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3. Medical

LDA can be used to put diseases into different categories, such as severe, mild, or moderate. There are several patient parameters that will go into conducting this classification task. This classification allows doctors to define the pace of the treatment. 

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LDA is a simple and well-understood technique that is commonly used in classification ML models. PCA and logistic regression are other dimensionality reduction techniques available to us. But when it comes to special classification problems, LDA is preferred over the other two. 

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What is linear discriminant analysis?

Linear Discriminant Analysis (LDA) is a classification algorithm to learn the underlying features which are good to discriminate a group of samples from all other groups. As a result of applying the LDA algorithm, we get a new feature set which can be used for prediction of group membership. For example, let's say that you collect IP addresses and you want to figure out which country they belong to. You have a training set of sample IP addresses and you can identify the country of origin with a very high accuracy. If you have a new IP address and you want to know what country it comes from, you can give it to a LDA and it will assign it to the class with the highest probability.

What are the applications of linear discriminant analysis?

Linear discriminant analysis (LDA) is a set of techniques in the supervised learning framework. LDA is a method, where the dependent variable is linearly separable in the feature space. LDA is used in Marketing, Finance, and other areas to perform a number of classification tasks such as customer profiling and fraud detection. For instance, consider that we want to find a linear combination of independent variables that separates two groups of data points. LDA finds a linear combination of the independent variables that produces maximal separation between the two groups of data points in the feature space.

What is Dimensionality Reduction?

Dimensionality reduction refers to a collection of techniques for reducing the number of variables in a dataset. The most common dimensionality reduction technique is Principal Components Analysis (PCA). PCA is the most popular dimensionality reduction technique due to its simplicity, mathematical elegance, and high statistical properties. PCA is used to reduce the dimensionality of a dataset by identifying the axis that contain the most variance along with the fewest errors.

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