**Linear discriminant analysis assignment help**

Linear Discriminant Analysis is a reduction technique used to ‘reduce’ the number of variables (dimensions) in a set of data, while retaining as much information of the data set as possible. It is used in machine learning as a pre-processing step and in pattern classification applications. The purpose of linear discriminant analysis is to project data that is located in a high dimensional space onto a low dimensional space to minimize resources and dimensional costs.

This technique was developed in 1936 by Ronald Fisher, and given the name Fisher’s Discriminant analysis or Linear Discriminant Analysis. Initially, linear discriminant analysis was performed as a two-class technique but later, this two-class version was advanced by CR Rao and named Multiple Regression Analysis. Linear discriminant analysis is considered an important part of supervised machine learning algorithms. Some of the applications of the dimensionality reduction provided by this technique include predictive analysis and image recognition.

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## Dimensionality reduction

Dimensionality reduction techniques are applied in data mining, machine learning, information retrieval, and bioinformatics. Their main purpose is to get rid of the dependent and redundant features of a data set by mapping the data set onto a lower dimension space. Data sets with multiple dimensions have numerous features that correlate with each other. With dimensionality reduction technique, multi-dimensional data can be plotted in just two or three dimensions. In other words, dimensionality reduction allows an overly complex data to be simplified and presented in an easy to understand manner.

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## How to build a linear discriminant analysis models

Linear discriminant analysis models use Bayes’ theorem to predict probabilities. They make estimations based on the probability that any new input set of data belongs to a given class. The class that has the highest probability is regarded as the output class after which, the linear discriminant analysis model makes a prediction. Here are a few things you should keep in mind when preparing a linear discriminant analysis model:

- Linear discriminant analysis is primarily used in classification problems in which you have a specified categorical output variable. It lets you perform both multi-class classification and binary classification.
- The standard linear discriminant analysis models utilize the Gaussian distribution to analyze the input variables. Make sure to check the univariate distributions to see to it that their attributes match Gaussian distribution.
- Outliers can cause skewness in the data used to separate classes in linear discriminant analysis. It is recommended that you remove them before you start constructing your model.
- Linear discriminant analysis models assume that the input variables have the same variance, hence it is important to have your data standardized before constructing such models. Keep the standard deviation at 1 and mean at 0.

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## How linear discriminant analysiscompares to other dimensionality reduction methods

There are two dimensionality reduction techniques that serve the same purpose as the linear discriminant analysis. These include:

- Principal component analysis
- Logic regression

However, these two techniques have certain characteristics that make them suitable for some specific situations and unsuitable for others. Here is how they compare to linear discriminant analysis:

### Linear discriminant analysis versus principal component analysis

Principal component analysis is an unsupervised algorithm, which means, it does not use class labels. It aims at locating the principal components that enhance variance in a given data set. Linear discriminant analysis differs from the principal component analysis in that it is a supervised algorithm. It utilizes class labels to locate the linear discriminants that maximize separation between different data classes.

Linear discriminant analysis is a more preferred technique than the principal component analysis in multi-class classification because when the data labels are available, the output tends to be much accurate. In some instances, however, principal component analysis performs better. Such instances include when the sample sizes of the classes being studied are relatively small. Most of the times, the two techniques are used hand in hand for dimensionality reduction. The principal component analysis is performed first followed by linear discriminant analysis.

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### Linear discriminant analysis versus logistic regression

Logistic regression is both powerful and easy to perform. However, it is only used in binary classification instances. While the technique can be generalized and applied in multi-class classifications, this doesn’t happen often. When it comes to solving multi-class classification problems, most data analysts will go for linear discriminant analysis. Also, logistic regression sometimes becomes unstable, when the data classes are isolated, and this is where linear discriminant analysis saves the day. Additionally, if there aren’t many samples from the parameters that need to be assessed, linear discriminant analysis becomes unstable too. Linear discriminant analysis can be used in such a situation, as it remains stable even when there are only a few samples to be estimated.

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## Applications of linear discriminant analysis in real life

Linear discriminant analysis is applied in many different disciplines including:

**Customer identification**: Linear discriminant analysis is used in businesses to identify the type of customers who are likely to purchase certain products. Using a simple questionnaire survey, a company can collect different customers’ features, and linear discriminant analysis can be used to select the features that describe which group of customers buy the product and which one does not. If you would like to learn more about how linear discriminant analysis is used in customer identification, contact our online linear discriminant analysis tutors.**Prediction**: Question “Will students pass an exam” can be thought as a prediction. We can use linear discriminant analysis to assign “exam” to one of two distinct groups named “pass” and “fail”.**Pattern recognition**: Linear discriminant analysis can be used to distinguish pedestrians from cars, dogs, and other moving objects on captured image sequence on the street.**Learning**: Teaching robots to act like humans can be thought as a classification problem. Linear discriminant analysis can be usedto assign tune, frequency, pitch, and other measurements of sound to different groups of words.

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## Extensions of linear discriminant analysis

Due to the ease of use of linear discriminant analysis, the technique has seen many variations and extensions. All of these have been developed to improve the efficacy and effectiveness of linear discriminant analysis. Here are a few examples of linear discriminant analysis extensions:

**Flexible discriminant analysis**: The traditional linear discriminant analysis can only use linear combination of inputs. With flexible discriminant analysis, data analysts can use both linear and non-linear combinations of inputs.**Quadratic discriminant analysis**: In this technique, each class uses its own prediction of variables for both single and multiple input variables.

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