With the advancement in technology and trends in connected-devices could consider huge data into account, their storage and privacy is a big issue to concern. Data hackers make algorithms to steal any such confidential information from a massive amount of data. So, data must be handled precisely which is also a time-consuming task. Also, we have seen, not all the data is required for inferences, reduction in data-dimensions can also help to govern datasets that could indirectly aid in the security and privacy of data.
In the core aspects of this blog, we will dwell on data dimensionality reduction techniques, it will cover the concept of Linear Discriminant Analysis(LDA), the difference of LDA with other dimension reduction technique(PCA) and related applications.
Machine Learning is divided into three vast areas named Supervised learning, Unsupervised Learning and Reinforcement Learning. In 1936, Ronald A.Fisher formulated Linear Discriminant first time and showed some practical uses as a classifier, it was described for a 2-class problem, and later generalized as ‘Multi-class Linear Discriminant Analysis’ or ‘Multiple Discriminant Analysis’ by C.R.Rao in the year 1948.
Linear Discriminant Analysis is the most commonly used dimensionality reduction technique in supervised learning. Basically, it is a preprocessing step for pattern classification and machine learning applications. It projects the dataset into moderate dimensional-space with a genuine class of separable features that minimize overfitting and computational costs.
With the aim to classify objects into one of two or more groups based on some set of parameters that describes objects, LDA has come up with specific functions and applications, we will learn about that in detail in the coming sections.
Under Linear Discriminant Analysis, we are basically looking for
Which set of parameters can best describe the association of the group for an object?
What is the best classification preceptor model that separates those groups?
It is widely used for modeling varieties in groups, i.e. distributing variables into two or more classes, suppose we have two classes and we need to classify them efficiently.
A view of the classification of various objects before and after implementing LDA
Classes can have multiple features, using one single feature to classify may yield in some kind of overlapping of variables, so there is a need of increasing the number of features to avoid overlapping that would result in proper classification in return.
Consider another simple example of dimensionality reduction and feature extraction, you want to check the quality of soap based on the information provided related to a soap including various features such as weight and volume of soap, peoples’ preferential score, odor, color, contrasts, etc. A small scenario to understand the problem more clearly;
Object to be tested -Soap;
To check the quality of a product- class category as ‘good’ or ‘bad’( dependent variable, categorical variable, measurement scale as a nominal scale);
Features to describe the product- various parameters that describe the soap (independent variable, measurement scale as nominal, ordinal, internal scale);
Pictorial view of an object, class category, and features extraction
When the target variable or dependent variable is decided then other related information can be dragged out from existing datasets to check the effectivity of features on the target variables. And hence, the data dimension gets reduced out and important related-features have stayed in the new dataset.
Difference between LDA and PCA
From the above discussion, we came to know that in general, the LDA approach is very similar to Principal Component Analysis( see the previous blog to get more information on PCA), both are linear transformation techniques for dimensionality reduction, but also pursuing some differences;
Flow chart showing the difference between LDA and PCA
Application of Linear Discriminant Analysis
There are various techniques used for the classification of data and reduction in dimension, among which Principal Component Analysis(PCA) and Linear Discriminant Analysis(LDA) are commonly used techniques. The condition where within -class frequencies are not equal, Linear Discriminant Analysis can assist data easily, their performance ability can be checked on randomly distributed test data. This method results in the maximization of the ratio between-class variance to the within-class variance for any dataset and maximizes separability.
LDA has been successfully used in various applications, as far as a problem is transformed into a classification problem, this technique can be implemented. For example, LDA can be used as a classification task for speech recognition, microarray data classification, face recognition, image retrieval, bioinformatics, biometrics, chemistry, etc. below here are other applications of LDA;
Conclusion
In this contribution, we have understood the introduction of Linear Discriminant Analysis technique used for dimensionality reduction in multivariate datasets. Recent technologies have to lead to the prevalence of datasets with large dimensions, huge orders, and intricate structures.
Such datasets stimulate the generalization of LDA into the more deeper research and development field. In the nutshell, LDA proposes schemas for features extractions and dimension reductions. For more blogs in analytics and new technologies do read Analytics Steps.
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