What is Multidimensional Scaling?

Introduction

In this blog, we will discuss multidimensional scaling. Multidimensional scaling is a concept that comes under the category of machine learning. In machine learning, we train or program the software or applications to predicate the result based on the data and experience stored in the machine. 

For example, image recognition is a commonly known machine learning application. In image recognition, the application has been trained with detailed data to recognize a specific image, like identifying a dog or a cat, or any living object.

Now, let's focus on multidimensional scaling and discuss the factors included in multidimensional scaling.

Introduction to Multidimensional Scaling

Multidimensional scaling is the graphical or visual representation of the datasets in the form of a distance or dissimilarities matrix between sets of objects. Here object term refers to anything, for example, jackets, perfumes, cars, bikes, etc. With the help of multidimensional scaling, we can calculate the similarity between the objects.

With the distance or dissimilarity value, we can conclude a representation of objects similar to each other. The closer the distance or less dissimilarity between the objects more similar they are, and the bigger the distance, the less similar the objects are.

The word dimension here refers to the attribute of a dataset. If there are two attributes in a dataset or matrix, then we will take a two-dimensional representation of the data, but this cannot be the case in every dataset.  

You might use multiple dimensions to represent the multiple attributes, but this can make our outcome complex to represent visually, and we will need help comprehending it.

It is best to use the three dimensions at most because, more than that, our brain can not process the information visually. But mathematically, we can achieve it.

The term scaling represents the measurement of the object. It is like a scale of two numbers in which one is higher and the other is lower that we can use to measure the preference or perception of the object for a user. 

For example, a scale from 1 to 5 represents a person's liking of street food.

Techniques of Multidimensional Scaling

There are multiple techniques available in multidimensional scaling that you can use. Their techniques depend on the input data you use for multidimensional scaling.

Metric Multidimensional scaling

Metric Multidimensional Scaling can be considered a technique for visualizing data: you input a distance matrix with the distances between a set number of data points, and the technique produces a graph displaying those observations.

Example

We have a matrix of distances between different cities. Let's name the city from A to E for simplicity. The distance is in KM.

From the matrix, we can observe that distances from one city to another like from A to B is 222 km and from A to C it's 240, and so on. The 0 value means the distance from city A To A.
 

As you can see, we have plotted the graph from the given matrix, and if we add the directions from north, south, east, and west, we can easily see the map.
 

Non-metric Multidimensional scaling

In the non-metric multidimensional scaling, we will use ordinal data. 

Ordinal data is the categorized statistical type where the distances between the categories are unknown, and the variables have natural, ordered categories. It also provides the output as a metric.
 

Individual Differences Scaling

This is the third method or technique we can use to implement multidimensional scaling. In individual differences scaling, we use the data based on personal human perception. This makes the individual difference scaling method different from the above two methods.

Individual difference scaling methods represents a more accurate model for implementing multidimensional scaling. In this method, we will not use a single dissimilarity matrix. There can be multiple inputs varies from person to person; that's why it is closer to reality.
 

Multidimensional Analysis of Preference

This is the fourth method in multidimensional scaling. Multidimensional analysis of preferences is the same as the individual difference scaling, but the data we will use to implement multidimensional scaling is different. We will use rating data in this technique, and as in the individual differences scaling method, we can have multiple rating data matrixes.