• ##### Clustering algorithms
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## Introductory Data Science

### What is a dimension?

You might have heard the word “dimension.” You might have heard people say the term “high dimensional data.” Let us discuss what this term dimension means.

Here is the tabular data from the previous lesson.

 Name Salary (\$) Age (Years) Jane 90000 52 John 85000 48 Delilah 75000 32 Dave 90000 53 Ellen 82000 44

We said that the actual data part in the table above is:

 90000 52 85000 48 75000 32 90000 53 82000 44

In this running example, we have two features or two columns, as explained in the previous lesson. We have five objects or five rows.

We call the data of our running example a two-dimensional dataset. That is the number of features is equal to the number of dimensions of the dataset. Again, the table above is a two-dimensional dataset because the table has two features or columns.

That is:

Number of features = number of dimensions

If we had three features or three columns, we would have called this a three-dimensional dataset. An example is provided below. The table below has three features and five objects.

 90000 52 10 85000 48 20 75000 32 30 90000 53 40 82000 44 20

If we had four features or four columns, we would have called this a four-dimensional dataset. An example is below.

 90000 52 10 50 85000 48 20 60 75000 32 30 30 90000 53 40 35 82000 44 20 40

I am sure, the idea is clear by this time. If the dataset has 1 feature, it is called, 1-dimensional; with 2 features it is called 2-dimensional, so and so forth. With n features or n columns, the data is called n-dimensional.

 Feature 1 Feature 2 Feature 3 Feature 4 —- —- Feature n 90000 52 10 50 43 85000 48 20 60 2 75000 32 30 30 73 90000 53 40 35 36 82000 44 20 40 90

Notice one thing here — regardless of the number of features or number of columns, or the number of dimensions, the data table can be stored in a two-dimensional array. That is, even one hundred-dimensional dataset can be kept in a 2D array or in a 2D matrix.

The word “dimension” in programming is used to count the number of cells. In data science, the word “dimension” has a different meaning. “Dimension” in data science refers to the mathematical space, such as the Euclidian space.

As an example, the following data table has three columns or three features. There are five objects or five rows.

 90000 52 10 85000 48 20 75000 32 30 90000 53 40 82000 44 20

In programming, we will say that this table can be stored in a 2-dimensional array of size 5 times 3. That means, it has five rows and three columns.

In data science, this table is called a three-dimensional dataset because it composes a mathematical space of three dimensions.

Similarly, a data table with four columns, such as the following one, is referred to as a four-dimensional dataset even though we store it in a two-dimensional array.

 90000 52 10 50 85000 48 20 60 75000 32 30 30 90000 53 40 35 82000 44 20 40

That is a higher number of features would mean a higher number of dimensional mathematical space. The physical memory space is the memory occupied with the corresponding two-dimensional array. The physical memory is a programming concept and always a 2-dimensional array for an any-dimensional dataset.

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