What does the z axis mean in kmeans, pca and tsne? what data does it add that 2d doesn't? what do the axis represent?

The context is as follows: I have data that has been plotted in a 2D graph on the left, and in a 3D graph on the right, using k-means clustering. However, I am unsure of what information the third dimension (z-axis) adds to the data, and what the x and y axes are measuring. The data itself consists of numerical columns extracted from an Excel sheet, measuring attributes such as area and circumference. While this data alone does not provide much insight, k-means clustering can generate graphs such as these, and I am unsure how to interpret them. Specifically, I would like to know what the third dimension adds to the 2D graph, and what additional information k-means clustering in 3D provides compared to 2D. Furthermore, I would like to understand what each of the x, y, and z axes represent in these graphs.

What does the z axis mean in kmeans, pca and tsne?

what data does it add that 2d doesn't?

what do the axis represent?

How can I convert the axis to square microns?

[Torsten]

We don't know the context of your questions. So it's impossible to answer them.

[Laura]

@Torsten

The context is as follows: I have data that has been plotted in a 2D graph on the left, and in a 3D graph on the right, using k-means clustering. However, I am unsure of what information the third dimension (z-axis) adds to the data, and what the x and y axes are measuring. The data itself consists of numerical columns extracted from an Excel sheet, measuring attributes such as area and circumference. While this data alone does not provide much insight, k-means clustering can generate graphs such as these, and I am unsure how to interpret them. Specifically, I would like to know what the third dimension adds to the 2D graph, and what additional information k-means clustering in 3D provides compared to 2D. Furthermore, I would like to understand what each of the x, y, and z axes represent in these graphs.

[Torsten]

What is the dimension of the data points you provide for clustering ?

[Laura]

@Torsten

18 columns of numerical values in an excel sheet, with each of the 18 columns of one row being treated as an 18 dimensional point for kmeans analysis. thanks for explanation

[Torsten]

I cannot imagine you gave 18 data columns to kmeans and got back a plot in 2d and 3d.

Maybe you called "pca" before to reduce the dimensionality of your data ?

[Torsten]

Then the points in 2d and 3d should represent your data classified by two or three principal components from pca. Subsequently, your data points in the coordinate systems of the two or three principal components are clustered.

In general, it is difficult to give a name or meaning to the two or three dimensions deduced by pca. You can only extract from the results how your 18 variables load on (correlate with) the factors extracted.

I recommend

https://link.springer.com/book/10.1007/978-3-658-32589-3

for reading. Since the book is written for marketing students, it's quite easy to understand with respect to the mathematics involved.

[Laura]

@Torsten

Thanks for the link.

To just clarify another aspect of my question, if I have 18 variables and implement only kmeans and I get out a 2d plot what is the difference between that 2d plot and the 3d plot?

[Torsten]

I'm not an expert in this field, but as far as I know, if you have 18 variables and use kmeans, you get a clustering in 18 dimensions. There is no dimensional reduction to 2d or 3d. Or did you notice something different ?

[Laura]

Thank you for your response. To clarify my question, if I have 3 variables and I apply k-means clustering to create a 2D plot, what specific information would be conveyed in the 2D plot that would not be evident in a 3D plot? And vice versa? @Torsten

[Torsten]

In my opinion, you can't apply k-means clustering to 3 variables to create a 2D plot. The plot will always be 3D without using pca or factor analysis first to reduce dimensionality. But if you can show me such a feature in kmeans, I will try to find out what you ask for.

[Laura]

@Torsten

well i guess the question i have been circling around is whats the difference between a 2d kmeans plot and a 3d kmeans plot? From your response I guess it can also mean that there were 2 clusters for the 2d plot the 3 clusters for the 3d plot. But if I have a kmeans output that can give me a 2d plot and also a 3d plot, what would be the differnce in the information given?

[Torsten]

You get a 2d plot from kmeans if you have 2 variable data and you get a 3d plot from kmeans if you have 3 variable data.

You cannot get a 2d and a 3d kmeans plot for the same data if you don't preprocess the data (e.g. using pca and choosing 2 components from your 18 variables for the 2d plot and 3 components from your 18 variables for the 3d plot).

At least this is what I think. If you have code that corrects me, you can include it here.

[Neo]

@Torsten

I think this is an interesting question, please check out my question that is asking something similar:

https://www.mathworks.com/matlabcentral/answers/1918610-my-minboundsphere-attempt-is-not-working-any-suggestions-on-how-to-fix?s_tid=srchtitle

I performed pca first then performed kmeans in a 3d plot, but i also got the same thing in a 2d plot (instead of spheres it was circles) but it appears everything else to be the same. Are these two different plots? What does the z component add?

[Torsten]

@Neo

What do you mean by: I performed kmeans in a 3d plot, but i also got the same thing in a 2d plot ?

Can you share a simple example for illustration purposes ?

Answer 1

[the cyclist]

All 2-dimensional plots in MATLAB can be rotated to be viewed from a different "point of view", but this is generally not useful (or worse) if the data don't have a z-component.

x = randn(50,1);
y = randn(50,1);

figure
scatter(x,y)

figure
scatter(x,y)
view(45,45)

[Laura]

The context is as follows: I have data that has been plotted in a 2D graph on the left, and in a 3D graph on the right, using k-means clustering. However, I am unsure of what information the third dimension (z-axis) adds to the data, and what the x and y axes are measuring. The data itself consists of numerical columns extracted from an Excel sheet, measuring attributes such as area and circumference. While this data alone does not provide much insight, k-means clustering can generate graphs such as these, and I am unsure how to interpret them. Specifically, I would like to know what the third dimension adds to the 2D graph, and what additional information k-means clustering in 3D provides compared to 2D. Furthermore, I would like to understand what each of the x, y, and z axes represent in these graphs. @the cyclist