Suppose we're given a 2 dimensional data field, and our data lines up as follows.

Suppose we wish to fit data, and our data is 1 dimensional, and it looks as follows.

Suppose we're given the following data points in a 2 dimensional space.

In 1 dimensional data sets that are numerical, this could be informative.

The musicians played off a three dimensional graph of weather data like this.

I can draw, really easily, a nice 1 dimensional space that follows these data points.

If I am able to project all the data points on this 1 dimensional space,

You place it in a science museum, it becomes a three dimensional visualization of data.

I now have a more challenging quiz for you in which I give you multivariant data in this case 2 dimensional data.

like a 4 dimensional or 5 dimensional figure.

Now, if you recall, each layer is actually a large two dimensional grid of tile data.

It has two dimensional data such as the age of a person and the person's income and this is obviously made up data.

And one thing that's very important is to combine traditional tabular data with three dimensional and geospatial information.

So now I'm going to show you a number of projects that we've built, from one dimensional, two dimensional, three dimensional and even four dimensional systems.

We have progressed from a zero dimensional point, to a one dimensional line segment, to a two dimensional triangle.

Sorting multi dimensional array

Insert 2 dimensional vector

Toward the Dimensional Gate.

Remember that now this state space is 3 dimensional, not 2 dimensional.

So you can basically program any three dimensional shape or one dimensional, two dimensional up into this chain completely passively.

Further, if you re represent each data vector using those eigenvectors, you'll find a 3 dimensional space where original data falls into a varity of different places.

However, I printed out a 2 dimensional table, not a 3 dimensional table.

And this data gets sent to a machine that slices the data into two dimensional representations of that product all the way through almost like slicing it like salami.

Data, data, data...

create scientific 2 dimensional graphs

It's a 3 dimensional state.

It's all very one dimensional.

Here's a 2 dimensional space.

So next, we will talk about two dimensional and three dimensional shapes of ellipticals.

Bing! That's data. Data, data, data.

Listen we can do a topological analysis of highly dimensional data to be analysed without predetermining the number of feature sets.

If each image is 50 by 50 pixels, each image itself becomes a data point in a 2500 dimensional feature space.

So, it works really well for low dimensional problems like 3 dimensional robot localization problems.

A two dimensional vector is needed

This is a 47 dimensional vector.

So it becomes slightly three dimensional.

It's truly a three dimensional space.

This is a three dimensional machine.

Often they are 3 dimensional vectors.

We take this curved 12 dimensional space, and transform it into a flat, four dimensional space.

Finally, I copy the 3 dimensional symbol for my policy straight into the 2 dimensional array.

And that's why my training examples are now N dimensional rather N plus one dimensional vectors.

Consider the following data set where plus indicates a positive traning example and minus a negative training example in this 2 dimensional space.

Obviously this is a 1 dimensional example and not 2 dimensional as the picture suggests over here.

We have a 3 dimensional state space.