They don't really scale to high dimensional spaces.

Images like these are very high dimensional statistics.

Data powers high tech societies.

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.

But in truly high dimensional space it has a very strong utility.

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.

These are potential sources for high speed data transmission.

I create mathematical objects, symmetrical objects, using Galois' language, in very high dimensional spaces.

like a 4 dimensional or 5 dimensional figure.

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.

We can do high frequency monitoring to get objective data.

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

One idea is that our three dimensional universe may be embedded in a high dimensional space, just as you can imagine on these sheets of paper.

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.

That's usually a problem, because if you have a high dimensional space, you just can't apply it.

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.

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

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.

Data, data, data...

And that signal is then converted back to a high speed data stream.

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

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

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.

create scientific 2 dimensional graphs

It's a 3 dimensional state.

It's all very one dimensional.

Here's a 2 dimensional space.

High, High!

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

And so this hypothesis has high bias and a value underfits this data set.

ShinHwa High! ShinHwa High! ShinHwa High!

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.

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

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