So, our data cubes can use these aggregation operations to simplify

a dataset and that provides a useful tool for investigating the dataset.

So for example, we can take our data cube in this case,

it has location horizontally,

products vertically and time in depth.

If we for example,

if we want to look at all of our sales of tea, coffee,

espresso or other products over time at different times,

but we don't care about the location,

then we can project this data cube

into basically this square region, this two-dimensional region.

So this is a two-dimensional projection that's summing up all of

the sales at any given time of a given product regardless of location.

So it's summing them up over all the locations and

that projection gives us something we can then visualize.

We can further summarize that projecting this two-dimensional data cube into

a one-dimensional data cube by summing in this case, over product.

We don't care about the differences of the products.

If we don't want to differentiate the product,

we can aggregate the product axis sum over that,

and now we have a one-dimensional basically,

just a list of numbers that tells us the amount of sales for the first quarter,

second quarter, third quarter or fourth quarter.

If we don't care about the time,

then we can just look at the total sales over a given amount of time,

over a given set of products,

over a given set of locations,

add all those up and that gives us a zero-dimensional data cube here.

So, here's an example using Tableau to show how

aggregations are used for data cube operations.

Here we have some dimensions of our data.

The data is collected over ten years.

So we have separate data by year and over a variety of different countries.

Then we've got the,

what I'm showing here is our standard method for plotting population logarithmically,

horizontally, over life expectancy vertically.

You'll see that we're averaging the data and we have a single data point.

We basically have a zero-dimensional data,

it's all being projected to a single point

because we're averaging over all these dimensions.

Specifically at the time dimension over all the years that we

have data and over all the countries that we have data.

If we want to disaggregate this data,

then we can do that by basically dragging into this marks area.

For example, country.

Now, we spread out the data,

each one of these data points represents

a different country that these averages are just averages over

the year that the data's collected on and add over the country and the region.

We can further disaggregate over the year and we get

this plot which shows you each country that's how it's changing over the year.

If we want to see correspondences between countries,

then I can drag the country into color so that each country gets its own color.

So you can see how the colors,

you can use the color to follow the country over the years it's been disaggregated.

We can start adding more and more dimensions from our data cube into this visualization.

So, when you're looking at an individual cell of these different forms of data cubes,

you can work from a less detailed view to a more detailed view.

A single cube when it's averaged,

could represent a range of products,

a range of locations,

a range of times or it could represent

the values in a specific location at a specific time.

In its disaggregated form it's representing an actual data point.

In its aggregated form,

it's representing an aggregate of the values over these ranges.

So, this could be the total sales of all products,

over all markets, over all time.

Then you can start to drill down to these details by basically focusing for example,

on a particular instance of time,

or on a particular product,

or on a particular type.

Each time you do that,

you're replacing an aggregated dimension where you have

a single value representing a range of one of

these dimensions with a specific product or a specific data point along that dimension,

a specific coordinate along that dimension.

So by doing that,

this data cube approach allows you while you're performing

your visualization to be able to drill down in the details

and tend to back out into more summary views.