Table $5$: Sensor Reading Cuboids

Table $5$ represents a series of cuboids, each with the number of scientific measures captured by different sensor devices in separate locations over a $3-$month period.

The Projects are funded by EU$,$ SFI, or US$.$

$2$ types of sensors are LIM$23$ and AL$100.$

The $3$ locations are Wicklow, Cork and Donegal.

The months are Jan, Feb, and Mar.

Q $5($a$)$

$[6$ Marks$]$

Explain the concept of the iceberg cubes with respect to partial materialisation. What does a minimum support of $25$ mean?

Write all of the base cuboids for $($SFI$.$LIM$23)$ to your exam paper.

Q $5($b$)$

Assume a threshold of $25$ for the data in Table $5.$ For each question below, explain your answer.

I. Why does only $1$ base cuboid for $($LIM$23,$ Wicklow$)$ appear?

II$.$ Why is the cuboid $($LIM$23,$Donegal,Jan$)$ omitted from the table?

III. How many AL$100$ sensors readings in total were captured for the EU project?

IV$.$ What are the missing values for $($LIM$23,*,*)$ in EU and SFI?

V $.$ What are the maximum number of US cuboids that could meet the iceberg threshold?

Q $5($c$)$

$[9$ Marks$]$

Describe how the Bottom$-$Up Construction algorithm $($BUC$)$ uses an Apriori function to optimise cuboid searching.

Use data from Table $5($expand the table with extra cuboids where necessary$)$ to go through the logic $($steps$)$ in the BUC algorithm.

$[$End of Question $5]$