# Re: W3C RDF Data Cube dimensions definition

```And statistical dimensions are different again - they are effectively the
independent variables that place a statistical value in a space and time
and subject. Roughly the same as OLAP - c.f.
https://en.wikipedia.org/wiki/Dimension_(data_warehouse)

This form of dimension is typically much more relevant in the "Web" part of
the problem - how things are characterised and organsied - whereas
coordinate dimensions are data details largely independent of the Web
aspects - its only serialisation where these pop up into the implementation
choices - and this is not independent of the whole data model and
serialisation choice (e.g. GML, geo-JSON).

Rob

On Fri, 3 Feb 2017 at 20:05 Jon Blower <j.d.blower@reading.ac.uk> wrote:

Hi Chris,

I think it’s quite difficult to define “dimension” properly and concisely
without getting circular (I tried once for some other documentation but I
couldn’t find a good solution. It reminds me of a sentence I read in an old
computer graphics book that tried to define “line” by saying “A line is a
line between two points”…).

But I think it’s useful to acknowledge that “dimension” can have different
connotations – i.e. it’s not always a physical dimension, and that you can
have a 1-dimensional geometry within a 3-dimensional physical space.

I would think that most people will understand what we mean by “dimension”
from a discursive description and a few examples.

Cheers,Jon

On 03/02/2017 08:28, "Linda van den Brink" <l.vandenbrink@geonovum.nl>
wrote:

Thanks for researching this!

To answer your question way at the bottom, I don't thing we need a
_normative_ definition. But a definition that makes clear what we mean when
we talk about dimensions in the BP, instead of just mentioning it casually
as we do now...

Or even a (small) section on dimensions among the introductory topics.

-----Oorspronkelijk bericht-----
Van: Little, Chris [mailto:chris.little@metoffice.gov.uk]
Verzonden: donderdag 2 februari 2017 18:02
Aan: Andrea Perego
CC: W3C SDW WG - Public
Onderwerp: W3C RDF Data Cube dimensions definition

Andrea,

The formal normative document at https://www.w3.org/TR/vocab-data-cube/
does not seem to actually define 'dimensions' or 'multi-dimensional', other
than as distinguishing aspects of a 'hypercube' of 'observations'.

Neither does the underlying SDMX ISO statistical document at
https://sdmx.org/?page_id=5008 :
"These metadata values and  concepts  can  be  understood  as  the
named  dimensions  of  a  multi-dimensional co-ordinate system, describing
what is often called a "cube" of data."

Section 5.2 is the most informative, but not normative:

"A statistical data set comprises a collection of observations made at
some points across some logical space. The collection can be characterized
by a set of dimensions that define what the observation applies to (e.g.
time, area, gender) along with metadata describing what has been measured
(e.g. economic activity, population), how it was measured and how the
observations are expressed (e.g. units, multipliers, status). We can think
of the statistical data set as a multi-dimensional space, or hyper-cube,
indexed by those dimensions. This space is commonly referred to as a cube
for short; though the name shouldn't be taken literally, it is not meant to
imply that there are exactly three dimensions (there can be more or fewer)
nor that all the dimensions are somehow similar in size.

A cube is organized according to a set of dimensions, attributes and
measures. ...

... The dimension components serve to identify the observations. A set
of values for all the dimension components is sufficient to identify a
single observation. Examples of dimensions include the time to which the
observation applies, or a geographic region which the observation
covers......"

Section 5.3 gives us the freedom to specialise:

".... In statistical applications it is common to work with slices in
which a single dimension is left unspecified. In particular, to refer to
such slices in which the single free dimension is time as Time Series and
to refer slices along non-time dimensions as Sections. Within the Data Cube
vocabulary we allow arbitrary dimensionality slices and do not give
different names to particular types of slice. Such sub-classes of slice
could be added in extension vocabularies."

Section 6 allows us to optionally order dimensions.

Section 6.1 The Data Cube vocabulary represents the dimensions,
attributes and measures as RDF properties.

The Integrity Check Sections IC-4/5 states that dimensions have range,
and every dimension with a range of 'concept' has a code list.

And what is interesting, 'dimension' is sub-classed into:
1. Dimension
2. measureDimension
3. timeDimension

A measureDimension indicates variables or types of data of interest, so
our CRSs are associated with Dimension, with the proviso that this includes
proper temporal CRSs. I posit that Calendars are NOT CRSs, but complex
entities in their own right and fit into the timeDimension, as this has
examples of dateTime, etc.

I.e. the Dimension has a specialisation with the ideas of a single
axis, one origin, +ve and -ve directions, and one Unit of Measure.

The timeDimension 'calendars have complicated cycles of durations,
counts  and units.

Sending this though I have not finished thinking about it or delving
yet.

Do we  need to have a normative definition of 'dimension'?

Chris

Chris Little
Co-Chair, OGC Meteorology & Oceanography Domain Working Group

IT Fellow - Operational Infrastructures
Met Office  FitzRoy Road  Exeter  Devon  EX1 3PB  United Kingdom
Tel: +44(0)1392 886278 <+44%201392%20886278>  Fax: +44(0)1392 885681
<+44%201392%20885681>  Mobile: +44(0)7753 880514 <+44%207753%20880514>
E-mail: chris.little@metoffice.gov.uk  http://www.metoffice.gov.uk

I am normally at work Tuesday, Wednesday and Thursday each week
```

Received on Monday, 6 February 2017 21:02:35 UTC