DM: RE: Prediction of values of 2 or more variables

[Gavin Meggs]

Colin,

I haven't yet formally introduced myself to the group, but I hope this
doesn't preclude me from offering advice!

You may find the technique of canonical correlation (from statistics) 
of
use. I have attached an html page (the links won't work) and the text
that it contains.

 
GAV

Data Mining Research - Canonical Correlation 
Overview 
------------
The following extract was taken from [1] (page 281) 

"Canonical correlation analysis involves partitioning a collection of
variables into two sets, an x-set and a y-set. The object is then to
find linear combinations N = a'x and O = b'y such that N and O have 
the
largest possible correlation. Such linear combinations can give 
insight
into the relationship between the two sets of variables. 

Canonical correlation analysis has certain maximal properties similar 
to
those of principal components analysis. However, whereas principal
components analysis considers interrelationships within a set of
variables, the focus of canonical correlation is the relationship
between two groups of variables. 

One way to view canonical correlation analysis is as an extension of
multiple regression. Recall that in multiple regression analysis the
variables are partitioned into an x-set containing q variables and a
y-set containing p=1 variable. The regression solution involves 
finding
the linear combination a'x which is most highly correlated with y. 

In canonical correlation analysis the y-set contains p>= 1 variables 
and
we look for vectors a and b for which the correlation between a'x and
b'y is maximized. If x is interpreted as "causing" y, then a'x may be
called the "best predictor" and b'y the "most predictable criterion".
However, there is no assumption of causal asymmetry in the mathematics
of canonical correlation analysis; x and y are treated 
symmetrically." 

References 

[1] Mardia,K V, Kent,J T and Bibby,J M: 'Multivariate Analysis',
Academic Press (1979) 

Data Mining Group, Gavin Meggs 


+--------------------------------------------------------+
Gavin Meggs                                               
Data Mining Group                     
BT Laboratories,                                  
Martlesham Heath
Ipswich,
Suffolk IP5 3RE

Tel:  (01473) 605502
Fax:  (01473) 642459
Email: gavin.meggs@bt-sys.bt.co.uk
+--------------------------------------------------------+


>----------
>From:  Ho K M[SMTP:hokokx@essex.ac.uk]
>Sent:  30 July 1997 10:17
>To:    datamine-l
>Subject:       DM: Prediction of values of 2 or more variables
>
>Does anyone know any technique that predicts values of 2 or more
>variables.
>
>Colin
>

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