Python Programming for Biology: Bioinformatics and Beyond

Vector data units

This  chapter  will  consider  all  units  of  data  (the  things  that  are  being  separated)  in  an

abstract  way.  All  data  in  a  given  unit  will  be  represented  numerically  and  all  different

kinds  of  information  will  be  placed  together  in  the  same  data  structure.  Doing  things  in

this  manner  enables  us  to  think  in  a  more  general,  mathematical  way  and  the

computational methods that we consider will work on any input data, whatever its origin.

To this end we will refer to each separable unit of data as a feature vector. A feature refers

to  a  different  kind  of  measurement,  whether  weight,  length,  height,  x-coordinate,  y-

coordinate  or  whatever.  A  vector  refers  to  the  placement  of  all  of  the  features  that  go

together  into  particular  slots  of  an  array.  For  example,  a  colour  may  be  described  as  an

array consisting of red, green and blue component values, i.e. color = (red, green, blue).

Vectors  are  often  used  to  describe  positions  in  three-dimensional  space,  and  in  the  same

way a more general feature vector can be thought of as a position in a feature space. The

only  difference  is  that  the  axes  of  a  feature  space  don’t  necessarily  represent  spatial

position;  the  axes  represent  whatever  is  being  measured  and  can  have  any  number  of

‘dimensions’,  one  for  each  feature.  Just  as  distances  can  be  measured  between  points  in

space, distances can also be measured in a feature space. We will often be measuring such

distances  for  the  purposes  of  separating  data,  as  a  means  of  measuring  the  degree  of

similarity  between  units  of  data.  This  is  not  to  suggest  that  the  usual  Cartesian  distance

(square root of the sum of square axis differences) is always the best measure; the distance

criterion should be chosen to be appropriate to the problem.

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