The most important issue here is not whether the features have a consistent number of dimensions, but whether the dimensions are in a consistent order for all features. Consider 2 features composed of categorical variables:

CASE1

person A = {american, female, christian, lesbian, sportspeople}

person B = {unknown, male, unknown, bisexual, unknown}

CASE2

person A = {american, christian, sportspeople}

person B = {male, muslim, bisexual, politicians}

In CASE1, there are still solutions that can resolve the problem, but in CASE2, the problem is not naturally easy to deal with.

Unfortunately, I am not familiar with this field either, and I am also waiting for answers to your question.

Dr. Wu above is right in my opinion.  You can chose to ignore dimensions that are not shared among all elements in your set, or, probably better, treat them as unknown or not applicable -- that difference can be essential.  Btw, time to update your affiliation Karthik!

Thank you so much for all your inputs. Appreciate your help.

Piet, I will update my profile :)

if you consider the following example:

X1={ x1, x2, ...,xn}

X2={y1, y2,....,ym}

X3={z1, z2,....,zk}

solution1:

you can re-build vectors in a new space by setting their dimension to max (n, m, k), and complete missed values with 0.

solution2:

you can use a feature selection method or dimentionality reduction method to create a new data-set with a fewer number of dimension (for example min (n,m,k)).

Hi, Karthik.

The former answers to your question present interesting solutions for comparing categorical data. However, in case you are dealing with numerical data (e.g. online signatures or speech signals), a classic method for solving this kind of problem is the Dynamic Time Warping (DTW). Notwithstanding, even in case your data are categorical (e.g. texts of different lengths, genetic sequences), there is a method very close to the DTW: the Edit Distance (ED), or Levenshtein distance. Both DTW and ED have their common roots in the Dynamic Programming Approach, and I could bet you may find or even adapt it to the specificities of your problem.

Thank you so much for the inputs.

My feature set is a numerical vector with various properties collected from different sources. It can grow/shrink in length based on the information available at the sources.

I will take into consideration all the suggestions provided. Thanks again to all of you!

Hi,

This is a very common problem in classification because local descriptor usually don't produce feature vectors of same dimension, mainly because of the varying number of feature points or regions.

A common way to deal with this problem is to use either the bag-of-features (BoF, inspired by the bag-of-words method) approach, or the Gaussian mixture model (GMM), or the Bag-of-region approach, or simply the principal component analysis (PCA) approach.

Thank you!!!