# How to model a multi-dimensional feature set for classification

I am new to statistical modelling and so please pardon if the question appears trivial.

I have a set of multi-dimensional data ($T$) where each dimension represents features ($f_i$) obtained from a mammogram. For example $T_1=(f_{11}, f_{21} f_{31},\ldots, f_{n1}); T_2= (f_{12}, f_{22}, f_{32},\ldots, f_{n2});\ldots; T_M$ .

Referring to the paper

Ge, Srinivasan & Krishnan (2002)
Cardiac arrhythmia classification using autoregressive modeling,
BioMedical Engineering OnLine, 1:5

(link), I am interested to know how to fit a polynomial or an AR model to begin with so that a general model may be obtained for classifying the feature sets into two classes; how many parameters are required, etc?

I fail to understand how and why to use the coefficients as features when we have the feature set? How to employ the features for deriving an AR model?

Say if I begin with AR model, how would I formulate so as to reach a general AR(p) model and so on?

I would be glad for pointers such as research papers which have explained model-based fitting techniques and other pointers would be really helpful.

From your description, it seems that the paper you cite has little relevance to your problem.

First, as far as I can tell, there is no time-varying aspect to your data, i.e. the features are different characteristics of the mammogram, not a single quantity changing over time like a lead in an electrocardiogram. Consequently, auto-regressive models do not seem particularly relevant.

There are however many other techniques for classification. If you already have a “correct” label (it's also called a “gold standard” or the “ground truth”) for a set of mammograms, creating a model to recognize which class they belong to is called supervised learning. Logistic regression would be a common technique for these kind of things but there are many other techniques in statistics and machine learning.

If you don't know which mammogram belong to which class (e.g. which one indicates a pathological condition) and you just want to split them in two tentative classes based on how similar they are to each other then you are looking for unsupervised learning techniques. Here you could for example consider some form of cluster analysis.

Note than in both cases (and in the paper you mentioned), what is being classified are not features but cases or exemplars (i.e. ECG recordings or mammograms). If your goal is not to classify mammograms but to understand the relations between different features you would typically use other techniques (e.g. factor analysis but cluster analysis is sometimes applied to variables or features as well).

• Thank you for your reply. I have gone through other papers like the one Parametric model for video content analysis where the features are extracted and the temporal features are also extracted and then AR model is built. What I do not understand is how to relate/link the features to an AR or MA or ARMA model. My objective is similar to the one in this paper where I will estimate the parameters of the AR model. So, is there any way that the features may be represented through some model?I am not clear about all this stuff. – Ria George Jun 17 '13 at 18:16
• Why an AR model? Surely, you goal is to investigate some question, produce a prediction, gain knowledge, analyze an experiment, make a decision, build a system, etc. and not to fit a model per se. What do your data represent? For example, what are the features/how are they extracted or produced? – Gala Jun 17 '13 at 18:22
• For example, let me take another case where the data represents the motion of a moving subject plus the distinguishing features like velocity,coordinates and angular displacement.These are extracted from videos similar to the paper (sec 2.4) "Parametric model for video content analysis". Lets say, that I use these measurements for detecting abnormal behavior. This paper mentions "We apply this parametric framework to model the video temporal relation with the spatial feature vector sequence of the frames". It is not necessary that I choose AR model. – Ria George Jun 17 '13 at 18:31
• One of the objective is to perform system identification using these features/motion data for which I need to have a mathematical representation.Hope I could explain myself as I do not have a clue where to go next. – Ria George Jun 17 '13 at 18:32
• I still have the feeling that you are jumping to the specifics of a particular technique instead of explaining clearly what data you actually have and what you are ultimately trying to achieve. Or are you just trying to learn about this type of things? In any case, you could perhaps ask other questions focusing on this, it sounds like a completely different problem to me. – Gala Jun 17 '13 at 18:40