# Calculating object distance/similarity in Bayesian Networks • ### Question

• I have a tree structure of attributes (observed/hidden). This structure is built using some objects (data points) and with the help of a prior domain ontology. Obviously, each object can be represented as a vector o=(x1, x2,..., xn) of observable variables.

I'm interested to know the similarity between two objects (o1 and o2)?

Would you please consider the following scenario and give me a viewpoint in Graphical Models? i.e I'm looking for a computational approach for object similarity in hierarchical attribute space.

Sunday, June 2, 2013 12:35 AM

### All replies

• Do you have any training data regarding similarity?  Or is it just a bag of points?  How many values does each attribute have?  What is the significance of the tree structure?
Monday, June 3, 2013 2:55 PM
• I have some training data (the relatedness value between some data points):

o1, o2, r

where "o1" and "o2" are data points and "r" is the value of relatedness.

I can build a binary or weighted feature vector. So the values of each attribute may be binary (0/1) or a real value between [0, 1].

The significance of tree structure is that it model the relatedness between observable features. Each hidden variable clusters some observable variable like latent tree model: http://www.jair.org/papers/paper2530.html

Monday, June 3, 2013 4:31 PM
• A latent tree model is simply a generative model of data.  The interior nodes exist to model correlation between leaves.  Similarity between objects is a rather different thing.  What do the observed "r" values represent, and how are they related to the tree?

Monday, June 3, 2013 4:59 PM
• Suppose I have a set of documents, for example:

d1="Emancipation Proclamation"

These documents are represented using term features (observed variables):

d1 = ("Emancipation", "Proclamation")

• 