Object categorization from image search: Difference between revisions

Revision as of 13:11, 26 December 2017

Revision as of 11:33, 28 February 2018

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<math>\displaystyle P(w|d) = \sum_{z=1}^Z P(w|z)P(z|d)</math>

An important assumption made in this model is that <math>\displaystyle w</math> and <math>\displaystyle d</math> are conditionally independent given <math>\displaystyle z</math>. Given a topic, the probability of a certain word appearing as part of that topic is independent of the rest of the image.<ref name = "hofmann">{{cite conference

| first = Thomas

| last = Hofmann

| title = Probabilistic Latent Semantic Analysis

| booktitle = Uncertainty in Artificial Intelligence

| year = 1999

| url = http://www.cs.brown.edu/~th/papers/Hofmann-UAI99.pdf}}</ref>

|deadurl = yes

|archiveurl = https://web.archive.org/web/20070710083034/http://www.cs.brown.edu/~th/papers/Hofmann-UAI99.pdf

|archivedate = 2007-07-10

|df =

}}</ref>

Training this model involves finding <math>\displaystyle P(w|z)</math> and <math>\displaystyle P(z|d)</math> that maximizes the likelihood of the observed words in each document. To do this, the [[expectation maximization]] algorithm is used, with the following [[objective function]]: