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I would like to know what is the relationship between multivariate analysis and other topics such as: linear regression, neural networks or support vector machines.

According to Wikipedia:

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.

And for what I know a neural network also allows having multiple outcomes. Also in the same wikipedia page in types of analysis they consider other techiques such as clustering, so what do they have in common multivariate analysis with these data mining techniques? Are one subset of the other or how is it?

I do not know too much about multivariate analysis, but I have learned neural networks, svm and clustering from the Computer Science point of view and not from the statistical one. Any help would be great.

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You are comparing apples to oranges. Multivariate is when you have more than one predictors. Whereas regression, neural networks are techniques which can handle both univariate and multivariate problems.

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