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In the textbook im reading about Deep Learning, i found :

When designing features or algorithms for learning features, our goal is usually to separate the factors of variation that explain the observed data [...] the factors are usually not combined by multiplication.

What's the meaning of the bold phrase ?

ps: what's your definition for "factors of variation" ?

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Factors of variation are some factors which determine varieties in observed data. If that factors change, the behavior of the data will change.

The bold phrase said these factors are usually independent and one factor does not change by changing the value of the others.

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  • $\begingroup$ Thanks for the great answer! I was reading Bengio Learning Deep Architectures for AI (2009) and I am pondering on a phrase: "We call these factors of variation because they are different aspects of the data that can vary separately and often independently." What is the difference between separately and independently? I supposed independently implies they do not interact with other factors, but that would also be implied by separately. Does separate just mean they are different? Do you have any thoughts? $\endgroup$ – layser Apr 13 '20 at 12:06
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    $\begingroup$ @layser my pleasue. "separately" means it can be changed individually but it can have some effects on other variables and vice versa. But, "independently" means it can be changed separately without any effect on other variables and vice versa. $\endgroup$ – OmG Apr 13 '20 at 13:11

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