I have been thinking about how words and phrases condense vast amount of information into small size and easy to utilize it. This feels like how eigen vectors condense large dataset and carry the essence of the data with them. Is this something that anyone feel interesting enough to research?

2 hours ago, Mahi_sayli said:

I have been thinking about how words and phrases condense vast amount of information into small size and easy to utilize it. This feels like how eigen vectors condense large dataset and carry the essence of the data with them. Is this something that anyone feel interesting enough to research?

Not sure I follow what you are trying to do here. Can you expand on your idea some more.

Eigenvectors are very specialised devices - There are many ways to represent (large) datasets and plenty of theory about that subject.

The simplest example would be the use of an average to represent a whole class of something.
And any statistician would quickly tell you that the average is of little use without a second measurement detailing the spread of the data.

Honestly I also have only abstract understanding. Let me try though, act of running can be described lot of words, but just one word gives us idea of what someone is doing when they run. Words in a way are principal components of certain information set. I am very sorry I am unable to express it but I will post later if i have better way to articulate it.

You sound like one who's read about quantum mechanics and is trying to extrapolate it to the familiar world of human affairs. Language that's used to talk about yes/no propositions (the one that rules the classical world) is alien to the eigenvalue/eigenvector world of quantum superpositions.

Eigenvalues and eigenvectors are also useful to talk about mechanical tensions and strains, moment of inertia, etc.

Just now, Mahi_sayli said:

Honestly I also have only abstract understanding. Let me try though, act of running can be described lot of words, but just one word gives us idea of what someone is doing when they run. Words in a way are principal components of certain information set. I am very sorry I am unable to express it but I will post later if i have better way to articulate it.

If you said "run" to me why should I not think of the ladder in your nylons or the pen where my daughter's rabbits play or....

Single words rarely provide enough context to convey meaning.

7 hours ago, joigus said:

You sound like one who's read about quantum mechanics and is trying to extrapolate it to the familiar world of human affairs. Language that's used to talk about yes/no propositions (the one that rules the classical world) is alien to the eigenvalue/eigenvector world of quantum superpositions.

Eigenvalues and eigenvectors are also useful to talk about mechanical tensions and strains, moment of inertia, etc.

They are also used in face recognition. See: https://en.wikipedia.org/wiki/Eigenface

Just now, KJW said:

They are also used in face recognition. See: https://en.wikipedia.org/wiki/Eigenface

Interesting, thanks. You can learn something new everyday if you keep listening. +1

6 hours ago, KJW said:

They are also used in face recognition. See: https://en.wikipedia.org/wiki/Eigenface

Very interesting. Thanks.

22 hours ago, Mahi_sayli said:

Honestly I also have only abstract understanding. Let me try though, act of running can be described lot of words, but just one word gives us idea of what someone is doing when they run. Words in a way are principal components of certain information set. I am very sorry I am unable to express it but I will post later if i have better way to articulate it.

Are you talking about etymology?

14 hours ago, KJW said:

They are also used in face recognition. See: https://en.wikipedia.org/wiki/Eigenface

Thank you! Yes exactly that what I was thinking about. Just how eigenfaces could be used to detect the facial features, can the eigen vector represent generic piece of information? Would those basically be words and phrases?

30 minutes ago, Sohan Lalwani said:

Are you talking about etymology?

33 minutes ago, Sohan Lalwani said:

Are you talking about etymology?

Yes Sohan. May be if we trace the word formations back to the origins, origins words would be actually eigen vectors.

1 hour ago, Mahi_sayli said:

Thank you! Yes exactly that what I was thinking about. Just how eigenfaces could be used to detect the facial features, can the eigen vector represent generic piece of information? Would those basically be words and phrases?

The phrase "origins words would actually be eigenvectors" is metaphorical or abstract, but it's not technically correct in a linguistic or mathematical sense unless you're trying to make a creative analogy. In linear algebra, eigenvectors are specific non-zero vectors that only scale (not rotate) when a linear transformation is applied. If you're metaphorically suggesting that original words behave like eigenvectors—maintaining a fundamental identity despite transformations—that’s poetic, but not standard usage.

10 minutes ago, Sohan Lalwani said:

The phrase "origins words would actually be eigenvectors" is metaphorical or abstract, but it's not technically correct in a linguistic or mathematical sense unless you're trying to make a creative analogy. In linear algebra, eigenvectors are specific non-zero vectors that only scale (not rotate) when a linear transformation is applied. If you're metaphorically suggesting that original words behave like eigenvectors—maintaining a fundamental identity despite transformations—that’s poetic, but not standard usage.

I guess I have been poetic rather than scientific. I am just trying to understand how does attention magic capture essence behind the series of words. Thanks for your comments.

Just now, Mahi_sayli said:

I guess I have been poetic rather than scientific. I am just trying to understand how does attention magic capture essence behind the series of words. Thanks for your comments.

I see, no problem :D