To normalize or not and other distance considerations

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From the course by University of Washington

Machine Learning: Clustering & Retrieval

1383 ratings

University of Washington

Machine Learning: Clustering & Retrieval

1383 ratings

Course 4 of 4 in the Specialization Machine Learning

Case Studies: Finding Similar Documents A reader is interested in a specific news article and you want to find similar articles to recommend. What is the right notion of similarity? Moreover, what if there are millions of other documents? Each time you want to a retrieve a new document, do you need to search through all other documents? How do you group similar documents together? How do you discover new, emerging topics that the documents cover? In this third case study, finding similar documents, you will examine similarity-based algorithms for retrieval. In this course, you will also examine structured representations for describing the documents in the corpus, including clustering and mixed membership models, such as latent Dirichlet allocation (LDA). You will implement expectation maximization (EM) to learn the document clusterings, and see how to scale the methods using MapReduce. Learning Outcomes: By the end of this course, you will be able to: -Create a document retrieval system using k-nearest neighbors. -Identify various similarity metrics for text data. -Reduce computations in k-nearest neighbor search by using KD-trees. -Produce approximate nearest neighbors using locality sensitive hashing. -Compare and contrast supervised and unsupervised learning tasks. -Cluster documents by topic using k-means. -Describe how to parallelize k-means using MapReduce. -Examine probabilistic clustering approaches using mixtures models. -Fit a mixture of Gaussian model using expectation maximization (EM). -Perform mixed membership modeling using latent Dirichlet allocation (LDA). -Describe the steps of a Gibbs sampler and how to use its output to draw inferences. -Compare and contrast initialization techniques for non-convex optimization objectives. -Implement these techniques in Python.

From the lesson

Nearest Neighbor Search

We start the course by considering a retrieval task of fetching a document similar to one someone is currently reading. We cast this problem as one of nearest neighbor search, which is a concept we have seen in the Foundations and Regression courses. However, here, you will take a deep dive into two critical components of the algorithms: the data representation and metric for measuring similarity between pairs of datapoints. You will examine the computational burden of the naive nearest neighbor search algorithm, and instead implement scalable alternatives using KD-trees for handling large datasets and locality sensitive hashing (LSH) for providing approximate nearest neighbors, even in high-dimensional spaces. You will explore all of these ideas on a Wikipedia dataset, comparing and contrasting the impact of the various choices you can make on the nearest neighbor results produced.

Document representation5:52

Distance metrics: Euclidean and scaled Euclidean6:42

Writing (scaled) Euclidean distance using (weighted) inner products4:01

Distance metrics: Cosine similarity9:00

To normalize or not and other distance considerations6:59

Meet the Instructors

Emily Fox
Amazon Professor of Machine Learning
Statistics
Carlos Guestrin
Amazon Professor of Machine Learning
Computer Science and Engineering

So what we saw was that the thing that made cosine similarity different than

the first presentation of just similarity between two articles that we had,

was the fact that in cosine similarity, you operate with normalized vectors.

So this begs the question of, should we normalize or not?

Should we use cosine similarity or

just a vanilla version of a similarity calculation?

Which is just the inner product between two vectors.

So, to think about this,

let's look at an example where we take two different documents, a green document and

a blue document, and let's compute the similarity between them.

Now let's simply double the length of each of these documents, and the way we're

going to double the length is just by taking our document and replicating it.

So it has exactly the same set of words, but just twice as many of those words.

Now when we think about computing our similarity in the original space,

the similarity was 13.

This was the number we computed before.

But now, when we think about computing the similarity for

the documents that are each twice as long, the similarity is 52.

So the similarity has increased by a factor of four, just by doubling

the length of the documents, not changing the content at all.

Is that really something that we want?

Do we want documents to be more similar as they become longer and longer, or

do we just care about the content of them, and not so much how long they are?

Well, if we normalize the documents, so here is this green document,

here is the normalization we did before, this was our normalized representation.

And now we go to compute the similarity with this normalized representation

of both the green document and separately the blue documents,

then we compute the similarity as 13 / 24.

And now if we think about doubling the length of each document again,

and then think about normalizing each of those documents that

were doubled in length, we get exactly the same normalized representation.

So we get exactly the same computed similarity.

So what we see is that cosine similarity is invariant to the length of

the documents, just the sheer number of words or the scale of that.

And it focuses much more on what the content of those words, or

the content of those documents in terms of which words appear.

So on the one hand, that seems really, really appealing.

But it's not something that's always desired.

We don't always want to be invariant to the length of the document.

Because what that's doing is it might be taking really dissimilar objects and

making them look more similar than they really are.

So for example, let's say we're reading a really long document.

This is maybe some article that appeared in The Atlantic.

And then, on the other hand, we have a really short tweet, very,

very little content to it.

If you look at the cosine similarity between these two,

that's going to make that tweet and

this really long article appear much more similar than they are in reality.

And if somebody's sitting there reading a really long article,

do we really want to suggest that they go and read a tweet?

Maybe not.

So instead, what people often do, is some compromise between this

normalization of cosine similarity, and just ignoring normalization altogether.

And what they do is cap the maximum word counts that appear in the vector.

So, up to this point, we've really focused on Euclidean distance and

cosine similarity as the two distance measures that we've examined,

because of our focus on document modeling, or document retrieval, in particular.

But there are lots and lots of other interesting distance metrics that we could

use things like Mahalanobis, rank-based, correlation-based, Manhattan,

Jaccard, Hamming and many others that we have not gone through in this course.

But there is one last thing that I wanted to mention that's really

commonly used out there in practice.

Which is to use different distance measures over different subsets of your

features.

So for example, in our document case, maybe we would have features of text of

the document, because that's what we've really been focusing on.

But maybe we also have counts of how many times somebody read that article, so

some numerical quantity, it's something that's inherently numerical.

So in this case, maybe we would use cosine similarity for

comparing text of the documents where we want this invariance to a scale or

the length of the document.

But for the counts, we definitely want the counts in their raw form,

no normalization of that, and so for that, maybe we'd use just Euclidean distance.

And so you can think about computing different types of distance measures over

our different features and then weighting them in whatever way you would like to,

like we talked about for weighted Euclidean.

But now, it doesn't have to be just weights over Euclidean distances.

It can be weights over all these different fun forms of distances, and

then use that as our measure of similarity between, in this case, documents.

And this is quite natural if we actually think about our housing application,

where if you think of a listing of a house,

you'll have some text description of that house.

And maybe you don't care if the real estate agent was really verbose or not, so

you want to be invariant to that and maybe you use cosine similarity to compare

the text of the different house listings.

But then for features like number of square feet, number of bedrooms and

bathrooms, the actual scale of these numbers matters a lot,

so using Euclidean distance would be quite natural.

Okay, so you see this type of things in lots and

lots of different application areas.

So in summary, what we've gone through so

far in this module is different notions of how we can represent our document,

and different ways in which we can compute the distance between two documents.

And these were these fundamental pieces to our nearest neighbor search.

And really the conclusion of what we've gone through, to this point,

is giving you a set of options to consider.

But hopefully the take-home message is to think carefully about what you're doing

and the implications of what you're doing.

There's no one right answer for how to go about something, but

it's very important to think about whatever choice you make,

what does that mean for the problem that you're looking at?

Okay, so maybe this whole module up to this point was a word of warning.

No, hopefully it was more than that, hopefully it gave you a set of tools you

can think about using in the building blocks for

learning about other tools out there.

[MUSIC]

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