User-movie Interactions

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來自 Princeton University 的課程

Networks Illustrated: Principles without Calculus

40 個評分

Princeton University

Networks Illustrated: Principles without Calculus

40 個評分

What makes WiFi faster at home than at a coffee shop? How does Google order its search results from the trillions of webpages on the Internet? Why does Verizon charge $15 for every GB of data we use? Is it really true that we are connected in six social steps or less? These are just a few of the many intriguing questions we can ask about the social and technical networks that form integral parts of our daily lives. This course is about exploring the answers, using a language that anyone can understand. We will focus on fundamental principles like “sharing is hard”, “crowds are wise”, and “network of networks” that have guided the design and sustainability of today’s networks, and summarize the theories behind everything from the social connections we make on platforms like Facebook to the technology upon which these websites run. Unlike other networking courses, the mathematics included here are no more complicated than adding and multiplying numbers. While mathematical details are necessary to fully specify the algorithms and systems we investigate, they are not required to understand the main ideas. We use illustrations, analogies, and anecdotes about networks as pedagogical tools in lieu of detailed equations. Please note that per Princeton University policy, no certificates, credentials or reports are awarded in connection with this course.

從本節課中

Movie Recommendation on Netflix

One of the perks of having a Netflix subscription is getting recommendations of movies to watch. Behind the scenes, Netflix uses powerful algorithms to determine which will be suggested to each person specifically. In this lesson, we will take a look at the main ideas behind these algorithms.

Netflix Timeline5:21

Video Streaming5:19

Recommendation is Everywhere3:24

Netflix Recommendation System5:20

Netflix Prize: Logistics7:38

Netflix Prize: The Competition4:33

Our Example3:48

Raw Average7:13

User-movie Interactions7:00

Baseline Predictor6:57

Cosine Similarity9:18

Similarity Values10:58

Leveraging Similarity8:30

Neighborhood Predictor4:44

Performance of Different Methods3:30

Copy of Cosine Similarity9:18

與講師見面

Christopher Brinton
Lecturer
Electrical Engineering
Mung Chiang
Professor
Electrical Engineering

So the first thing we want to take into account are user to movie interactions,

so, we'll look at each user, each movie in isolation and we won't take into

account similarities amongst them, right now, we'll just look at each one in

isolation. and see what we can do about making the

prediction a little better. And so the first thing you'll notice

let's just take a look at this chart over here and we've highlighted, user D and

movie three. So one thing you'll notice about user D

is that seems kind of harsh in his reviews right?

Because he gave a two when everyone else is giving a four or a five.

He gave a three to this movie which everyone else gave a four or five, he

gave a one where we have two other fours over here.

He gave a two. Where again, there's a lot of values

higher. So he seems, he seems kind of harsh, like

a harsh reviewer. And then on the other hand, if you look

at movie three, you know, movie three seems to get pretty good ratings, except,

with the exception of the harsh critic D who gave it a three, which is still

average. it's getting all fours and fives, whereas

other movies are a bit lower, so you could say movie three might be a really

good movie, right. so, that's the idea here behind, biasing,

right, some, some just tend to have higher mean or average values then

others, that's why we can't just average the entire table.

We have to take, it's better to take the columns into account as well and the rows

and the columns separately. So, this whole idea again, first of easy

or harsh reviewers, you can Also imagine that some reviewers, maybe

reviewer A over here might just be much easier than the others.

you know, whereas D is much harsher and he tends to rate much lower.

again people rate differently and we, we pointed out user D for being that one

harsh reviewer. at the same time on the movie side

there's some movies are good. Some movies are bad, you know, some

movies are just higher quality than others and are better perceived by the

public. so movie three seems to be a really,

really good movie whereas two might be a little lower quality or at least

perceived less well by the overall general opinion.

And so you know, again movie three is what we pointed out as well here.

And this really forms the basis for what we call the baseline predictor.

And the baseline predictor. And what we do is we take each of these

rating values or we, we start with the average actually and we take we take that

raw average, remember last, from last time that was just the 3.5 then we add in

a bias for the user and we add in a bias for the movie.

So the biases are going to be positive if it's better received or if you tend to be

a more lenient critic. And they're going to be negative if it's

a movie that's, tends to be worse or if the critic tends to be more harsh.

And so we have to find the bias for each of these users.

And that's, that's the whole idea here, is that we really need to to find those

those bias values. And so finding the bias is, is somewhat

of an art actually. there, there is a quote unquote right way

to do it probably which would be that we have to solve a complicated optimization

problem. [SOUND] Optimization right over here and

but we're not dealing with any calculus or linear algebra in this course.

We won't go that far, we won't deal with that.

We will just look at a simpler approach to doing this.

And so we need to find the bias values so we'll try to do something intuitive.

Why don't we just compare it to the mean value?

Right, so let's just compare it to what the mean was.

Again, remember the mean at the overall data set was 3.5 so let's see how much

higher or lower the mean is than 3.5, and that's how we find the bias.

So we take the average, of the lower column.

We'll start with, maybe we'll start with the harsh critic in D, so we'll take.

2 plus 3 plus 1 plus 2 is the average of these values 2, 3, 1 and 2.

Again remember we're not including anything that is in the test set when we

do these biases out. Divide that by 4, just for those values,

and that is 8 divided by 4, which is 2. But then that we actually have to

subtract out the mean because we want to do it relative to the overall mean, so we

do 2 minus 3.5. So we've just can write up here this is

really minus 3.5, this is minus 3.5. So we get 2 minus 3.5 which is negative

1.5. So that's the bias and that should make

sense because D is a harsh critic so he's well below the average rating of minus

1.5. He was below the average of 3.5.

And now let's try the good movie, or movie three, so we can take the average

of the values again. So this is for D.

Now we'll try three. So, you, we add up 4 plus 5 plus 3 plus 5

and again, there's five of those, there's four, sorry, there's four of those

values. this we don't have and this is in the

test sets, we don't use it. So this comes out to be 17 over 4, which

is, 4.25. And then remember we subtract 3.5 from

all of these values, minus 3.5, minus 3.5.

And this is 4.25 minus 3.5, which gives us positive 0.75.

So, for D we have a negative value of negative 1.5 and for 3 we have positive

of 0.75 which is significantly above zero, or it's above zero reasonably

enough, which is what we expected, because we expected that 3 was a much

better movie than the others. And so the key idea here, again though,

is that you can't use the test set. So the test set has to go.

And because we're not using that in these prediction schemes because we're, that's

what we're going to test the RMSE on. And so we can do the rest of the values

out and I've do note, I've given the values at the end of the columns or rows

here. So the bias for A is positive 0.83, for B

is 0.5, for C is negative 1. really easy to see we could do C is, for

instance, right now there's only two values, there's a two and a three here,

so we just do 2 plus 3 divided by 2 minus 3.5, which is 5 divided by 2, which is

2.5 minus 3.5 which is negative 1.0. And you can verify the rest of these

also. and then on the movie side, again, two is

pretty negative movie actually. 3 plus 2 plus 2 divided, divided by 3,

and then, subtract out, the mean of 3.5 from that.

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