August 5, 2013

ML ♡ Hadoop @ Spotify

If it’s slow, buy more racks

I’m Erik Bernhardsson

Master’s in Physics from KTH in StockholmStarted at Spotify in 2008, managed the Analytics team for two yearsMoved to NYC in 2011, now the Engineering Manager of the Discovery team at Spotify in NYC

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August 5, 2013

What’s Spotify? What are the challenges?

Started in 2006Currently has 24 million users6 million paying usersAvailable in 20 countriesAbout 300 engineers, of which 70 in NYC

And adding 20K every day...

Big challenge: Spotify has over 20 million tracks

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Good and bad news: we also have 100B streams

Let’s use collaborative filtering!

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Hey,I like tracks P, Q, R, S!

Well,I like tracks Q, R, S, T!

Then you should check out track P!

Nice! Btw try track T!

Hadoop at Spotify

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Back in 2009

Matrix factorization causing cluster to overheat? Don’t worry, put up curtain

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Source:

Hadoop today700 nodes at our data center in London

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The Discover page

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Here’s a secret behind the Discover page

It’s precomputed every night

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HADOOP

Cassandra Bartender

Log streams

Music recs

hdfs2cass

Here’s a secret behind the Discover page

It’s precomputed every night

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HADOOP

Cassandra Bartender

Log streams

Music recs

hdfs2cass

Here’s a secret behind the Discover page

It’s precomputed every night

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HADOOP

Cassandra Bartender

Log streams

Music recs

hdfs2cass

https://github.com/spotify/luigi

Here’s a secret behind the Discover page

It’s precomputed every night

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HADOOP

Cassandra Bartender

Log streams

Music recs

hdfs2cass

https://github.com/spotify/luigi

https://github.com/spotify/hdfs2cass

OK so how do we come up with recommendations?

Let’s do collaborative filtering!In particular, implicit collaborative filteringIn particular, matrix factorization (aka latent factor methods)

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Stop!!!

Break it down!!

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AP AP AP AP AP AP

Hadoop(>100B streams)

Play track zplay track y

play track x

5k tracks/s

Step 1: Collect data

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Step 2: Put everything into a big sparse matrix

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Using some definition of correlation. Eg. for Pearson:

cij =

Pu NuiNuj

pPu N

2ui

qPu N

2uj

but it’s very slow because:

N =

0

BBBBBB@

0 7 21 05 0 0 14 0 13 90 0 0 719 1 0 130 3 0 0

1

CCCCCCA

NTN =

0

BB@

402 19 52 28819 59 147 1352 147 610 117288 13 117 300

1

CCA

O(U · (N/I)2)...where U = number of users

I = number of itemsN = number of nonzero entries

⇡ 107 · (1010/107)2 = 1013 mapper outputs

It’s an extremely sparse matrix

M =

0

BBBBBBBBBBBB@

......

.... . . . . . 53 . . . . . .

......

.... . . . . . . . . 12 . . .

......

.... . . 7 . . . . . . . . .

......

...

1

CCCCCCCCCCCCA

It’s a very big matrix too:

M =

0

BBB@

c11 c12 . . . c1nc21 c22 . . . c2n...

...cm1 cm2 . . . cmn

1

CCCA

| {z }107 items

9>>>>>>>>>=

>>>>>>>>>;

107 users

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Matrix example

Roughly 25 billion nonzero entriesTotal size is roughly 25 billion * 12 bytes = 300 GB (“medium data”)

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Matrix example

Roughly 25 billion nonzero entriesTotal size is roughly 25 billion * 12 bytes = 300 GB (“medium data”)

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Erik

Never gonna give you up

Erik listened to Never gonna give you up 1

times

Idea is to find vectors for each user and itemHere’s how it looks like algebraically:

Step 3: Matrix factorization

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Turns out people have been doing this in NLP for a while

M =

0

BBB@

c11 c12 . . . c1nc21 c22 . . . c2n...

...cm1 cm2 . . . cmn

1

CCCA

| {z }Lots of words

9>>>>>>>>=

>>>>>>>>;

Lots of documents

Or more generally:

P =

0

BBB@

p11 p12 . . . p1np21 p22 . . . p2n...

...pm1 pm2 . . . pmn

1

CCCA

The idea with matrix factorization is to represent this probability distribu-tion like this:

pui = aTubi

M 0 = ATB

0

BBBBBB@

1

CCCCCCA⇡

0

BBBBBB@

1

CCCCCCA

| {z }f

� � f

0

BBBBBB@

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

1

CCCCCCA

| {z }probabilities for next event

⇡

0

BBBBBB@

. .

. .

. .

. .

. .

. .

1

CCCCCCA

| {z }user vectors

✓. . . . . . .. . . . . . .

◆

| {z }item vectors

We can look at it as a probability distribution:0

BBBBBB@

0 0.07 0.21 00.05 0 0 0.010.04 0 0.13 0.090 0 0 0.07

0.19 0.01 0 0.130 0.03 0 0

1

CCCCCCA

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For instance, for PLSA

Probabilistic Latent Semantic Indexing (Hoffman, 1999)Invented as a method intended for text classification

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P =

0

BBBBBB@

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

1

CCCCCCA⇡

0

BBBBBB@

. .

. .

. .

. .

. .

. .

1

CCCCCCA

| {z }user vectors

✓. . . . . . .. . . . . . .

◆

| {z }item vectors

PLSA0

BBBBBB@

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

1

CCCCCCA

| {z }P (u,i)=

PzP (u|z)P (i,z)

⇡

0

BBBBBB@

. .

. .

. .

. .

. .

. .

1

CCCCCCA

| {z }P (u|z)

✓. . . . . . .. . . . . . .

◆

| {z }P (i,z)

X

u

P (u|z) = 1

X

i,z

P (i, z) = 1

So in general we want to optimize

logY

P (u, i)Nui =X

u,i

Nui logP (u, i) =X

u,i

Nui logX

z

P (u|z)P (i, z)

N logP =

0

BBBBBB@

0 7 21 05 0 0 14 0 13 90 0 0 719 1 0 130 3 0 0

1

CCCCCCAlog

0

BBBBBB@

0

BBBBBB@

. .

. .

. .

. .

. .

. .

1

CCCCCCA

✓. . . .. . . .

◆

1

CCCCCCA

KOREN

N =

0

BBBBBB@

0 7 21 05 0 0 14 0 13 90 0 0 719 1 0 130 3 0 0

1

CCCCCCA

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Why are vectors nice?

Super small fingerprints of the musical style or the user’s tasteUsually something like 40-200 elementsHard to illustrate 40 dimensions in a 2 dimensional slide, but here’s an attempt:

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0.87 1.17 -0.26 0.56 2.21 0.77 -0.03

Latent factor 1

Latent factor 2

track x's vector

Track X:

Another example of tracks in two dimensions

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Implementing matrix factorization is a little tricky

Iterative algorithms that stake many steps to converge40 parameters for each item and userSo something like 1.2 billion parameters

“Google News Personalization: Scalable Online Collaborative Filtering”

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One iteration, one map/reduce job

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Reduce stepMap step

u % K = 0i % L = 0

u % K = 0i % L = 1 ... u % K = 0

i % L = L-1

u % K = 1i % L = 0

u % K = 1i % L = 1 ... ...

... ... ... ...

u % K = K-1i % L = 0 ... ... u % K = K-1

i % L = L-1

item vectorsitem%L=0

item vectorsitem%L=1

item vectorsi % L = L-1

user vectorsu % K = 0

user vectorsu % K = 1

user vectorsu % K = K-1

all log entriesu % K = 1i % L = 1

u % K = 0

u % K = 1

u % K = K-1

One iteration, one map/reduce job

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Reduce stepMap step

u % K = 0i % L = 0

u % K = 0i % L = 1 ... u % K = 0

i % L = L-1

u % K = 1i % L = 0

u % K = 1i % L = 1 ... ...

... ... ... ...

u % K = K-1i % L = 0 ... ... u % K = K-1

i % L = L-1

item vectorsitem%L=0

item vectorsitem%L=1

item vectorsi % L = L-1

user vectorsu % K = 0

user vectorsu % K = 1

user vectorsu % K = K-1

all log entriesu % K = 1i % L = 1

u % K = 0

u % K = 1

u % K = K-1

Here’s what happens in one map shard

Input is a bunch of (user, item, count) tuplesuser is the same modulo K for all usersitem is the same modulo L for all items

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One map taskDistributed

cache:All user vectors where u % K = x

Distributed cache:

All item vectors where i % L = y

Mapper Emit contributions

Map input:tuples (u, i, count)

where u % K = x

andi % L = y

Reducer New vector!

Might take a while to converge

Start with random vectors around the origin

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Hadoop?

Yeah we could probably do it in Spark 10x or 100x faster.Still, Hadoop is a great way to scale things horizontally.

????

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Nice compact vectors and it’s super fast to compute similarity

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Latent factor 1

Latent factor 2

track xtrack y

cos(x, y) = HIGH

IPMF item item:

P (i ! j) = exp(bTj bi)/Zi =

exp(bTj bi)P

k exp(bTk bi)

VECTORS:pui = aTubi

simij = cos(bi,bj) =bTi bj

|bi||bj|

O(f)

i j simi,j

2pac 2pac 1.02pac Notorious B.I.G. 0.912pac Dr. Dre 0.872pac Florence + the Machine 0.26Florence + the Machine Lana Del Rey 0.81

IPMF item item MDS:

P (i ! j) = exp(bTj bi)/Zi =

exp(� |bj � bi|2)Pk exp(� |bk � bi|2)

simij = � |bj � bi|2

(u, i, count)

@L

@au

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IPMF item item:

P (i ! j) = exp(bTj bi)/Zi =

exp(bTj bi)P

k exp(bTk bi)

VECTORS:pui = aTubi

simij = cos(bi,bj) =bTi bj

|bi||bj|

O(f)

i j simi,j

2pac 2pac 1.02pac Notorious B.I.G. 0.912pac Dr. Dre 0.872pac Florence + the Machine 0.26Florence + the Machine Lana Del Rey 0.81

IPMF item item MDS:

P (i ! j) = exp(bTj bi)/Zi =

exp(� |bj � bi|2)Pk exp(� |bk � bi|2)

simij = � |bj � bi|2

(u, i, count)

@L

@au

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Music recommendations are now just dot products

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Latent factor 1

Latent factor 2

track x

User u's vector

track y

It’s still tricky to search for similar tracks though

We have many million tracks and you don’t want to compute cosine for all pairs

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Approximate nearest neighbors to the rescue!

Cut the space recursively by random plane.If two points are close, they are more likely to end up on the same side of each plane.

https://github.com/spotify/annoy

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How do you retrain the model?

It takes a long time to train a full factorization model.We want to update user vectors much more frequently (at least daily!)However, item vectors are fairly stable.Throw away user vectors and recreate them from scratch!

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The pipeline

“Hack” to recalculate user vectors more frequently.

Is this a little complicated? Yeah probably.

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May 2013 logs

Matrix factorization

Item vectors

User vectors

June 2013 logs

Matrix factorization

Item vectors

User vectors

+ more logs

Seeding

User vectors (1)

Logs

User vectors (2)

More logs

User vectors (3)

More logs

User vectors (4)

More logs

User vectors (5)

More logs

Time

Ideal case

Put all vectors in Cassandra/Memcached, use Storm to update in real time

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But Hadoop is pretty nice at parallelizing recommendations

24 core but not a lot of RAM? mmap is your friend

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One map reduce job

Recs!

ANN index of all vectors

Distributed cache:User vectors

M M

M M

DC

M M

M M

DC

M M

M M

DC

Music recommendations!

Our latest baby, the Discover page. Featuring lots of different types of recommendations. Expect this to change quite a lot in the next few months!

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More music recommendations!

Radio!

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More music recommendations!

Related artists

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Thanks!

Btw, we’re hiring Machine Learning Engineersand Data Engineers!Email me at erikbern@spotify.com!