from web to map: exploring the world of music

DistributedComputing

Group

From Web to Map: Exploring the World of Music

Olga GoussevskaiaMichael KuhnMichael LorenziRoger Wattenhofer

Web Intelligence 2008Sydney, Australia

2Olga Goussevskaia, ETH Zurich @ Web Intelligence 2008 2

• Storage media– Vinyl records– Compact cassetts– Compact discs

• An Album is stored on a single physical storage medium– Sequence of songs given by album– Album is typically listened to as a whole

Music in the old days

organization by album


Music today

• Huge offer, easily available – filesharing, iTunes, Amazon, etc.

• Large collections– The entire collection is stored on

a single electronic storage medium

– Organization by albums (and other lists) is no longer appropriate

organize by similarity!


Overview

• Define music similarity

• From Perception to Web– Build a graph of songs

• From Web to Map– Embed the graph into

Euclidean space

• Application prototype: www.musicexplorer.org


Music Similarity

• Audio content analysis• Metadata analysis• Collaborative filtering

– “people who listen to this song also listen to that song”

Similar or different???


From Perception to Web• Data from last.fm (20M users)

– Top-50 lists (290K lists, 1.5M distinct songs)– Co-occurrence analysis (normalization

cosine(si,sj)=nij/(ninj)1/2)– 1012 (O(TB)!) pair-wise similarity values

• Building a graph G– Edge weight w(si,sj) = 1/cosine(si,sj)– Sparsening: co-occ ≥ 2, w(si,sj) ≥ threshold– sim(si, sj) = length(shortestPathG(si, sj)) – Still n = 430K, m = 6.3M, and ever growing

• How to operate on G? (assuming G is sparse: m=O(n logn))

– Shortest path computation cost: O(m+logn)=O(n logn)– Memory needed to retrieve one value sim(si, sj):

O(m)=O(n logn)

Order of seconds on a state-of-the-art PC!

Need to store the whole G, even if I only have 50 songs in my collection!


From Web to Map• Embedding: map vertices of G into points in Euclidean

space, s.t. dG/dE (stretch) is “minimized”.

• Computation cost of sim(i,j): O(1) time, O(1) memory per item

• Embedding algorithms:– Multi Dimensional Scaling (MDS): O(dn2)– Spring embedding (Fruchterman-Reingold): O(n2 + m)– MIS-filtering: O(n log2 Δ)– High-dimensional embedding: O(nl2 + lm)– Landmark MDS (LMDS): O(nld + l3)

– Adaptive computation/quality tradeoff– Suitable for dynamic settings


Iterative Embedding• Assumption: some links erroneously shortcut certain paths

E [# random edges] = X

• Repeat (X / f) times– embed G (using e.g. LMDS)– Remove (from G) fraction f of edges with highest stretch dE/dG

• Example: Kleinberg graph (20x20 grid, f = 0.003)

Spring embedding output

After 6 rounds After 12 rounds After 30 rounds


Evaluation

• Music Taxonomy (www.allmusic.com)– Control set: 7K songs with genre information

Genre distance dS= LCA (least

common ancestor)

How well does the resulting map represent music similarity?

http://www.allmusic.com/


Evaluation: Quality Measures

• Distance comparison QL: average similarity increase as a function of genre distance ds

• Embedding smoothness QR: average # of genre re-occurrences on a random line

Avg. similarity of pairs (si,sj) w/ ds(i,j)=h

Songs that belong to distant genres should be far away in the embedding.

Genre transitions in the embedding should be “smooth”.


Evaluation: Iterative Embedding

After 30 rounds, f=0.5%LMDS output

(430K nodes, 10 dimensions)


Evaluation

Closest neighbors

in 10D


Applications: Music Explorer

• www.musicexplorer.org– Web service to query

coordinates (current DB with 430K titles)

– Visualization in 2D– Zoom level according to

song popularity– Playlist generation based on

trajectories


Blues

Rock

Text

START

END

Blues-Rock

Electric Blues

Playlist generation• Interpolation between start and end-point

– Smooth transition from one style to the other– In reality: 10 dimensions


Music in Euclidean Space

• Performance– Similarity computation comes almost for free: O(1) time– Memory footprint is extremly low: O(1) per song

– All information can be saved in the file, no server connection required.

• Applications– Trajectories (playlists, ...)– Volumes (region of interest, ...)– Notion of direction

coordinates are well suited for mobile applications

coordinates are well suited for similarity based organization


Towards a new world of music?• Euclidean representation

– Efficient similarity computation (time and memory)– No server needed: distributed applications

– Building blocks for new functionalities:

• New scenarios:– Mobile file sharing– P2P overlay based on the map– Innovations at home

– “Play anything hip-hip… not this and not closely related songs… go towards Detroit house, be there in an hour”

– Automatic DJ (collect feedback from mobiles, generate playlists based on guests regions of interest)

Trajectories(Playlists)

Volumes(Interest Regions)

Notion of Direction(Browsing)


Conclusions

• Necessary?


Thanks for your Attention

• Questions?

from web to map: exploring the world of music

Documents

eth zurich

sj thresholdsimsi

graph of songs

new itemsolga goussevskaia

o1 computingmemory cost

computation cost of

map vertices of g

o1 memory