Distributed Computing Group From Web to Map: Exploring the World of Music Olga Goussevskaia Michael Kuhn Michael Lorenzi Roger Wattenhofer Web Intelligence 2008 Sydney, Australia

2 Olga Goussevskaia, ETH Web Intelligence 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

3 Olga Goussevskaia, ETH Web Intelligence 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!

4 Olga Goussevskaia, ETH Web Intelligence 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:

5 Olga Goussevskaia, ETH Web Intelligence Music Similarity Audio content analysis Metadata analysis Collaborative filtering –“people who listen to this song also listen to that song” Similar or different???

6 Olga Goussevskaia, ETH Web Intelligence From Perception to Web Data from last.fm (20M users) –Top-50 lists (290K lists, 1.5M distinct songs) –Co-occurrence analysis (normalization cosine(s i,s j )=n ij /(n i n j ) 1/2 ) –10 12 (O(TB)!) pair-wise similarity values Building a graph G –Edge weight w(s i,s j ) = 1/cosine(s i,s j ) –Sparsening: co-occ ≥ 2, w(s i,s j ) ≥ threshold –sim(s i, s j ) = length(shortestPath G (s i, s j )) –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(s i, s j ): 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!

7 Olga Goussevskaia, ETH Web Intelligence From Web to Map Embedding: map vertices of G into points in Euclidean space, s.t. d G /d E (stretch) is “minimized”. Computation cost of sim(i,j): O(1) time, O(1) memory per item Embedding algorithms: –Multi Dimensional Scaling (MDS): O(dn 2 ) –Spring embedding (Fruchterman-Reingold): O(n 2 + m) –MIS-filtering: O(n log 2 Δ) –High-dimensional embedding: O(nl 2 + lm) –Landmark MDS (LMDS): O(nld + l 3 ) –Adaptive computation/quality tradeoff –Suitable for dynamic settings

8 Olga Goussevskaia, ETH Web Intelligence 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 d E /d G Example: Kleinberg graph (20x20 grid, f = 0.003) Spring embedding output After 6 rounds After 12 rounds After 30 rounds

9 Olga Goussevskaia, ETH Web Intelligence Evaluation Music Taxonomy ( –Control set: 7K songs with genre information Genre distance d S = LCA (least common ancestor) How well does the resulting map represent music similarity?

10 Olga Goussevskaia, ETH Web Intelligence Evaluation: Quality Measures Distance comparison Q L : average similarity increase as a function of genre distance d s Embedding smoothness Q R : average # of genre re- occurrences on a random line Avg. similarity of pairs (s i,s j ) w/ d s (i,j)=h Songs that belong to distant genres should be far away in the embedding. Genre transitions in the embedding should be “smooth”.

11 Olga Goussevskaia, ETH Web Intelligence Evaluation: Iterative Embedding After 30 rounds, f=0.5% LMDS output (430K nodes, 10 dimensions)

12 Olga Goussevskaia, ETH Web Intelligence Evaluation Closest neighbors in 10D

13 Olga Goussevskaia, ETH Web Intelligence Applications: Music Explorer –Web service to query coordinates (current DB with 430K titles) –Visualization in 2D –Zoom level according to song popularity –Playlist generation based on trajectories

14 Olga Goussevskaia, ETH Web Intelligence Playlist generation Interpolation between start and end-point –Smooth transition from one style to the other –In reality: 10 dimensions

15 Olga Goussevskaia, ETH Web Intelligence 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

16 Olga Goussevskaia, ETH Web Intelligence 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)

17 Olga Goussevskaia, ETH Web Intelligence Conclusions Necessary?

18 Olga Goussevskaia, ETH Web Intelligence Thanks for your Attention Questions?