Closed form solutions Quick test/train cycle Few components: no interaction Relatively new task Self-contained
Frontend and Speaker recognition • Standard question: why use STT features? • No convincing alternative: why? • Unlike linguistic content, speaker characteristics do not show on spectrogram • Unknown distortions in the spectrogram contain the information => Purely mathematical signal processing
SWAMP • SWAMP=Sweeping metric parameterization
• Input: MFCC • Output: Ranked SWAMP features • Basic idea: speech is a time curve on a
manifold
Metaphors: surface and grid
Z 21.0
t=4 -2 10.7
0
0.4
X -2
t=1
Y 0
t=2
2
t=3
2
Why Isometric Features? • Simple algebra and Gaussian OK
SWAMP: isometric
MFCC
Sweeping metric • Defines the shape of the squares [Scroedinger, Levin]
• Intuition: fast is imprecise Defined locally around y
Sweeping metric(2) • Each square has its metric g
Idea: triangulation • Characterize all points by relative distance • Flatten out surface
“Geodesic lengths”
Classical Metric Multidimensional Scaling (CMDS) • Visualization technique used in psychology mi
SB
Boston NYC
Dallas
SB
0
2663
2521
1326
0
190
1551
0
1373
Boston NYC Dallas
0
Isometric coordinates
Distances and MDS • Summary: – Find local metrics – Find geolen distances by integration
– SVD the distance matrix (MDS) mi
SB
Boston
NYC
Dallas
SB
0
2663
2521
1326
0
190
1551
0
1373
Boston NYC Dallas
0
Implementation details • Vector quantization: curse of dimensionality • Voronoi regions: locally linear regions • Adjacency: join squares of the surface • Tunneling: accidentally go “under” surface • Floyd-Warshall: complete paths
Vector Quantization • Curse of dimensionality prevents from computing local metrics (space not compactly populated) • Alternative (e.g. Levin): RiemannChristoffel symbol of the second kind
• Large ODE
Vector Quantization • Our solution: locally linear regions • Simplifies the geolen computation as well • Problem: VQ distortion is initialized with the contravariant coordinates
Voronoi regions • Polyhedral geodesics are straight lines if local embeddings are linear • Problem: Dirichlet/Voronoi interface is quadratic • Newton/Raphson solution of the Lagrangian Voronoi interface
Floyd-Warshall (or Dijkstra) • From local geolens to complete graph • Local geolens: Completed geolen
Tunneling and Adjacency • Use time structure to avoid going under the manifold
Z 21.0
-2 10.7
0
0.4
X -2 Y 0
2 2
Properties • Unique under any invertible constant distortion • Robust to quasi-stationary noise • Isometric • Time-distortion can be recovered by extending the vector (WRONG?) • Expensive
Zero Collar • Zero collar requires precise speech/non speech • Morph filter minimizes the risk (trim a little from both ends) • Apply 0.3s bridging rule • (old system): 19.33% spkr error => 18.71%
Results • • • • • •
Zero collar is sharp Length of shows affects performance Last year: 18.8% spkr time err This year: 13.5% (18.6% relative) Only participant (PSTL) last year Lowest error
Scaling (CMDS). ⢠Visualization technique used in psychology mi. SB. Boston NYC ... From local geolens to complete graph. ⢠Local geolens: Completed geolen ...
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