So far:• Historical introduction• Mathematical background (e.g., pattern classification,

acoustics)• Feature extraction for speech recognition (and some

neural processing)• What sound units are typically defined• Audio signal processing topics (pitch extraction,

perceptual audio coding, source separation, music analysis)

• Now – back to pattern recognition, but include time

Deterministic Sequence Recognition

Sequence recognition for ASR

• ASR = static pattern classification + sequence recognition

• Deterministic sequence recognition: template matching

• Templates are typically word-based;don’t need phonetic sound units per se

• Still need to put together local distances into something global (per word or utterance)

Front end analysis

• Basic approach the same for deterministic, statistical:– 25 ms windows (e.g., Hamming), 10 ms steps (a

frame)– Some kind of cepstral analysis (e.g., MFCC or PLP)– Cepstral vector at time n called xn

Speech sound categories

• Words, phones most common• For template-based ASR, mostly words• For template-based ASR, local distances based

on examples (reference frames) versus input frames

From Frames to Sequence

• Easy if local matches are all correct (never happens!)

• Local matches are unreliable• Need measure of goodness of fit• Need to integrate into global measure• Need to consider all possible sequences

Templates: Isolated Word Example

• Matrix for comparison between frames• Word template = multiple feature vectors• Reference template = • Input template = • Need to find D( , )

Xkref

X in

X inXkref

Templates Matching Problem

• Time Normalization• Which references to use• Defining distances/costs• Endpoints for input templates

Time Normalization

• Linear Time Normalization• Nonlinear Time Normalization – Dynamic Time

Warp (DTW)

Linear Time Normalization: Limitations

• Speech sounds stretch/compress differently• Stop consonants versus vowels• Need to normalize differently

Generalized Time Warping

• Permit many more variations• Ideally, compare all possible time warpings• Vintsyuk (1968): use dynamic programming

Dynamic programming

• Bellman optimality principle (1962): optimal policy given optimal policies from sub problems

• Best path through grid: if best path goes through grid point, best path includes best partial path to grid point

• Classic example: knapsack problem

Knapsack problem

• Stuffing a sack with items, different value• Goal: maximize value in sack• Key point 1: If max size is 10, and we know

values of solutions for max size of 9, we can compute the final answer knowing the value of adding items.

• Key point 2: Point 1 sounds recursive, but can be made efficiently nonrecursive by building a table

Basic DTW step w/ simple local constraints. Each (i,j) cell has local distance d and cumulative distortion D. The eqn shows the basic computational step.

Dynamic Time Warp (DTW)

• Apply DP to ASR: Vintsyuk, Bridle, Sakoe• Let D(i,j) = total distortion up to frame i in

input and frame j in reference• Let d(i,j) = local distance between frame i in

input and frame j in reference• Let p(i,j) = set of possible predecessors to

frame i in input and frame j in reference• D(i,j) = d(i, j) + minp(i,j) D(p(i,j))

DTW steps

(1) Compute local distance d in 1st column(1st frame of input) for each reference template.Let D(0,j) = d(0,j) for each cell in each template

(2) For i=1 (2nd column), j=0, compute d(i,j) add to min of all possible predecessor values of D to get local value of D; repeat for each frame in each template.

(3) Repeat (2) for each column to the end of input(4) For each template, find best D in last column of input(5) Choose the word for the template with smallest D

DTW Complexity

• O(Nframesref . Nframesin . Ntemplates)

• Storage, though can just be O(Nframesref . Ntemplates)

(store current column and previous column)• Constant reduction: global constraints• Constant reduction: local constraints

Typical global slope constraints for dynamic programming

Which reference templates?

• All examples?• Prototypes?• DTW-based global distances permit clustering

DTW-based K-means

• (1) Initialize (how many, where)• (2) Assign examples to closest center (DTW

distance)• (3) For each cluster, find template with

minimum value for maximum distance, call it the center

• (4) Repeat (2) and (3) until some stopping criterion is reached

• (5) Use center templates as references for ASR

Defining local distance

• Normalizing for scale• Cepstral weighting• Perceptual weighting, e.g., JND• Learning distances, e.g., with ANN, statistics

Endpoint detection: big problem!

• Sounds easy• Hard in practice (noise, reverb, gain issues)• Simple systems use energy, time thresholds• More complex ones also use spectrum• Can be tuned• Not robust

Connected Word ASR by DTW

• Time normalization• Recognition• Segmentation• Can’t have templates for all utterances• DP to the rescue

DP for Connected Word ASR by DTW

• Vintsyuk, Bridle, Sakoe• Sakoe: 2-level algorithm• Vintsyuk, Bridle: one stage• Ney explanation

Ney, H., “The use of a one-stage dynamic programming algorithm for connected word recognition,” IEEE Trans. Acoust. Speech Signal Process. 32: 263-271, 1984

Connected Algorithm• In principle: one big distortion matrix

(for 20,000 words, 50 frames/word, 1000 frame input [10 seconds] would be 109 cells!)

• Also required, backtracking matrix (since word segmentation not known)

• Get best distortion• Backtrack to get words• Fundamental principle: find best segmentation

and classification as part of the same process, not as sequential steps

DTW path for connected words

DTW for connected words

• In principle, backtracking matrix points backto best previous cell

• Mostly just need backtrack to end of previous word

• Simplifications possible

Storage efficiency

• Distortion matrix -> 2 columns• Backtracking matrix -> 2 rows• “From template” points to template with

lowest cost ending here• “From frame” points to end frame of previous

word

More on connected templates

• “Within word” local constraints• “Between word” local constraints• Grammars• Transition costs

Knowledge-based segmentation

• DTW combines segmentation, time norm, recognition; all segmentations considered

• Same feature vectors used everywhere• Could segment separately, using acoustic-

phonetic features cleverly• Example: FEATURE, Ron Cole (1983)

Limitations of DTW approach

• No structure from subword units• Average or exemplar values only• Cross-word pronunciation effects not handled• Limited flexibility for distance/distortion• Limited mathematical basis• -> Statistics!

Epilog: “episodic” ASR

• Having examples can get interesting again when there are many of them

• Potentially an augmentation of stat methods• Recent experiments show decent results• Somewhat different properties ->

combination

The rest of the course• Statistical ASR• Speech synthesis• Speaker recognition• Speaker diarization• Oral presentations on your projects• Written report on your project

Class project timing• Week of April 30: no class Monday, double class

Wednesday May 2 (is that what people want?)• 8 oral presentations by individuals, 12 minutes each

+ 3 minutes for questions• 2 oral presentations by pairs – 17 minutes each + 3

minutes for questions• 3:10 PM to 6 PM with a 10 minute mid-session break• Written report due Wednesday May 9, no late

submissions (email attachment is fine)