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CTC segmentation can be used to find utterance alignments within large audio files.

Usage

The CTC segmentation package is not standalone, as it needs a neural network with CTC output. It is integrated in these frameworks:

It can also be used with other frameworks:

<details><summary>Wav2vec2 example code</summary><div>
import torch
import numpy as np
from typing import List
import ctc_segmentation
from datasets import load_dataset
from transformers import Wav2Vec2Processor, Wav2Vec2ForCTC, Wav2Vec2CTCTokenizer

# load model, processor and tokenizer
model_name = "jonatasgrosman/wav2vec2-large-xlsr-53-english"
processor = Wav2Vec2Processor.from_pretrained(model_name)
tokenizer = Wav2Vec2CTCTokenizer.from_pretrained(model_name)
model = Wav2Vec2ForCTC.from_pretrained(model_name)

# load dummy dataset and read soundfiles
SAMPLERATE = 16000
ds = load_dataset("patrickvonplaten/librispeech_asr_dummy", "clean", split="validation")
audio = ds[0]["audio"]["array"]
transcripts = ["A MAN SAID TO THE UNIVERSE", "SIR I EXIST"]

def align_with_transcript(
    audio : np.ndarray,
    transcripts : List[str],
    samplerate : int = SAMPLERATE,
    model : Wav2Vec2ForCTC = model,
    processor : Wav2Vec2Processor = processor,
    tokenizer : Wav2Vec2CTCTokenizer = tokenizer
):
    assert audio.ndim == 1
    # Run prediction, get logits and probabilities
    inputs = processor(audio, return_tensors="pt", padding="longest")
    with torch.no_grad():
        logits = model(inputs.input_values).logits.cpu()[0]
        probs = torch.nn.functional.softmax(logits,dim=-1)
    
    # Tokenize transcripts
    vocab = tokenizer.get_vocab()
    inv_vocab = {v:k for k,v in vocab.items()}
    unk_id = vocab["<unk>"]
    
    tokens = []
    for transcript in transcripts:
        assert len(transcript) > 0
        tok_ids = tokenizer(transcript.replace("\n"," ").lower())['input_ids']
        tok_ids = np.array(tok_ids,dtype=np.int)
        tokens.append(tok_ids[tok_ids != unk_id])
    
    # Align
    char_list = [inv_vocab[i] for i in range(len(inv_vocab))]
    config = ctc_segmentation.CtcSegmentationParameters(char_list=char_list)
    config.index_duration = audio.shape[0] / probs.size()[0] / samplerate
    
    ground_truth_mat, utt_begin_indices = ctc_segmentation.prepare_token_list(config, tokens)
    timings, char_probs, state_list = ctc_segmentation.ctc_segmentation(config, probs.numpy(), ground_truth_mat)
    segments = ctc_segmentation.determine_utterance_segments(config, utt_begin_indices, char_probs, timings, transcripts)
    return [{"text" : t, "start" : p[0], "end" : p[1], "conf" : p[2]} for t,p in zip(transcripts, segments)]
    
def get_word_timestamps(
    audio : np.ndarray,
    samplerate : int = SAMPLERATE,
    model : Wav2Vec2ForCTC = model,
    processor : Wav2Vec2Processor = processor,
    tokenizer : Wav2Vec2CTCTokenizer = tokenizer
):
    assert audio.ndim == 1
    # Run prediction, get logits and probabilities
    inputs = processor(audio, return_tensors="pt", padding="longest")
    with torch.no_grad():
        logits = model(inputs.input_values).logits.cpu()[0]
        probs = torch.nn.functional.softmax(logits,dim=-1)
        
    predicted_ids = torch.argmax(logits, dim=-1)
    pred_transcript = processor.decode(predicted_ids)
    
    # Split the transcription into words
    words = pred_transcript.split(" ")
    
    # Align
    vocab = tokenizer.get_vocab()
    inv_vocab = {v:k for k,v in vocab.items()}
    char_list = [inv_vocab[i] for i in range(len(inv_vocab))]
    config = ctc_segmentation.CtcSegmentationParameters(char_list=char_list)
    config.index_duration = audio.shape[0] / probs.size()[0] / samplerate
    
    ground_truth_mat, utt_begin_indices = ctc_segmentation.prepare_text(config, words)
    timings, char_probs, state_list = ctc_segmentation.ctc_segmentation(config, probs.numpy(), ground_truth_mat)
    segments = ctc_segmentation.determine_utterance_segments(config, utt_begin_indices, char_probs, timings, words)
    return [{"text" : w, "start" : p[0], "end" : p[1], "conf" : p[2]} for w,p in zip(words, segments)]

print(align_with_transcript(audio,transcripts))
# [{'text': 'A MAN SAID TO THE UNIVERSE', 'start': 0.08124999999999993, 'end': 2.034375, 'conf': 0.0}, 
#  {'text': 'SIR I EXIST', 'start': 2.3260775862068965, 'end': 4.078771551724138, 'conf': 0.0}]

print(get_word_timestamps(audio))
# [{'text': 'a', 'start': 0.08124999999999993, 'end': 0.5912715517241378, 'conf': 0.9999501323699951}, 
# {'text': 'man', 'start': 0.5912715517241378, 'end': 0.9219827586206896, 'conf': 0.9409108982174931}, 
# {'text': 'said', 'start': 0.9219827586206896, 'end': 1.2326508620689656, 'conf': 0.7700278702302796}, 
# {'text': 'to', 'start': 1.2326508620689656, 'end': 1.3529094827586206, 'conf': 0.5094435178226225}, 
# {'text': 'the', 'start': 1.3529094827586206, 'end': 1.4831896551724135, 'conf': 0.4580493446392211}, 
# {'text': 'universe', 'start': 1.4831896551724135, 'end': 2.034375, 'conf': 0.9285054256219009}, 
# {'text': 'sir', 'start': 2.3260775862068965, 'end': 3.036530172413793, 'conf': 0.0}, 
# {'text': 'i', 'start': 3.036530172413793, 'end': 3.347198275862069, 'conf': 0.7995760873559864}, 
# {'text': 'exist', 'start': 3.347198275862069, 'end': 4.078771551724138, 'conf': 0.0}]
</div></details>

Installation

pip install ctc-segmentation
git clone https://github.com/lumaku/ctc-segmentation
cd ctc-segmentation
cythonize -3 ctc_segmentation/ctc_segmentation_dyn.pyx
python setup.py build
python setup.py install --optimize=1 --skip-build

How it works

1. Forward propagation

Character probabilites from each time step are obtained from a CTC-based network. With these, transition probabilities are mapped into a trellis diagram. To account for preambles or unrelated segments in audio files, the transition cost are set to zero for the start-of-sentence or blank token.

Forward trellis

2. Backtracking

Starting from the time step with the highest probability for the last character, backtracking determines the most probable path of characters through all time steps.

Backward path

3. Confidence score

As this method generates a probability for each aligned character, a confidence score for each utterance can be derived. For example, if a word within an utterance is missing, this value is low.

Confidence score

The confidence score helps to detect and filter-out bad utterances.

Parameters

There are several notable parameters to adjust the working of the algorithm that can be found in the class CtcSegmentationParameters:

Data preparation parameters

Alignment parameters

Time stamp parameters

Directly set the parameter index_duration to give the corresponding time duration of one CTC output index (in seconds).

Example: For a given sample rate, say, 16kHz, fs=16000. Then, how many sample points correspond to one ctc output index? In some ASR systems, this can be calculated from the hop length of the windowing times encoder subsampling factor. For example, if the hop length of the frontend windowing is 128, and the subsampling factor in the encoder is 4, totalling 512 sample points for one CTC index. Then index_duration = 512 / 16000.

Note: In earlier versions, index_duration was not used and the time stamps were determined from the values of subsampling_factor and frame_duration_ms. To derive index_duration from these values, calculateframe_duration_ms * subsampling_factor / 1000.

Confidence score parameters

Character probabilities over each L frames are accumulated to calculate the confidence score. The L value can be adapted with with score_min_mean_over_L . A lower L makes the score more sensitive to error in the transcription, but also errors in the ASR model.

Toolkit Integration

CTC segmentation requires CTC activations of an already trained CTC-based network. Example code can be found in the alignment scripts asr_align.py of ESPnet 1 or ESpnet 2.

Steps to alignment for regular ASR

  1. First, the ground truth text need to be converted into a matrix: Use prepare_token_list from a ground truth sequence that was already coverted to a sequence of tokens (recommended). Alternatively, use prepare_text on raw text, this method filters characters not in the dictionary and can break longer tokens into smaller tokens.
  2. ctc_segmentation computes character-wise alignments from the CTC log posterior probabilites.
  3. determine_utterance_segments converts char-wise alignments to utterance-wise alignments.
  4. In a post-processing step, segments may be filtered by their confidence value.

Steps to alignment for different use-cases

Sometimes the ground truth data is not text, but a sequence of tokens, or a list of protein segments. In this case, use either prepare_token_list or replace it with a function that suits better for your data. For examples, see the prepare_* functions in ctc_segmentation.py, or the example included in the NeMo toolkit.

Segments clean-up

Segments that were written to a segments file can be filtered using the confidence score. This is the minium confidence score in log space as described in the paper.

Utterances with a low confidence score are discarded in a data clean-up. This parameter may need adjustment depending on dataset, ASR model and used text conversion.

min_confidence_score=1.5
awk -v ms=${min_confidence_score} '{ if ($5 > ms) {print} }' ${unfiltered} > ${filtered}

FAQ

<details><summary>Example for `prepare_token_list`</summary><div>

Let's say we have a text text = ["cat"] and a dictionary that includes the word cat as well as its parts: char_list = ["•", "UNK", "a", "c", "t", "cat"]. The "tokenize" method that uses the preprocess_fn will produce:

text = ["cat"]
char_list = ["•", "UNK", "a", "c", "t", "cat"]
token_list = [tokenize(utt) for utt in text]
token_list
# [array([5])]
ground_truth_mat, utt_begin_indices = prepare_token_list(config, text)
ground_truth_mat
# array([[-1],
#        [ 0],
#        [ 5],
#        [ 0]])
</div></details> <details><summary>Example for `prepare_text`</summary><div> Toy example:
text = ["cat"]
char_list = ["•", "UNK", "a", "c", "t", "cat"]
ground_truth_mat, utt_begin_indices = prepare_text(config, text, char_list)
# array([[-1, -1, -1],
#        [ 0, -1, -1],
#        [ 3, -1, -1],
#        [ 2, -1, -1],
#        [ 4, -1,  5],
#        [ 0, -1, -1]])

Here, the partial characters are detected (3,2,4), as well as the full "cat" token (5). This is done to have a better time resolution for the alignment.

Full example with a bpe 500 model char list from Tedlium 2:


from ctc_segmentation import CtcSegmentationParameters
from ctc_segmentation import prepare_text

char_list = [ "<unk>", "'", "a", "ab", "able", "ace", "ach", "ack",
"act","ad","ag", "age", "ain", "al", "alk", "all", "ally", "am",
"ame", "an","and", "ans", "ant", "ap", "ar", "ard", "are",
"art","as", "ase","ass", "ast", "at", "ate", "ated", "ater", "ation",
"ations", "ause","ay", "b", "ber", "ble", "c", "ce", "cent",
"ces","ch", "ci", "ck","co", "ct", "d", "de", "du", "e", "ear",
"ect", "ed", "een", "el","ell", "em", "en", "ence", "ens",
"ent","enty", "ep", "er", "ere","ers", "es", "ess", "est", "et", "f",
"fe", "ff", "g", "ge", "gh","ght", "h", "her", "hing", "ht",
"i","ia", "ial", "ib", "ic","ical", "ice", "ich", "ict", "id", "ide",
"ie", "ies", "if","iff","ig", "ight", "ign", "il", "ild", "ill","im",
"in", "ind","ine", "ing", "ink", "int", "ion", "ions", "ip",
"ir","ire","is","ish", "ist", "it", "ite", "ith", "itt", "ittle",
"ity", "iv","ive", "ix", "iz", "j", "k", "ke", "king", "l",
"ld","le","ll","ly", "m", "ment", "ms", "n", "nd", "nder", "nt", "o",
"od","ody", "og", "ol", "olog", "om", "ome", "on",
"one","ong","oo","ood", "ook", "op", "or", "ore", "orm", "ort",
"ory", "os","ose", "ot", "other", "ou", "ould", "ound",
"ount","our","ous","ousand", "out", "ow", "own", "p", "ph", "ple",
"pp", "pt","q", "qu", "r", "ra", "rain", "re", "reat", "red",
"ree","res","ro","rou", "rough", "round", "ru", "ry", "s", "se",
"sel", "so","st","t", "ter", "th", "ther", "ty", "u", "ually",
"ud","ue", "ul","ult", "um", "un", "und", "ur", "ure", "us", "use",
"ust", "ut","v","ve", "vel", "ven", "ver", "very", "ves", "ving","w",
"way","x", "y", "z", "ăť", "ō", "▁", "▁a", "▁ab",
"▁about","▁ac","▁act","▁actually", "▁ad", "▁af", "▁ag", "▁al",
"▁all", "▁also","▁am", "▁an", "▁and", "▁any", "▁ar",
"▁are","▁around", "▁as","▁at","▁b", "▁back", "▁be", "▁bec",
"▁because", "▁been", "▁being","▁bet", "▁bl", "▁br", "▁bu",
"▁but","▁by", "▁c", "▁call","▁can","▁ch", "▁chan", "▁cl", "▁co",
"▁com", "▁comm", "▁comp","▁con", "▁cont", "▁could", "▁d",
"▁day","▁de", "▁des","▁did","▁diff", "▁differe", "▁different",
"▁dis", "▁do", "▁does","▁don", "▁down", "▁e", "▁en",
"▁even","▁every", "▁ex", "▁exp","▁f","▁fe", "▁fir", "▁first",
"▁five", "▁for", "▁fr", "▁from", "▁g","▁get", "▁go",
"▁going","▁good", "▁got", "▁h", "▁ha","▁had","▁happ", "▁has",
"▁have", "▁he", "▁her", "▁here", "▁his","▁how", "▁hum",
"▁hundred","▁i", "▁ide", "▁if", "▁im", "▁imp","▁in","▁ind", "▁int",
"▁inter", "▁into", "▁is", "▁it", "▁j", "▁just","▁k","▁kind",
"▁kn","▁know", "▁l", "▁le", "▁let", "▁li", "▁life","▁like",
"▁little", "▁lo", "▁look", "▁lot", "▁m",
"▁ma","▁make","▁man","▁many", "▁may", "▁me", "▁mo", "▁more",
"▁most","▁mu", "▁much", "▁my", "▁n", "▁ne", "▁need", "▁new",
"▁no","▁not","▁now", "▁o", "▁of", "▁on", "▁one","▁only", "▁or",
"▁other", "▁our","▁out", "▁over", "▁p", "▁part", "▁pe",
"▁peop","▁people","▁per","▁ph", "▁pl", "▁po", "▁pr", "▁pre", "▁pro",
"▁put", "▁qu", "▁r","▁re", "▁real", "▁really", "▁res",
"▁right","▁ro", "▁s","▁sa","▁said", "▁say", "▁sc", "▁se", "▁see",
"▁sh", "▁she", "▁show", "▁so","▁som", "▁some", "▁somet","▁something",
"▁sp","▁spe", "▁st","▁start", "▁su", "▁sy", "▁t", "▁ta",
"▁take","▁talk", "▁te","▁th","▁than", "▁that", "▁the", "▁their",
"▁them", "▁then", "▁there","▁these", "▁they", "▁thing",
"▁things","▁think", "▁this","▁those","▁thousand", "▁three",
"▁through", "▁tim", "▁time", "▁to", "▁tr","▁tw", "▁two", "▁u",
"▁un","▁under", "▁up", "▁us","▁v", "▁very","▁w", "▁want", "▁was",
"▁way", "▁we", "▁well", "▁were","▁wh","▁what", "▁when",
"▁where","▁which", "▁who", "▁why", "▁will","▁with", "▁wor", "▁work",
"▁world", "▁would", "▁y","▁year","▁years", "▁you", "▁your"]

text = ["I ▁really ▁like ▁technology",
 "The ▁quick ▁brown ▁fox ▁jumps ▁over ▁the ▁lazy ▁dog.",
 "unknown chars äüößß-!$ "]
config = CtcSegmentationParameters()
config.char_list = char_list
ground_truth_mat, utt_begin_indices = prepare_text(config, text)

# ground_truth_mat
# array([[ -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  0,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [190, 410,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55, 193, 411,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  2,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [137,  13,  -1,  -1, 412,  -1,  -1,  -1,  -1,  -1],
#        [137, 140,  15,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [240, 141,  -1,  16,  -1,  -1, 413,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [137, 356,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 87,  -1, 359,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [134,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55, 135,  -1,  -1, 361,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [209, 438,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55,  -1, 442,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 43,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 83,  47,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [145,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [137, 153,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 79, 152,  -1, 154,  -1,  -1,  -1,  -1,  -1,  -1],
#        [240,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  0,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 83,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [188,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [214, 189, 409,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 87,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 43,  91,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [134,  49,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 40, 266,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [190,  -1, 275,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149, 198,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [237, 181,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [145,  -1, 182,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 76, 311,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [239,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [133, 350,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [214,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [142, 220,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [183,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [204,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149, 386,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [229,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55, 230,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [190,  69, 233,  -1, 395,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [209, 438,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 83, 211, 443,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 55,  -1,  -1, 446,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [137, 356,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  2,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [241,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [240,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [244,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 52, 292,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149,  -1, 301,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 79, 152,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  0,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [214,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [145, 221,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [134,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [145,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [149,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [237, 181,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [145,  -1, 182,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 43,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [ 83,  47,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  2,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [190,  24,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [204,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1],
#        [  0,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1,  -1]])

In the example, parts of the word "▁really" were separated into the token ids: [244, 410, 411, 412, 413] This corresponds to ['▁', '▁r', '▁re', '▁real', '▁really']

The CTC segmentation algorithm then iterates over these tokens in the ground truth, calculates the transition probabilities for each token from lpz and decides for the transition(s) with the token combination that has the highest accumulated transition probability.

</div></details>

Reference

The full paper can be found in the preprint https://arxiv.org/abs/2007.09127 or published at https://doi.org/10.1007/978-3-030-60276-5_27. The code used in the paper is archived in https://github.com/cornerfarmer/ctc_segmentation. To cite this work:

@InProceedings{ctcsegmentation,
author="K{\"u}rzinger, Ludwig
and Winkelbauer, Dominik
and Li, Lujun
and Watzel, Tobias
and Rigoll, Gerhard",
editor="Karpov, Alexey
and Potapova, Rodmonga",
title="CTC-Segmentation of Large Corpora for German End-to-End Speech Recognition",
booktitle="Speech and Computer",
year="2020",
publisher="Springer International Publishing",
address="Cham",
pages="267--278",
abstract="Recent end-to-end Automatic Speech Recognition (ASR) systems demonstrated the ability to outperform conventional hybrid DNN/HMM ASR. Aside from architectural improvements in those systems, those models grew in terms of depth, parameters and model capacity. However, these models also require more training data to achieve comparable performance.",
isbn="978-3-030-60276-5"
}