Kaldi HCLG 深入理解

1. 相关部分包含的主要任务

1.1 WFST Key Concepts

1. determinization
2. minimization
3. composition
4. equivalent
5. epsilon-free
6. functional
7. on-demand algorithm
8. weight-pushing
9. epsilon removal

1.2 HMM Key Concepts

1. Markov Chain
2. Hidden Markov Model
3. Forward-backward algorithm
4. Viterbi algorithm
5. E-M for mixture of Gaussians

2. HCLG

L.fst: The Phonetic Dictionary FST

L maps monophone sequences to words.

The file L.fst is the Finite State Transducer form of the lexicon with phone symbols on the input and word symbols on the output.

L_disambig.fst:The Phonetic Dictionary with Disambiguation Symbols FST

A lexicon with disambiguation symbols

G.fst:The Language Model FST

FSA grammar (can be built from an n-gram grammar).

C.fst:The Context FST

C maps triphone sequences to monophones.

Expands the phones into context-dependent phones.

H.fst:The HMM FST

H maps multiple HMM states (a.k.a. transition-ids in Kaldi-speak) to context-dependent triphones.

Expands out the HMMs. On the right are the context-dependent phones and on the left are the pdf-ids. 

HCLG.fst: final graph

总结一下：

构图过程 G -> L -> C -> H

          G: 作为 acceptor (输入 symbol 与输出相同)，用于对grammar 或者 language model 进行编码

          L:  Lexicon, 其输出 symbol 是 words, 输入 symbol 是 phones

          C:  context-dependency 其输出 symbol 是 phones, 其输入 symbol 为表示context-dependency phones

              如： vector ctx_window = { 12, 15, 21 };

                      含义：id = 15 的 phone 为 中心 phone, left phone id = 12, right phone id = 21

          H: 包括HMM definitions,其输出 symbol 为context-dependency phones, 其输入 symbol 为transitions-ids(即 对 pdf-id 和 其它信息编码后的 id) 

 

            asl=="add-self-loops” 

          rds=="remove-disambiguation-symbols”, 

          and H' is H without the self-loops:

         HCLG = asl(min(rds(det(H' o min(det(C o min(det(L o G))))))))