| { | |
| "paper_id": "O06-2005", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T08:07:46.062456Z" | |
| }, | |
| "title": "A Fast Framework for the Constrained Mean Trajectory Segment Model by Avoidance of Redundant Computation on Segment 1", | |
| "authors": [ | |
| { | |
| "first": "Yun", | |
| "middle": [], | |
| "last": "Tang", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Chinese Academy of Sciences", | |
| "location": { | |
| "addrLine": "nlpr", | |
| "postBox": "P.O.Box 2728", | |
| "postCode": "100080", | |
| "settlement": "Beijing" | |
| } | |
| }, | |
| "email": "tangyun@nlpr.ia.ac.cn" | |
| }, | |
| { | |
| "first": "Wenju", | |
| "middle": [], | |
| "last": "Liu", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Chinese Academy of Sciences", | |
| "location": { | |
| "addrLine": "nlpr", | |
| "postBox": "P.O.Box 2728", | |
| "postCode": "100080", | |
| "settlement": "Beijing" | |
| } | |
| }, | |
| "email": "" | |
| }, | |
| { | |
| "first": "Yiyan", | |
| "middle": [], | |
| "last": "Zhang", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| }, | |
| { | |
| "first": "Bo", | |
| "middle": [], | |
| "last": "Xu", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Chinese Academy of Sciences", | |
| "location": { | |
| "addrLine": "nlpr", | |
| "postBox": "P.O.Box 2728", | |
| "postCode": "100080", | |
| "settlement": "Beijing" | |
| } | |
| }, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "The segment model (SM) is a family of methods that use the segmental distribution rather than frame-based density (e.g. HMM) to represent the underlying characteristics of the observation sequence. It has been proved to be more precise than HMM. However, their high level of complexity prevents these models from being used in practical systems. In this paper, we propose a framework that can reduce the computational complexity of the Constrained Mean Trajectory Segment Model (CMTSM), one type of SM, by fixing the number of regions in a segment so as to share the intermediate computation results. Our work is twofold. First, we compare the complexity of SM with that of HMM and point out the source of the complexity in SM. Secondly, a fast CMTSM framework is proposed, and two examples are used to illustrate this framework. The fast CMTSM achieves a 95.0% string accurate rate in the speaker-independent test on our mandarin digit string data corpus, which is much higher than the performance obtained with HMM-based system. At the mean time, we successfully keep the computation complexity of SM at the same level as that of HMM.", | |
| "pdf_parse": { | |
| "paper_id": "O06-2005", | |
| "_pdf_hash": "", | |
| "abstract": [ | |
| { | |
| "text": "The segment model (SM) is a family of methods that use the segmental distribution rather than frame-based density (e.g. HMM) to represent the underlying characteristics of the observation sequence. It has been proved to be more precise than HMM. However, their high level of complexity prevents these models from being used in practical systems. In this paper, we propose a framework that can reduce the computational complexity of the Constrained Mean Trajectory Segment Model (CMTSM), one type of SM, by fixing the number of regions in a segment so as to share the intermediate computation results. Our work is twofold. First, we compare the complexity of SM with that of HMM and point out the source of the complexity in SM. Secondly, a fast CMTSM framework is proposed, and two examples are used to illustrate this framework. The fast CMTSM achieves a 95.0% string accurate rate in the speaker-independent test on our mandarin digit string data corpus, which is much higher than the performance obtained with HMM-based system. At the mean time, we successfully keep the computation complexity of SM at the same level as that of HMM.", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| ], | |
| "body_text": [ | |
| { | |
| "text": "The Hidden Markov Model (HMM) [Rabiner et al. 1993 ] has been used successfully for acoustic modeling in many speech recognition systems. Given the state sequence, feature vectors are assumed to be conditionally independent, and the task of extracting the trajectory can be elegantly achieved by applying the Viterbi algorithm frame by frame. However, the above assumption is far from realistic, which limits the HMM's ability to capture the relations within a segment. Another weakness of HMM is that it is not accurate enough to represent a non-stationary observation sequence by means of a piecewise constant state [Deng et al. 1994; Hon et al. 1999] . In order to handle these problems, a lot of methods have been proposed, including SM [Ostendorf et al. 1996] , which is a family of methods among them.", | |
| "cite_spans": [ | |
| { | |
| "start": 30, | |
| "end": 50, | |
| "text": "[Rabiner et al. 1993", | |
| "ref_id": "BIBREF10" | |
| }, | |
| { | |
| "start": 618, | |
| "end": 636, | |
| "text": "[Deng et al. 1994;", | |
| "ref_id": "BIBREF0" | |
| }, | |
| { | |
| "start": 637, | |
| "end": 653, | |
| "text": "Hon et al. 1999]", | |
| "ref_id": "BIBREF5" | |
| }, | |
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| "start": 741, | |
| "end": 764, | |
| "text": "[Ostendorf et al. 1996]", | |
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| ], | |
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| "section": "Introduction", | |
| "sec_num": "1." | |
| }, | |
| { | |
| "text": "SM is totally different from HMM in terms of its segmental decoding method and potential for accomplishing some tasks effectively that are naturally difficult for an HMM based system, since it integrates more segmental information into the decoding process, produces the n-best list during the decoding process etc. However, the good acoustic modeling of SM is at the cost of high computation, which is much higher than that of HMM. It prevents SM from being applied in practical systems. The high complexity of SM is mainly due to the segment evaluation process. Segment evaluation cannot be decomposed and the intermediate computation information is not shareable between different segments even when two segments only differ by one frame. Previous work accelerated SM using efficient segment pruning algorithms. V. Digalakis et al. [1992] proposed a pruning method to speed up SM. They estimate the score of a segment from part of the segment. Then those hypotheses with low likelihood are pruned before the whole segment is evaluated. The amount of reduction in computation depends on the discrimination ability of the feature vector. S. Lee et al. [1998] and J. Glass [2003] proposed a landmark-based algorithm that reduces the search space by detecting the potential boundaries of phonemes with the aid of special features or HMM decoders, so that the number of the possible hypothesized segments in the search space can be reduced greatly. However, since the detection of boundaries is unreliable and not accurate enough, the efficiency of this algorithm is discounted. The most important point is that the speed of SM based on the above methods is still far slower than that of HMM, since the computations performed by these algorithms are based on segments, while in the case of HMM, they are based on frames. In this paper, we propose a framework to reduce the complexity of the Constrained Mean Trajectory Segment Model (CMTSM) [Ostendorf et al. 1996] , one family of SM. In this new framework, CMTSM can divide segment computations into frame computations, which are shared between different segments; thus, the redundant computations of segments can be avoided. Guided by this framework, we have measured the complexity of Stochastic Segment Model (SSM) [Ostendorf et al. 1989 ] based on the number of Gaussian mixture models evaluated during recognition, and found that the complexity is not proportional to the product of the model's number and the maximum allowable duration, but is only related to the number of models, or more exactly, to the number of regions in the system.", | |
| "cite_spans": [ | |
| { | |
| "start": 818, | |
| "end": 841, | |
| "text": "Digalakis et al. [1992]", | |
| "ref_id": "BIBREF2" | |
| }, | |
| { | |
| "start": 1142, | |
| "end": 1159, | |
| "text": "Lee et al. [1998]", | |
| "ref_id": "BIBREF6" | |
| }, | |
| { | |
| "start": 1167, | |
| "end": 1179, | |
| "text": "Glass [2003]", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 1939, | |
| "end": 1962, | |
| "text": "[Ostendorf et al. 1996]", | |
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| }, | |
| { | |
| "start": 2267, | |
| "end": 2289, | |
| "text": "[Ostendorf et al. 1989", | |
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| } | |
| ], | |
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| "section": "Introduction", | |
| "sec_num": "1." | |
| }, | |
| { | |
| "text": "The complexity of SSM is on the same level as that of HMM. The speed of the Parametric Trajectory Model (PTM) [Gish et al. 1992; Deng et al. 1994] , another type of CMTSM, can also be greatly enhanced with some minor modifications of the original algorithm, based on our framework.", | |
| "cite_spans": [ | |
| { | |
| "start": 110, | |
| "end": 128, | |
| "text": "[Gish et al. 1992;", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 129, | |
| "end": 146, | |
| "text": "Deng et al. 1994]", | |
| "ref_id": "BIBREF0" | |
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| "section": "Introduction", | |
| "sec_num": "1." | |
| }, | |
| { | |
| "text": "The rest of this paper is organized as follows. SM is introduced in the next section by comparing HMM with SM in terms of modeling and decoding. Then, in Section 3, we present the fast framework for CMTSM and two examples, the fast SSM and the fixed PTM, illustrate it. Section 4 presents experimental results obtained with the fast framework. Finally, conclusions are drawn in Section 5.", | |
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| "section": "Introduction", | |
| "sec_num": "1." | |
| }, | |
| { | |
| "text": "In HMM, the model unit is the state, and the relations among feature vectors are represented by the relations among the states mapping to these features. In SM, the model unit is based on segments, such as phonemes, syllables, and words. Hence, the relations between feature vectors in the same segment are modeled directly. The probability density of a variable length feature sequence 1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Introduction to the Segment Model", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "1 2 { , ,... } l l x x x x =", | |
| "cite_spans": [], | |
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| "eq_spans": [], | |
| "section": "Introduction to the Segment Model", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "measured by SM can be represented as follows:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Introduction to the Segment Model", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "1 1 1 ( | ) ( | ) ( | ) l l l p x f x g x \u03b1 \u03b1 \u03b1 = ,", | |
| "eq_num": "(1)" | |
| } | |
| ], | |
| "section": "Introduction to the Segment Model", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "where \u03b1 is the label of the acoustic model, ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Introduction to the Segment Model", | |
| "sec_num": "2.1" | |
| }, | |
| { | |
| "text": "The goal of a speech recognizer is to find the most likely word sequence given sentence 1 T", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "x . Let 1 N \u03b1 be the label sequence of acoustic models representing words intended by the speaker, ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "who produces 1 T x above. That is, 1 1 1 1 1 1 1 1 , , arg max ( | ) arg max ( ) ( | ) N N N N T N T N N N p x p p x \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 = = ,", | |
| "eq_num": "(2)" | |
| } | |
| ], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "1 ( 1) 1 ( 1) 1 1 1 ( | ) ( | ) max ( | ) T N N N S i S i T N i i S i S i S S i i p x p x p x \u03b1 \u03b1 \u03b1 \u2212 + \u2212 + \u2208\u039b = = = \u2248 \u2211 \u220f \u220f ,", | |
| "eq_num": "( ) ( ) 1" | |
| } | |
| ], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "( ) S i S i \u2212 < ,", | |
| "eq_num": "(3)( 1)" | |
| } | |
| ], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "0", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "S = and ( ) S N T = , where , T N \u039b", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "is the segmentation boundary set dividing a T -length sequence into N parts and ( ) S i is the boundary point of segment i .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding Comparison between HMM and SM", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "The above decoding process is accomplished by the Viterbi algorithm in HMM. We will take a left-to-right HMM without state skipping as an example to illustrate decoding in HMM:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "* * 1 1 ( , ) ln ( | , ) max ( ( , )). , 1 | |, 2 m m m i j i J i p x i J j i m T i L \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u2212 \u2212 \u2264 \u2264 = + \u2264 \u2264 \u2264 \u2264\u2126 \u2264 \u2264 ,", | |
| "eq_num": "(4)" | |
| } | |
| ], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "where", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "* ( , ) m J i \u03b1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "is the maximum accumulated score for the state sequence from the 1-th frame to the m -th frame, given state i and model label \u03b1 for frame m", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "x ; ( | , ) m p x i \u03b1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "is the state score of frame m", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "x ; \u2126 is the number of models; L \u03b1 is the number of states for \u03b1 .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "The above formula can be applied to all internal states of each model (i.e., 2 i \u2265 ). At the boundary of the model, i.e., 1 i = , the formula is in the following form:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "* * * 1 1 1 | | ( ,1) ln ( | ,1) max [ ( , ) ln( ( )), ( ,1)]. m m m m J px J L p J \u03b2 \u03b2 \u03b1 \u03b1 \u03b2 \u03b1 \u03b1 \u2212 \u2212 \u2264 \u2264\u2126 = + + (5)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "The final solution for the best path is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "* * 1 max[ ( , ] T J J L \u03b1 \u03b1 \u03b1 \u2264 \u2264\u2126 = ,", | |
| "eq_num": "(6)" | |
| } | |
| ], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "and the best path can be obtained by backtracking the best final score.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "The cost of the Viterbi algorithm is essentially the cost of computing the state scores. According to (4) and (5), the amount of computation required for the state scores is proportional to the number of states in each model and the observation sequence length. If the pruning is not considered, the approximate time complexity for the Viterbi algorithm is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "( | | ) S O T L C \u22c5 \u2126 \u22c5 \u22c5", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": ", where S C is the time cost of computing ( | , )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "m p x i \u03b1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "and L is the average number of states in each model.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in HMM", | |
| "sec_num": "2.2.1" | |
| }, | |
| { | |
| "text": "SMs have to explore all possible segment boundaries due to the segmental decoding, whereas the problem of obtaining exact acoustic model boundaries can be avoided with HMM, since the frame that the exit state maps to is the boundary of the model. Though the decoding procedure can be performed by means of dynamic programming, the complexity of SM is still much higher than that of HMM. The decoding formula for SM is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "* * , max{ ln[ ( | )]( ) ln[ ( )] }, m m J J p x m P C \u03c4 \u03c4 \u03c4 \u03b1 \u03b1 \u03c4 \u03b1 = + \u2212 + +", | |
| "eq_num": "(7)" | |
| } | |
| ], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": "Avoidance of Redundant Computation on Segment where * m J is the accumulated score of the best model sequence ending at time point m and C is the insert factor for each segment. The best segment sequence can be obtained by back-tracking from the best final score * T J .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": "Given the beginning (or end) point of models, the decoder has to hypothesize segments with different durations, from the minimum to the maximum length, to determine the other boundary point of the segment that may spring from this point. Assuming that the maximum allowed duration is max L , we find that the time complexity of SM is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": "max ( | | ) Seg O C T L \u22c5 \u22c5 \u2126 \u22c5", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": ", where Seg C is the time cost of a segment and is comparable with or even more complex than S C L \u22c5 in HMM. Hence, SM is more costly than HMM.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Decoding in SM", | |
| "sec_num": "2.2.2" | |
| }, | |
| { | |
| "text": "As discussed in Section 2.2.2, the high complexity of SM is due to two factors. First, SM explores more hypothesized models than HMM does in each frame; second, in each frame, SM needs to measure the densities of segments that pass this point, whereas HMM only needs to evaluate the densities of states mapping to this point. The second factor is more important for current SM systems, since density evaluation represents the lion's share in the whole computation. Figure 1 shows the percentage of the time spent on density evaluation against the total time needed for the digit string recognition task with HMM and SSM. The model unit for SSM and HMM is the context independent whole-word. The computation involved in density evaluation is extremely time-consuming in the case of the conventional SSM and 97.6% of the time is spent obtaining segment scores, whereas the corresponding percentage in the case of HMM is only 51.4%. The time cost ratio for density evaluation in SM is much higher than that in HMM. The key advantage of our fast framework is that it changes the computation in SM from segment-based style to frame-based style and the frame-based results can be shared by different segments. Such transformation can be achieved in one family of SM, i.e., CMTSM.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 465, | |
| "end": 473, | |
| "text": "Figure 1", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Fast Framework for CMTSM", | |
| "sec_num": "3." | |
| }, | |
| { | |
| "text": "In the fast SM, which we will describe below, the time cost ratio for density evaluation is lowered to 64.2%, close to that of HMM. The details of experimental setup and total time used for decoding will be given in Section 4 ( ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fast Framework for CMTSM", | |
| "sec_num": "3." | |
| }, | |
| { | |
| "text": "Those SMs, including SSM and PTM, whose segmental distributions are modeled by means of region distributions while frame-based features are assumed to be conditionally independent given the region sequence, are called CMTSM. The so-called region here is similar to the conception of the state in HMM, which is the basic unit used to measure the probability distribution of a frame. The value of", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "1 ( | ) l f x \u03b1 in (1)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "is the product of a series of frame-based region scores [Ostendorf et al. 1996] :", | |
| "cite_spans": [ | |
| { | |
| "start": 56, | |
| "end": 79, | |
| "text": "[Ostendorf et al. 1996]", | |
| "ref_id": "BIBREF9" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "1 1 ln ( | ) ln ( | , , ) l l i i i f x px rl \u03b1 \u03b1 = = \u2211 ,", | |
| "eq_num": "(8)" | |
| } | |
| ], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "where ( | , , ) i", | |
| "cite_spans": [ | |
| { | |
| "start": 6, | |
| "end": 15, | |
| "text": "( | , , )", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "i p x r l \u03b1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "is the score of region i r in frame i", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "x for model \u03b1 , given duration l .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The mapping of a feature vector to a region is only related to the segment duration and its position in the segment. So the measurement of the frame score for a specific region is unrelated to other frames or other regions.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The assumption, frame-based features being assumed to be conditionally independent given the region sequence in CMTSM, guarantees to change the density evaluation from segment-based style to frame-based style, and the segment score can be obtained by recombining the region scores in an efficient way. However, these frame-based results can not be shared among different segments, since region models are conditional on the segment duration, as Equation (8) shows. We relax the modeling condition by assuming that the region model is independent of the segment duration. In order to achieve this, we use linear time resampling to map the variable length segment 1 l x to a fixed length feature sequence l L y , so all the segment models have the same duration. In other words, the duration can be ignored in region models. In this way, the region scores can be shared by segments with different durations. The resampling function is [Ostendorf et al. 1989] , 0 ,", | |
| "cite_spans": [ | |
| { | |
| "start": 933, | |
| "end": 956, | |
| "text": "[Ostendorf et al. 1989]", | |
| "ref_id": "BIBREF7" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "i i l L y x i L \u23a2 \u23a5 \u22c5 \u23a2 \u23a5 \u23a3 \u23a6 = \u2264 <", | |
| "eq_num": "(9)" | |
| } | |
| ], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "where z \u23a2 \u23a5 \u23a3 \u23a6 is the largest integer n z \u2264 . Equation (8) can be simplified as", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "1 1 ln ( | ) ln ( | , ) L l i i i f x py r \u03b1 \u03b1 = = \u2211 .", | |
| "eq_num": "(10)" | |
| } | |
| ], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In short, to speed up CMTSM, we first resample a variable length segment to obtain a fixed length sequence and then measure region models using the fixed length segment model. In our implementation, a memory table is used to store the region scores in different frames. The computation at each feature frame consists of two parts: the computations for all the region models mapping to that frame, and addition operations needed to obtain the scores of segments over that frame; whereas the conventional SMs have to completely measure all the segments that pass that frame. This is the framework we propose to reduce the complexity of", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Figure 1. Percentage of the time for density evaluation in the decoding", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "CMTSM. In the following, two examples will be given to illustrate the framework.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Avoidance of Redundant Computation on Segment", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "SSM represents a variable length observation sequence by means of a fixed length region sequence. A resampling function is used to map the variable length segment 1 l x to the fixed length model region sequence 1 L y . Two kinds of resampling can be adopted to map a variable length sequences to a fixed L-length sequence. One is space-based resampling, and the other is linear time resampling [Ostendorf et al. 1989] . Space resampling chooses L sampling points, which are equidistant (Euclidean distance) along the segment trajectory, by means of interpolation. The linear time resampling is similar to (9). The two resampling functions have similar performances as reported by M. Ostendorf. Given model \u03b1 , the log conditional", | |
| "cite_spans": [ | |
| { | |
| "start": 394, | |
| "end": 417, | |
| "text": "[Ostendorf et al. 1989]", | |
| "ref_id": "BIBREF7" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "probability of a segment 1 l x is 1 1 log[ ( | )] log[ ( | , )] log[ ( | )] L l i i i P x a p y a r P l \u03bb \u03b1 = = + \u2211 ,", | |
| "eq_num": "(11)" | |
| } | |
| ], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "where ( | ) P l \u03b1 is the duration distribution of the segment, given \u03b1 .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "According to (11), Seg C is proportional to the number of regions in the model and can be represented as R C L \u22c5 , where R C is the time cost of region model ( | , )", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "i i p y a r and L is the average number of region models. The complexity of SSM is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "max ( | | ) R O T L C L \u22c5 \u2126 \u22c5 \u22c5", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "\u22c5 , according to the conclusion drawn in Section 2.2.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "Based on the discussion of the fast CMTSM, SSM can be greatly accelerated by choosing the linear time resampling, and the computation of region scores in (11) can be shared by segments with different durations. The total cost of the SSM algorithm is essentially the cost of computing the region scores. Thus, the time complexity, measured based on the number of evaluated region models, is", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "( | | ) R O T L C \u22c5 \u2126 \u22c5 \u22c5 .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Complexity of SSM", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "In PTM, the features in a segment are modeled by means of parameterization through constant, linear, or higher order polynomial regression instead of by using a sequence of regions to represent the curve of the trajectory. Given model \u03b1 , a speech segment 1 l x can be modeled as", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "0 1 ( ) ( ) 1 p P i i p i x B p E l \u03b1 \u03b1 = \u2212 \u239b \u239e = + \u03a3 \u239c \u239f \u2212 \u239d \u23a0 \u2211 ,", | |
| "eq_num": "(12)" | |
| } | |
| ], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "where ) ( p B \u03b1", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "is the polynomial regression coefficient of order P and i E is a residual error with covariance matrix \u03b1 \u03a3 after fitting data using the first term in (12). The frame score with", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "duration l is, / 2 1 / 2 1 0 0 1 ( | , ) , ( 2 ) | | 1 1 1 e x p { ( ( ) ) ( ( ) ) } . 2 1 1 i i d p p P P i i p p p x r i i x B p x B p l l \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03c0 \u2212 = = = \u2211 \u2212 \u2212 \u239b \u239e \u239b \u239e \u2032 \u2212 \u2212 \u2211 \u2212 \u239c \u239f \u239c \u239f \u2212 \u2212 \u239d \u23a0 \u239d \u23a0 \u2211 \u2211", | |
| "eq_num": "(13)" | |
| } | |
| ], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "In the conventional method, the region models are conditional on the segment duration. The durations of segments are different and so are the P -order polynomials in (12). As a result, the frame score ( | , ) p x r i i \u03b1 calculated using (13) can not be shared among different segments, even when two segments only differ from each other by one frame. For example, assume that two segments for the same model both begin at the 1-st frame and that the first one ends at the 10-th frame and the other at the 15-th frame. The polynomial coefficients of these two segments are listed in Table 1 .", | |
| "cite_spans": [ | |
| { | |
| "start": 201, | |
| "end": 208, | |
| "text": "( | , )", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [ | |
| { | |
| "start": 583, | |
| "end": 590, | |
| "text": "Table 1", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Fast PTM", | |
| "sec_num": "3.2" | |
| }, | |
| { | |
| "text": "No.i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 i/10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ----i/15 0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67 0.73 0.80 0.87 0.93 1.00", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Rate", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In fast PTM, we also fix the number of regions in the model and use the linear time resampling to map a variable length segment to the region sequence with a fixed duration, so the region model is independent of the segment duration. In this way, the speed of PTM can be greatly enhanced.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Rate", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "There are two main factors that limit errors introduced by resampling of the original feature on an acceptable scale, and these errors do little harm to the accuracy of the system. The first is the slowly time varying nature of speech signals [Rabiner et al. 1993] , which can be seen as a quasi-stationary process. The speech feature vector is similar to the nearby feature vectors. Usually, the length of a region sequence in our system is longer than the average length of an observation sequence, so the region model can well approximate the feature that would appear in the corresponding position of a segment. The second factor is that resampled features are used in both the training phase and recognition phase, which guarantees the compatibility of resampled features with models. Figure 2 shows the trajectories of a speech data sequence and two man-made data sequences produced by 5-order polynomial regression. One polynomial fit the original observation sequence, and the other one fit the fixed length observation sequence resampled from the original features. The fixed length was 56. All the trajectories are shown in normalized time axes in Figure 2 . It can be seen that the two regression trajectories are almost tiled together and that the linear time resampling does little harm to the model. ", | |
| "cite_spans": [ | |
| { | |
| "start": 243, | |
| "end": 264, | |
| "text": "[Rabiner et al. 1993]", | |
| "ref_id": "BIBREF10" | |
| } | |
| ], | |
| "ref_spans": [ | |
| { | |
| "start": 790, | |
| "end": 798, | |
| "text": "Figure 2", | |
| "ref_id": "FIGREF2" | |
| }, | |
| { | |
| "start": 1158, | |
| "end": 1166, | |
| "text": "Figure 2", | |
| "ref_id": "FIGREF2" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Rate", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Our methods were verified on a mandarin digit string recognition system. Digit string recognition has achieved a satisfied performance in English [Rabiner et al. 1989] . However, due to the serious confusion among mandarin digits, the state-of-the-art of mandarin digital string recognition systems does not match that of the English counterpart. The performance of a recognition system depends not only on the size of the vocabulary but also on the degree of confusability among words in the vocabulary. Mandarin is a monosyllabic and tonal language, in which a syllable is composed of a syllable initial, syllable final, and tone. Insertion or deletion errors mainly exist in non-syllable initial words, e.g., \"1,\" \"2,\" and \"5.\" If a digit's syllable final is similar to that of non-syllable initial words, it is difficult to segment the non-syllable initial words and segmentation errors tend to occur, such as the confusability between \"5\" and \"55.\" Substitution errors mainly occur among \"6,\" \"9,\" and \"yiao\" (\"yiao\" is the variation of \"1\"), or between \"2\" and \"8\" because of the similarity of their syllable finals.", | |
| "cite_spans": [ | |
| { | |
| "start": 146, | |
| "end": 167, | |
| "text": "[Rabiner et al. 1989]", | |
| "ref_id": "BIBREF11" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Experiments and Results", | |
| "sec_num": "4." | |
| }, | |
| { | |
| "text": "Data Corpus: the mandarin digit string database includes the speech of 55 males, each of which made 80 utterances. The length of each utterance varies from 1 to 7 digits with an average length of 4. The vocabulary is \"0\" to \"9\"and \"yiao1.\" Statistical results show that all digits have the same probability of being uttered, and that the connections among digits are considered and balanced. At the same time, the positions (start/middle/end) of the digits in strings are also balanced [Deng et al. 2000] . We took the speech of the first 40 speakers (ordered by the name of speakers) as the training set and the data from the remaining 15 speakers as the test set. The frame size of acoustic features was 25.6 ms and the frame shift was 10ms. For each frame, a 39-dimension vector, composed of 12 MFCC and 1 normalized energy, 13 first order deviations and 13 secondary deviations, was calculated.", | |
| "cite_spans": [ | |
| { | |
| "start": 486, | |
| "end": 504, | |
| "text": "[Deng et al. 2000]", | |
| "ref_id": "BIBREF1" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Experimental Setup", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "Baseline Systems: three systems were studied, HMM, SSM, and PTM. The state in HMM (or region in SSM) was modeled by the Gaussian Mixture Model (GMM). In all the experiments, a diagonal covariance matrix was assumed for each GMM. Table 2 compares the baselines' configures. Sts is the number of states, Res is the number of regions, MCs is the number of mixture components, \"ID\" means the acoustic unit is modeled by the whole-word (context independent), and \"D\" means the acoustic unit is tri-word based (context dependent) in Table 2 . The HMMs in the experiments were structured left to right with 8 states, 6 emitting distributions, and no state skipping, except for the \"silence\" model, which had 3 states and 1 emitting distribution. HMMI was decoded with the conventional Viterbi algorithm, and HMMII adopted a two-pass search strategy: the first pass was implemented using the forward Viterbi algorithm, and the second pass using the backward A* decoding to integrate the duration distribution [Deng et al. 2000] . HMMII was modeled using the tri-word model, while the other systems were modeled by the whole-word model. SSMI and SSMII were two SSM systems. SSMI had Gaussian densities comparable with those of HMMI so that a comparison of the performance between SSM and HMM would be meaningful. SSMII, which had more region models and mixture components than SSMI, achieved the best performance in the digit string recognition task. The baseline PTM was consisted of three sub-segments [Deng et al. 1994] and the polynomial regression order was 2. Table 3 compares the modeling ability of HMM and SSM. It can be seen that SSM achieved better performance than HMM. SSMI performed better than not only HMMI but also HMMII. When the number of regions and mixture components increased, SSMII achieved 95% string accuracy for mandarin digit strings. \"S Cor,\" \"W err,\" \" Ins err,\" \"Del err\" and \"Sub err\" are the string correction rate, word error rate, insertion error rate, deletion error rate and the", | |
| "cite_spans": [ | |
| { | |
| "start": 1001, | |
| "end": 1019, | |
| "text": "[Deng et al. 2000]", | |
| "ref_id": "BIBREF1" | |
| }, | |
| { | |
| "start": 1495, | |
| "end": 1513, | |
| "text": "[Deng et al. 1994]", | |
| "ref_id": "BIBREF0" | |
| } | |
| ], | |
| "ref_spans": [ | |
| { | |
| "start": 229, | |
| "end": 236, | |
| "text": "Table 2", | |
| "ref_id": "TABREF2" | |
| }, | |
| { | |
| "start": 527, | |
| "end": 534, | |
| "text": "Table 2", | |
| "ref_id": "TABREF2" | |
| }, | |
| { | |
| "start": 1557, | |
| "end": 1564, | |
| "text": "Table 3", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Experimental Setup", | |
| "sec_num": "4.1" | |
| }, | |
| { | |
| "text": "substitution error rate respectively.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Avoidance of Redundant Computation on Segment", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "For the purpose of comparison, the number of regions in a sub-region sequence was fixed at 20 and the total number of region models was 60 (20 \u00d7 3) in each fast PTM. The feature frames in a segment were mapping to these 60 region models using the time linear resampling. The other parameters were the same as those for the baseline PTM system. Table 4 presents the recognition results obtained with the fixed PTM and the original PTM. It shows that the performance of the PTM system was slightly downgraded following the modifications but still acceptable (0.6% string accuracy loss). The efficiency of the different recognition systems, including the conventional SSM, fast SSM, PTM, fixed PTM, and HMM, is compared in Table 5 . We used the utterances of one person (80 strings) in the test set. As shown in Table 5 , the fast algorithm boosted SMs and reduced the complexity of SM to the same level of that of HMM. The most noticeable achievement was made by the fixed PTM system, which was 90 times faster than the original one. ", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 344, | |
| "end": 351, | |
| "text": "Table 4", | |
| "ref_id": "TABREF3" | |
| }, | |
| { | |
| "start": 720, | |
| "end": 727, | |
| "text": "Table 5", | |
| "ref_id": "TABREF1" | |
| }, | |
| { | |
| "start": 809, | |
| "end": 816, | |
| "text": "Table 5", | |
| "ref_id": "TABREF1" | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Table 3. Comparison of digit string recognition performance achieved with SSM and HMM", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In this paper, a fast framework has been proposed to boost the speed of CMTSM based on the assumption that the region model of SM is independent from the segment duration, so that intermediate results are shared during the computation of segment scores. Two examples, SSM and PTM, have been used to illustrate this framework. The improved systems are far more effective than the original models. Based on this framework, it is potential to implement SM to LVCSR [Tang et al. 2005] in current computation condition and this will be our focus of future work.", | |
| "cite_spans": [ | |
| { | |
| "start": 462, | |
| "end": 480, | |
| "text": "[Tang et al. 2005]", | |
| "ref_id": "BIBREF12" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Conclusions", | |
| "sec_num": "5." | |
| }, | |
| { | |
| "text": "This work was supported in part by the China National Nature Science Foundation (No. 60172055) and", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [ | |
| { | |
| "text": "The authors would like to thank the anonymous reviewers and Mr. Ludwig for their useful comments.", | |
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| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Acknowledgements", | |
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| "text": "is a segment level score, such as the duration score.", | |
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| "text": "or y f or or i gi nal speech dat a sequence Fi t t i ng t r aj ect or y f or or i gi nal speech dat a sequence Fi t t i ng t r aj ect or y f or 56 f i xed r e-sam pl e speech dat a sequence Or i gi nal speech dat a t r aj ect or yTr aj ect or y pr oduced by f i t t i ng t he or i gi nal dat a Tr aj ect or y pr oduced by f i t t i ng t he r esam pl i ng dat a", | |
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| "text": "Trajectories for an original data sequence and two man-made data sequences produced by polynomial regression.", | |
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| "content": "<table><tr><td>100%</td><td/><td>97. 6%</td></tr><tr><td>80%</td><td/><td/></tr><tr><td/><td/><td/><td>64. 2%</td></tr><tr><td>60%</td><td>51. 4%</td><td/></tr><tr><td>40%</td><td/><td/></tr><tr><td>20%</td><td/><td/></tr><tr><td>0%</td><td/><td/></tr><tr><td colspan=\"2\">HMM ( Uni phone, Vi t er bi )</td><td>SSM</td><td>Fas t SSM</td></tr></table>", | |
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| "content": "<table><tr><td>Model</td><td>Sts (Res)</td><td>MCs</td><td>Type</td></tr><tr><td>HMMI</td><td>8</td><td>16</td><td>ID</td></tr><tr><td>HMMII</td><td>8</td><td>16</td><td>D</td></tr><tr><td>SSMI</td><td>25</td><td>5</td><td>ID</td></tr><tr><td>SSMII</td><td>40</td><td>10</td><td>ID</td></tr><tr><td>PTM</td><td/><td>15</td><td>ID</td></tr></table>", | |
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| "content": "<table><tr><td>Methods</td><td>S Corr.</td><td colspan=\"2\">W err Ins err Del err Sub err</td></tr><tr><td>PTM</td><td colspan=\"2\">95.10% 1.53% 0.30% 0.24%</td><td>0.99%</td></tr><tr><td colspan=\"3\">Fixed PTM 94.50% 1.82% 0.14% 0.68%</td><td>1.00%</td></tr></table>", | |
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| "content": "<table><tr><td/><td>T (s)</td></tr><tr><td>HMMI</td><td>35</td></tr><tr><td>HMMII</td><td>87</td></tr><tr><td>Conventional SSMI</td><td>1816</td></tr><tr><td>Fast SSMI</td><td>101</td></tr><tr><td>Fast SSMII</td><td>162</td></tr><tr><td>PTM</td><td>23854</td></tr><tr><td>Fixed PTM</td><td>271</td></tr></table>", | |
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