李 锵，李晨曦，关 欣
AuthorsHTML:李 锵，李晨曦，关 欣
AuthorsListE:Li Qiang，Li Chenxi，Guan Xin
AuthorsHTMLE:Li Qiang，Li Chenxi，Guan Xin
Unit:天津大学微电子学院，天津 300072
Unit_EngLish:School of Microelectronics，Tianjin University，Tianjin 300072，China
Abstract_Chinese:现有的一阶隐马尔可夫模型(hidden Markov model，HMM)用于钢琴指法标注不能结合音符序列的长程信息，导致标注结果存在物理不可弹指法，且演奏效率较低，因此本文提出了一种基于判决隐马尔可夫模型和改进维特比算法的钢琴指法自动标注算法．结合指法规则的先验知识，在HMM中引入了判决函数，从而能够去除错误的穿跨指和超出可弹跨度的指法．在预测指法路径时，改进了维特比算法的寻优规则，首先根据先验知识对音符序列进行八度分段，并改进初始指法的确定方法，最后选择穿跨指数最少、演奏效率最高的指法序列为最优指法．为了表征算法的性能，文中还提出了不可弹指法占比率和欠合理率两种新的评价指标来衡量指法的可弹性和演奏效率．通过实验验证，文中算法相较于现有标注模型在一致率和两种新的指标上提升效果显著．另外，为了对比在小数据集下传统方法和深度学习方法的性能，还与Bi-LSTM＋CRF进行了对比实验，训练时分别采用原始音符序列和音符差分序列，实验结果显示利用音符差分序列可以有效提高标注结果的一致率，由此可见，相较于原始音符序列，指法标注和音符差分序列的关系更密切，从而进一步验证了本文算法结合音符差分信息改进HMM的有效性．但现有数据量下，深度学习模型在不可弹指法率和欠合理率上差于本文算法．
Abstract_English:The existing first-order hidden Markov model(HMM)is used for piano fingering annotation without com-bining long-distance information of the note sequence．Therefore，an automatic piano fingering annotation algorithm based on decision HMM and the improved Viterbi algorithm is proposed．Taking prior knowledge of fingering into consideration，a judgment function was added to the traditional first-order HMM to remove wrong cross fingering and fingering beyond the bulletable span．During the prediction period，the optimization rules of the Viterbi algo-rithm were refined．First，the note sequence was segmented according to octaves，and the initial fingering method was modified．Subsequently，we chose a fingering sequence with the least number of cross fingering and whose performance was as efficient as that during optical fingering．To measure the performance of the proposed algorithm，two new evaluation metrics，the incapable-performing fingering ratio and the unreasonable fingering rate，were introduced to measure the flexibility and efficiency of fingering．Compared with the existing labeling model，the experiments showed that the proposed algorithm improved both the consistency rate and the two new in-dicators．In addition，to compare the performance of traditional methods with deep learning methods in small data sets，Bi-LSTM+CRF was added．The results showed that the inelastic fingering rate and unreasonable rate in deep learning were not as effective as those in the algorithm．
Keyword_Chinese:钢琴指法；判决隐马尔可夫模型；先验知识；改进维特比算法
Keywords_English:piano fingering；judgement-HMM；prior knowledge；improved Viterbi alogrithm

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