Component Complexity Analysis Of Mixed Music Based On Sparse Representation

As an important research topic in the field of computer science and management science,NP-Hard problems are usually rather complex and difficult to solve.Research work in this field has important research and application value in the fields of model optimization,data analysis and management decision-making.Sparse representation is a typical multidimensional NP-Hard problem,and a data-driven analysis method,which is not sensitive to the quality of data annotation.It can decompose data samples into the product of general component dictionary and coefficient vector to realize the analysis of all main components of mixed data.However,the sparse constraints commonly used in existing sparse modeling algorithms are not precise enough in the field of data analysis;there is also a lack of effective complexity feature definition method,which needs to be improved to meet the needs of mixed source data analysis.Mix instruments music data is a typical kind of audio time-varying data,whose characteristics are same with many other time-varying data.However,there are some problems in the analysis of mixed component music data,such as the difficulty of data annotation,the difficulty of minor component analysis,the poor interpretability and intuitiveness of the method.Similar situation also exists in other mixed time-varying data,which requires targeted processing to obtain more precise and deeper analysis results,so as to be applied in public place sound management,music data analysis management and other data analysis applications.In order to solve these problems,the sparse constraints used in sparse representation algorithm are studied in this paper.Mixed component time-varying data represented by mixed music data is analyzed to present a set of complexity feature definition methods and analysis methods,and a new modeling paradigm is proposed to improve the accuracy of sparse representation algorithm,so as the other NPH algorithms.The main content is as follows:(1)A sparse complexity index SPI(Sparse Performance Index)is presented based on the analysis of mixed music data and sparse modeling algorithm,which is introduced for complexity analyze and sparse representation algorithm optimizing.Its value range,expected value,continuity,differentiability and physical significance is analyzed,its rationality and reliability as a sparse complexity measurement feature will also be proved in theory.Its data analysis performance is tested by mixed music data and other kinds of time-varying data.(2)A mixed music data analysis method based on SPI?K-SVD&OMP sparse representation algorithm and multi-dimensional component dictionary is proposed.Its parameter setting and calculation process are introduced in detail,and its advantages in interpretability,non-main component sensitivity,universality and scalability are introduced in combination with practical application requirements.Results are tested by string quartet and violin&piano Sonata.(3)A SPI based sparse modeling theoretical paradigm is proposed to solve the problems of existing sparse representation algorithm and theoretical paradigms,which is a typical NP complete problem.The accuracy and technical methods of the sparse modeling process have also been improved.Its convergence domain and the advantages in sparse modeling process is discussed.The convergence and sparse modeling effect are tested by on multiple datasets including time-varying simulation data.