CN110493701B - HRTF (head related transfer function) personalization method based on sparse principal component analysis - Google Patents

HRTF (head related transfer function) personalization method based on sparse principal component analysis Download PDF

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CN110493701B
CN110493701B CN201910642057.4A CN201910642057A CN110493701B CN 110493701 B CN110493701 B CN 110493701B CN 201910642057 A CN201910642057 A CN 201910642057A CN 110493701 B CN110493701 B CN 110493701B
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曾向阳
路东东
王海涛
周治宇
马慧颖
晋安其
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Abstract

The invention discloses a method for realizing HRTF personalization based on a sparse principal component analysis, which comprises the steps of firstly, using a principal component analysis method to reduce the dimension of the HRTF; then, reducing the dimension of the physiological parameters by using a sparse principal component analysis method; and finally, taking the physiological parameters subjected to dimension reduction as input, taking the HRTF subjected to dimension reduction as output, and applying a generalized regression neural network to perform nonlinear fitting. The invention applies sparse principal component analysis to realize the dimension reduction of three-dimensional physiological parameters, and reduces original dozens of dimensions of physiological parameters into several dimensions without influencing the structure of data. Local convergence of data when the correlation method is applied to dimension reduction processing is avoided, and the dimension reduction effect is improved. And the data subjected to dimensionality reduction is applied to carry out regression on the HRTF principal component coefficients, so that the regression time is reduced, and the overfitting risk is avoided. The HRTF personalization can be better realized by applying the three-dimensional physiological parameters subjected to dimension reduction.

Description

HRTF (head related transfer function) personalization method based on sparse principal component analysis
Technical Field
The patent relates to an HRTF personalization method, in particular to an HRTF personalization method based on sparse principal component analysis.
Background
A Head Related Transfer Function (HRTF) is a frequency-domain acoustic Transfer Function for describing that sound emitted from a free-field sound source reaches both ears after being scattered and reflected by physiological structures such as the Head, pinna, and trunk. Each sound source spatial position corresponds to a pair of HRTFs, which are generally functions of the distance of the sound source to the center of the head, the azimuth, elevation, and frequency of the sound source. Since the physiological structure and size of different individuals are different, and HRTFs are closely related to the physiological structure and size, they are physical quantities with distinct personalized features.
The filtering effect of physiological structures such as the trunk, the head and the auricle has more significant influence on the acoustic signal, that is, the physiological structures have more significant influence on the HRTF.
The literature "Martens W L.principles components and reconstruction of spectral documents to temporal direction. in: Proceedings of 1987International computer Music Conference,1987, 274-281". A method for personalizing head-related transfer functions by using human body morphological characteristics is disclosed, namely, head-related transfer functions are approximately estimated by using the correlation between basis functions and human body measurement items. In this paper, the authors select empirically the physiological parameters needed to build the model. Document "method of personalization of head-related transfer functions". A new method for constructing physiological parameters required by a model is disclosed. According to the method, all physiological parameters provided by the CIPIC database are subjected to correlation analysis, and irrelevant physiological parameters are selected as the physiological parameters required by the construction model. The physiological parameters obtained through experience are not persuasive in theory, and compared with the physiological parameters obtained through correlation analysis, the physiological parameters obtained through the correlation analysis theoretically have certain theoretical basis, however, the correlation analysis only considers the correlation between the physiological parameters, and does not consider the correlation between the physiological parameters and the HRTF. Meanwhile, the physiological parameters aimed at by the method are two-position physiological parameters, the physiological parameters are widely distributed and have weak local correlation, and the physiological parameters are all correlated when the three-dimensional physiological parameters are subjected to dimension reduction by applying the correlation due to relatively dense aggregation, so that the method is not applicable to the three-dimensional physiological parameters. Therefore, in order to realize HRTF personalization by directly applying three-dimensional physiological parameters, a sparse principal component analysis-based method is provided herein to realize HRTF personalization.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an HRTF personalization method based on sparse principal component analysis.
The patent proposes a sparse principal component analysis-based method to achieve HRTF personalization. The invention comprises three steps: (1) reducing the dimension of the HRTF by using a Principal Component Analysis (PCA); (2) reducing the dimension of the physiological parameter by applying a Sparse Principal Component Analysis (SPCA); (3) taking the physiological parameters after dimension reduction as input, taking the HRTF after dimension reduction as output, and applying a Generalized Regression Neural Network (GRNN) to perform nonlinear fitting.
Technical scheme
The technical scheme adopted by the invention for solving the technical problem is that the HRTF personalization method based on sparse principal component analysis comprises the following steps:
step 1: selecting all tested HRTFs in a certain determined direction, performing principal component analysis on the HRTFs in the direction to obtain principal components of the direction:
(1) selecting all tested HRTFs with azimuth angle (theta, phi) to form a vector HijWherein i is a tested sequence, j is a frequency serial number, the tested number is m, theta is an azimuth angle, and phi is a pitch angle;
(2) to HijThe following normalization process was performed:
Figure GDA0002604441870000021
wherein the content of the first and second substances,
Figure GDA0002604441870000022
Figure GDA0002604441870000023
is HijA normalized head-related transfer function;
(3) performing principal component analysis on the normalized head-related transfer function:
Figure GDA0002604441870000024
wherein, Pm×nIs a score matrix of m × n for principal component analysis; w is a load matrix of n × n of principal component analysis, T represents the transpose of the matrix;
step two: and reducing the dimension of the three-dimensional physiological parameters by using an SPCA method.
(1) All tested physiological parameters are formed into vectors of X ═ { X ═ X1,x2,…,xn}∈Rp×nWhere p represents the physiological parameter dimension of a single test subject and n represents the number of test subjects. Singular Value Decomposition (SVD) is performed on X.
X＝UDVT(3)
Where Z ═ UD is the principal component of vector X, and V is the load matrix of vector X.
(2) In this patent, we introduce sparse loadings to estimate the principal components. The sparse load is regressed by an elastic network. For the ith principal component, define Zi＝UiDii
Figure GDA0002604441870000031
Wherein the content of the first and second substances,
Figure GDA0002604441870000032
is the first order norm of β; λ, λ1Is a resilient penalty function.
(4) Vector alpha corresponding to first L principal components of X principal component analysisjForming a new initialization matrix A; setting a random initialization matrix B ═ beta at the same time1,…,βL]。
(5) In the given case of a, the elastic net regression problem is solved:
Figure GDA0002604441870000033
wherein λ is1，λ1,jAre all elastic penalty functions
(6) Update B ═ β1,…,βL]Calculating XTXB＝UDVTSimultaneously update A ═ UVT。
(7) Repeating the steps (5) and (6) until the convergence of B
(8) Normalized betajAnd obtaining the sparse load matrix.
(9) And obtaining main components representing the physiological parameters according to the sparse load matrix.
Step three: and (3) taking the obtained physiological parameters as input, taking the principal component coefficients subjected to HRTF dimensionality reduction as output, and performing regression by applying GRNN. And restoring the regressed main component to obtain the restored HRTF.
Advantageous effects
The dimension reduction of three-dimensional physiological parameters can be realized by applying sparse principal component analysis, and original dozens of dimensions of physiological parameters are reduced into dozens of dimensions without influencing the structure of data. The three-dimensional physiological parameters are processed by applying sparse principal component analysis, so that the local convergence of data is avoided when a correlation method is applied to dimension reduction processing, and the dimension reduction effect is improved. And the data subjected to dimensionality reduction is applied to carry out regression on the HRTF principal component coefficients, so that the regression time is reduced, and the overfitting risk is avoided. The HRTF personalization can be better realized by applying the three-dimensional physiological parameters subjected to dimension reduction.
Drawings
FIG. 1 is a flowchart of HRTF personalization based on sparse principal component analysis;
fig. 2. experimental HRTFs were regressed by physiological parameters selected from sparse principal components, 063 (0 ° ).
Detailed description of the invention
Refer to fig. 1. The HRTF personalization process is specifically described for HRTFs with an azimuth angle θ equal to 0 ° and a pitch angle Φ equal to 0 °.
Step 1: selecting all tested HRTFs in the direction (0 degrees and 0 degrees), and performing principal component analysis on the HRTFs in the direction to obtain principal components of the direction:
(1) selecting all tested HRTFs with the azimuth of (0 degrees and 0 degrees) to form a vector HijWherein i is a tested sequence, j is a frequency serial number, the tested number is m, the azimuth angle theta is 0 DEG, and the pitch angle phi is 0 DEG;
(2) to HijThe following normalization process was performed:
Figure GDA0002604441870000041
wherein the content of the first and second substances,
Figure GDA0002604441870000042
Figure GDA0002604441870000043
is HijA normalized head-related transfer function;
(3) performing principal component analysis on the normalized head-related transfer function:
Figure GDA0002604441870000044
wherein, Pm×nIs a score matrix of m × n for principal component analysis; w is a load matrix of n × n of principal component analysis, T represents the transpose of the matrix;
step two: and reducing the dimension of the three-dimensional physiological parameters by using an SPCA method.
(1) Forming a tested physiological parameter with the number of 001-062 into a vector X ═ { X ═ X1,x2,…,xn}∈Rp×nWhere p represents the physiological parameter dimension of a single test subject and n represents the number of test subjects. Singular Value Decomposition (SVD) is performed on X.
X＝UDVT(3)
Where Z ═ UD is the principal component of vector X, and V is the load matrix of vector X.
(2) In this patent, we introduce sparse loadings to estimate the principal components. The sparse load is regressed by an elastic network. For the ith principal component, define Zi＝UiDii
Figure GDA0002604441870000045
Wherein the content of the first and second substances,
Figure GDA0002604441870000051
is the first order norm of β; λ, λ1Is a resilient penalty function.
(3) Vector omega corresponding to first L principal components of X principal component analysisjForming a new initialization matrix; setting a random initialization matrix B ═ beta at the same time1,…,βL]。
(4) In the given case of a, the elastic net regression problem is solved:
Figure GDA0002604441870000052
wherein λ is1，λ1,jAre all elastic penalty functions
(5) Update B ═ β1,…,βL]Calculating XTXB＝UDVTSimultaneously update A ═ UVT。
(6) Repeating the steps (5) and (6) until the convergence of B
(7) Normalized betajAnd obtaining the sparse load matrix.
(8) And obtaining main components representing the physiological parameters according to the sparse load matrix.
Step three: and (3) taking the obtained physiological parameters with the sparse principal component accumulation percentage of 95% as input, taking the principal component coefficients subjected to HRTF dimensionality reduction as output, and applying GRNN to carry out regression. And restoring the regressed main component to obtain the restored HRTF.
The tested sample with the number 063 is taken as a test sample, the physiological parameter of 063 with the sparse principal component accumulation percentage of 95% is selected as input, the trained GRNN network is used for training, and the training result is shown in figure 2. As can be seen from fig. 2, the trained HRTF is not much different from the original HRTF, and the result is better than that in the comparative paper.

Claims (1)

1. A head-related transfer function (HRTF) personalization method based on sparse principal component analysis comprises the following steps:
the method comprises the following steps: selecting all tested HRTFs in a certain determined direction, performing principal component analysis on the HRTFs in the direction to obtain principal components of the direction:
(1) selecting all tested HRTFs with azimuth angle (theta, phi) to form a vector HijWherein i is a tested sequence, j is a frequency serial number, the tested number is m, theta is an azimuth angle, and phi is a pitch angle;
(2) to HijThe following normalization process was performed:
Figure FDA0002622100800000011
wherein the content of the first and second substances,
Figure FDA0002622100800000012
Figure FDA0002622100800000013
is HijA normalized head-related transfer function;
(3) performing principal component analysis on the normalized head-related transfer function:
Figure FDA0002622100800000014
wherein, Pm×nIs a score matrix of m × n for principal component analysis; w is a load matrix of n × n of principal component analysis, T represents the transpose of the matrix;
step two: applying a sparse principal component analysis method, namely an SPCA method to reduce the dimension of the three-dimensional physiological parameters:
(1) all tested physiological parameters are formed into vectors of X ═ { X ═ X1,x2,…,xn}∈Rp×nWherein p represents a single physiological parameter dimension of the subject and n represents the number of subjects; performing Singular Value Decomposition (SVD) on X;
X＝UDVT(3)
wherein, Z ═ UD is the principal component of vector X, V is the load matrix of vector X;
(2) in this patent, we introduce sparse loads to estimate the principal components; the sparse load is regressed through an elastic network; for the ith principal component, define Zi＝UiDii
Figure FDA0002622100800000015
Wherein the content of the first and second substances,
Figure FDA0002622100800000016
is the first order norm of β; λ, λ1Is a resilient penalty function;
(4) analysis of X principal ComponentsVector α corresponding to the first L principal components of (a)jForming a new initialization matrix A; setting a random initialization matrix B ═ beta at the same time1,…,βL]；
(5) In the given case of a, the elastic net regression problem is solved:
Figure FDA0002622100800000021
wherein λ is1，λ1,jAre all elastic penalty functions
(6) Update B ═ β1,…,βL]Calculating XTXB＝UDVTSimultaneously update A ═ UVT；
(7) Repeating the steps (5) and (6) until the convergence of B
(8) Normalized betajObtaining a sparse load matrix;
(9) acquiring main components representing physiological parameters according to the sparse load matrix;
step three: taking the obtained physiological parameters as input, taking principal component coefficients subjected to HRTF dimensionality reduction as output, and applying a generalized regression neural network GRNN to carry out regression; and restoring the regressed main component to obtain the restored HRTF.
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