CN109065070B - A Dimensionality Reduction Method of Audio Feature Signal Based on Kernel Function - Google Patents

Abstract

The invention relates to a kernel function-based audio characteristic signal dimension reduction method, and belongs to the technical field of audio signal processing. The invention carries out dimension reduction processing on the characteristic parameters of the audio signals, achieves the required dimension reduction effect while not discarding the audio characteristic information quantity, visually displays the final dimension reduction data, and carries out comparison analysis on the results obtained by adopting other audio characteristic parameter dimension reduction methods. The invention carries out dimension reduction on the audio characteristic parameters, mainly carries out dimension reduction processing on a linear prediction coefficient, a linear prediction cepstrum coefficient and a Mel frequency cepstrum coefficient of an audio coefficient field, and visually displays the data result after dimension reduction. The audio feature dimension reduction processing of the invention can be used for monitoring broadcast signals and quickly identifying and processing audio signals. The method has simple algorithm, uses the nonlinear kernel function to represent the mapping relation between the Gaussian observation space and the hidden space, and avoids the defects of limited use range and poor dimension reduction effect of a linear mapping method.

Description

A Dimensionality Reduction Method of Audio Feature Signal Based on Kernel Function

technical field

The invention relates to a dimensionality reduction method for an audio feature signal based on a kernel function, and belongs to the technical field of audio feature signal processing.

Background technique

In order to realize the management and control of wireless audio broadcasting, and conduct safe and efficient real-time monitoring and screening of audio broadcasting, the rapid processing of audio information is related to the process speed of the entire process, and the feature signal dimensionality reduction processing of audio is the core of audio information processing. Efficiency and credibility must also become urgent problems to be solved at present. At present, most of the dimensionality reduction methods for audio feature signals mainly include local preservation projection method, multi-dimensional scaling method, local linear embedding method, principal component analysis method and so on. Most of these dimensionality reduction algorithms have high complexity, and the purpose of dimensionality reduction is achieved by discarding some characteristic signals, which will cause unpredictable errors in practical engineering applications. The present invention is proposed to address the above drawbacks.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a dimensionality reduction method for audio feature signal based on kernel function. (MFCC) performs dimensionality reduction analysis to reduce the data dimension and improve the information processing rate.

The technical solutions of the present invention are as follows: a dimensionality reduction method for audio feature signals based on a kernel function. The method includes the following specific steps:

(1) Audio signal collection: collect audio signals to obtain audio samples.

(2) Audio signal preprocessing: convert the analog signal in the collected audio sample into a digital signal, and write the digital signal into a WAV file. Filter, pre-emphasize and frame the digital signal written in the WAV file.

(3) Feature parameter extraction: Extract high-dimensional feature parameters for linear prediction coefficients (LPC), linear prediction cepstral coefficients (LPCC), and Mel frequency cepstral coefficients (MFCC) in the processed digital signal.

(4) Construction of the dimensionality reduction model: the above-mentioned extracted feature parameters are sent into the dimensionality reduction model built by the kernel trick to directly obtain low-dimensional hidden variables, and the low-dimensional hidden variables are the dimensionality reduction. The data. Its core is to use Gaussian regression process model (GPR) to nonlinearly model the relationship between latent variables and observed variables.

(5) Dimensionality reduction analysis: Visually display (2D/3D) data after dimensionality reduction, and compare it with the results obtained by other dimensionality reduction methods.

The above-mentioned dimensionality reduction method based on the audio feature signal of a kernel function, the audio collection described in step (1) is to collect audio samples by an audio collection device, and the audio collection device sets the sampling frequency when the audio signal is collected (the sampling frequency satisfies the Nyquist sampling theorem), number of sampling channels, quantization accuracy.

In the above-mentioned dimensionality reduction method of the audio feature signal based on the kernel function, the audio signal preprocessing in step (2) comprises the following steps:

(1) Use the rectangular window function w(n) (the upper limit frequency is generally taken as f _H = 3400 Hz, and the lower limit frequency f _L = 60 ~ 100 Hz) to filter the collected audio signal x (n) to obtain the signal y _a (n), in

(2) Perform pre-emphasis processing on the filtered signal y _a (n) by the differential method to obtain the signal y _b (n), where y _b (n)=y(n)-αy(n-1) (α is The pre-emphasis coefficient is generally close to 1). Boosts high frequencies and suppresses low frequencies to flatten the spectrum of the signal.

(3) The short-term analysis of the framed speech signal is to divide the signal into several speech segments, one segment is called a frame, and the time range of each segment is between 10 and 30 ms. In order to ensure a smooth transition between frames, there is a partial overlap between frames, and the overlapping part is called frame shift, and the frame shift takes 1/2 or 1/3 of the frame length.

In the above-mentioned dimensionality reduction method of the audio feature signal based on kernel function, step (3) feature parameter extraction comprises the following steps:

(1) Linear Prediction Coefficient (LPC): Use programming to call the LPC function package, set the frame length, frame shift, window function, and order parameters of LPC, and perform eigenvalues on the preprocessed audio signal in the above step (2). , put into the specified table 1.

(2) Linear prediction cepstral coefficient (LPCC): use programming to call the LPCC function package, set the frame length, frame shift, window function, and order parameters of LPCC, and perform the preprocessed audio signal in the above step (2). Extraction of eigenvalues and put them into the specified table 2.

(3) Mel frequency cepstral coefficient (MFCC): use programming to call the MFCC function package, set the frame length, frame shift, window function, and order parameters of the MFCC, and perform the preprocessed audio signal in the above step (2). Extract the eigenvalues and put them in the specified table 3.

In the above-mentioned dimensionality reduction method of audio feature signal based on kernel function, the building of the dimensionality reduction model in step (4) includes the following steps:

维度为q，记观测空间为

维度为d(q<d)。假设观测值与隐空间参量之间存在y＝f(z)+ε关系，噪声ε服从均值为0，方差为β的高斯分布，并假设隐函数f是满足高斯过程的平方指数核函数(1) Building the feature dimensionality reduction model First, the latent space is recorded as

The dimension is q, and the observation space is recorded as

The dimension is d (q<d). Assume that there is a y=f(z)+ε relationship between the observed value and the latent space parameter, the noise ε obeys a Gaussian distribution with a mean of 0 and a variance of β, and assumes that the implicit function f is a square exponential kernel function that satisfies the Gaussian process

其中σ为平方指数核的系数参数，l表示z与z′两点之间距离影响因数参数，β表示模型的一个超参量参数，σ(z,z′)表示的是Kroneckerdelta函数，核函数中要求解的参量为θ(σ,l,β)。当z与z′很接近时其核函数取得最大值，距离很远时取得最小值。为了便于后续推导，先给出协方差矩阵的计算公式，其公式为

where σ is the coefficient parameter of the square exponential kernel, l represents the distance influencing factor parameter between the two points z and z', β represents a hyperparameter parameter of the model, σ(z, z') represents the Kroneckerdelta function, in the kernel function The parameters to be solved are θ(σ,l,β). When z and z' are very close, the kernel function obtains the maximum value, and when the distance is very far, the kernel function obtains the minimum value. In order to facilitate the subsequent derivation, the calculation formula of the covariance matrix is given first, and its formula is

(2) Assuming that the d-dimensional observation space is independently sampled, the observation probability about Y can be obtained, where y _:,i is the n element of the i-th dimension in the observation value space Y

In order to obtain a better dimensionality reduction effect, the relevant algorithm is used to obtain the best hyperparameters of the kernel function to maximize the above probability. Here, the particle swarm optimization algorithm is used to solve it, and θ(σ,l,β) _Denoted as A = (a ₁ , a ₂ , a ₃ ), where the speed of particle i is denoted as vi = (v _i1 , v _i2 , v _i3 ), and the best position the particle passes through is denoted as p _g = ( p _g1 ,p _g2 ,p _g3 ), the particle swarm algorithm uses the following equation to continuously update the position of the particle

其中w是非负的惯性因子；加速常数c₁与c₂是非负数；r₁与r₂是在[0 1]范围内变换的随机数。利用粒子群优化算法当前位置、经验位置和邻居位信息进行粒子状态的调整，将粒子群优化算法这种信息交换模式应用到核参数优化过程中，粒子受到自身经验和群里经验的双重影响，故而有较好的全局寻优能力和收敛速度。

where w is a non-negative inertia factor; acceleration constants c ₁ and c ₂ are non-negative numbers; r ₁ and r ₂ are random numbers transformed in the range of [0 1]. Particle swarm optimization algorithm current position, experience position and neighbor position information are used to adjust the particle state, and the information exchange mode of particle swarm optimization algorithm is applied to the process of kernel parameter optimization. Therefore, it has better global optimization ability and convergence speed.

The kernel function used in this model is a nonlinear kernel function, and the obtained kernel parameters θ(σ, l, β) are brought back into the model, and the above-extracted characteristic parameters are sent into the dimensionality reduction model to obtain hidden parameters, so The hidden parameters are the data after dimensionality reduction.

In the above-mentioned dimensionality reduction analysis method based on audio feature signal, in step (5), the above-mentioned dimensionality reduction data is displayed in two-dimensional or three-dimensional visualization, and then the results of other dimensionality reduction algorithms are analyzed and compared.

The advantages of the present invention and the existing kernel function-based audio feature signal dimensionality reduction method are as follows:

(1) The present invention uses a nonlinear kernel function to represent the direct relationship between the observation space data and the parameters of the latent space, avoiding the disadvantage of poor dimensionality reduction effect for some audio feature data caused by linear mapping.

(2) The present invention uses the particle swarm algorithm to solve the hyperparameters in the kernel function. The excellent global optimization ability of the particle swarm and the directionality of the swarm particles can quickly find the optimal hyperparameters, which is also the same for subsequent replacement of other kernel functions. Extremely convenient.

(3) The novel audio feature dimensionality reduction algorithm proposed by the present invention is simple in theory, easy to implement in programming, more suitable for application in practical engineering projects, and has substantial changes in the improvement of audio information processing speed.

Description of drawings

Fig. 1 dimensionality reduction analysis flow chart of the present invention;

Fig. 2 signal preprocessing flow chart of the present invention;

Fig. 3 feature parameter extraction and dimensionality reduction processing flow chart of the present invention;

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1-3, a dimensionality reduction method of audio feature signal based on kernel function, the specific steps are:

(1) Audio signal collection: collect audio signals to obtain audio samples.

(2) Audio signal preprocessing: convert the analog signal in the collected audio sample into a digital signal, and write the digital signal into a WAV file. Filter, pre-emphasize, and frame the digital signal to be written into the WAV file.

(3) Feature parameter extraction: Extract high-dimensional feature parameters for linear prediction coefficients (LPC), linear prediction cepstral coefficients (LPCC), and Mel frequency cepstral coefficients (MFCC) in the processed digital signal.

(4) Construction of the dimensionality reduction model: the above-mentioned extracted feature parameters are sent into the dimensionality reduction model built by the kernel trick to directly obtain low-dimensional hidden variables, and the low-dimensional hidden variables are the dimensionality reduction. The data.

(5) Dimensionality reduction analysis: Visually display (2D/3D) data after dimensionality reduction, and compare it with the results obtained by other dimensionality reduction methods.

The audio collection is to collect audio samples through an audio collection device. When the audio collection device collects audio signals, the sampling frequency is set to 44.1Hz (the sampling frequency satisfies the Nyquist sampling theorem). The number of channels is mono, and the quantization precision is 16bit.

The signal preprocessing includes the following steps:

(1) Use the rectangular window function w(n) (the upper limit frequency is generally taken as f _H = 3400 Hz, and the lower limit frequency f _L = 60 ~ 100 Hz) to filter the collected audio signal x (n) to obtain the signal y _a (n), in

(2) Perform pre-emphasis processing on the filtered signal y _a (n) by the differential method to obtain the signal y _b (n), where y _b (n)=y(n)-αy(n-1) (α is The pre-emphasis coefficient is generally close to 1).

(3) The signal y _b (n) obtained by pre-emphasis processing is divided into several speech segments, one segment is called a frame, and the time range of each segment is between 10 and 30 ms. There is a partial overlap between frames, the overlapping part is called frame shift, and the frame shift takes 1/2 or 1/3 of the frame length.

The feature parameter extraction includes the following steps:

(1) Linear Prediction Coefficient (LPC): Use programming to call the LPC function package, set the frame length, frame shift, window function, and order parameters of LPC, and perform eigenvalues on the preprocessed audio signal in the above step (2). , into the specified table 1.

(2) Linear prediction cepstral coefficient (LPCC): use programming to call the LPCC function package, set the frame length, frame shift, window function, and order parameters of LPCC, and perform the preprocessed audio signal in the above step (2). The extraction of eigenvalues is put into the specified table 2.

(3) Mel frequency cepstral coefficient (MFCC): use programming to call the MFCC function package, set the frame length, frame shift, window function, and order parameters of the MFCC, and perform the preprocessed audio signal in the above step (2). Extract the eigenvalues and put them in the specified table 3.

The construction of the dimensionality reduction model includes the following steps:

观测空间为

(1) The hidden space parameter is recorded as

The observation space is

That is, the dimension of the hidden space is q, and the dimension of the observation space is d (q<d). Assuming that there is a y=f(z)+ε relationship between the observed value and the hidden space parameters, the noise ε follows a Gaussian distribution with a mean of 0 and a variance of ξ. And assume that the implicit function f is a square exponential kernel function satisfying a Gaussian process:

where σ is the coefficient parameter of the square exponential kernel, l represents the distance influencing factor parameter between the two points z and z', β represents a hyperparameter parameter of the model, σ(z, z') represents the Kronecker delta function, the kernel function The parameters to be solved in are θ(σ,l,β). When z and z' are very close, the kernel function obtains the maximum value, and when the distance is very far, the kernel function obtains the minimum value. The formula for calculating the covariance matrix is:

(2) Assuming that the d-dimensional observation space is independently sampled, the observation probability about Y can be obtained, where y _:,i is the n element of the i-th dimension in the observation value space Y

In the present invention, the particle swarm optimization algorithm is used to solve its parameters, and θ(σ, l, β) is denoted as A=(a ₁ , a ₂ , a ₃ ), and the speed of particle _i is denoted as vi = (v _i1 ,v _i2 ,v _i3 ), the best position where the particle passes through is denoted as p _g =(p _g1 ,p _g2 ,p _g3 ), the particle swarm algorithm position iterative update formula:

where w is a non-negative inertia factor; acceleration constants c ₁ and c ₂ are non-negative numbers; r ₁ and r ₂ are random numbers transformed in the range of [0 1]. Bring the obtained kernel parameters θ(σ, l, β) back into the model to obtain a dimensionality reduction model based on the kernel function, and send the above extracted feature parameters into the dimensionality reduction model to obtain hidden parameters, which are dimensionality reduction. data after.

In the dimensionality reduction analysis, because people live in three-dimensional space, it is impossible to imagine the space beyond three-dimensional space, and it is difficult to directly analyze the dimensionality reduction results with many data sets. The dimensionality reduction process is carried out in the dimensional model, and the obtained hidden parameter data is saved and displayed visually, so as to facilitate the comparative analysis with other dimensionality reduction models. The present invention is not limited to the above-mentioned embodiments, and the dimensionality reduction algorithm thereof can also be applied to other related fields within the scope of knowledge possessed by those of ordinary skill in the art.

Claims (3)

1. A kernel function-based audio feature signal dimension reduction method is characterized in that: the method comprises the following specific steps:

(1) audio signal acquisition: collecting an audio signal to obtain an audio sample;

(2) audio signal preprocessing: converting analog signals in the collected audio samples into digital signals, writing the digital signals into a WAV file, and performing filtering, pre-emphasis and framing processing on the digital signals written into the WAV file;

(3) characteristic parameter extraction: extracting characteristic parameters of a linear prediction coefficient, a linear prediction cepstrum coefficient and a Mel frequency cepstrum coefficient in the processed digital signal;

building a dimension reduction model: sending the extracted characteristic parameters into a dimensionality reduction model built by a nucleation skill to directly obtain low-dimensional hidden variables, wherein the low-dimensional hidden variables are dimensionality reduced data;

the dimension reduction model is specifically built as follows:

(1) the dimension reduction model is built by first recording the hidden space as

Dimension q, let observation space be

Dimension d, q<d, assuming that a relation of y ═ f (z) + epsilon exists between the observed value and the hidden space parameter, the noise epsilon follows a gaussian distribution with mean 0 and variance β, and assuming that the hidden function f is a squared exponential kernel function satisfying the gaussian process:

wherein σ is a coefficient parameter of a square exponential kernel, l represents a distance influence factor parameter between z and z ', β represents a hyper-parameter of the model, σ (z, z ') represents a Kronecker delta function, the parameter requiring solution in the kernel function is θ (σ, l, β), it can be known from the above formula that the kernel function obtains a maximum value when z and z ' are very close, and obtains a minimum value when the distance is very far, and a calculation formula of a covariance matrix of the kernel function:

(2) assuming independent sampling of the d-dimensional observation space, the probability of observation for Y, where Y is_:,iFor n elements of the i-th dimension in the observation space Y

Solving the parameters by a particle swarm optimization algorithm, and recording theta (sigma, l, beta) as A ═ a₁,a₂,a₃) Wherein the velocity of the particle i is denoted v_i＝(v_i1,v_i2,v_i3) The best position where the particle passes is denoted p_g＝(p_g1,p_g2,p_g3) And a particle swarm algorithm position iteration formula:

(4) wherein w is a non-negative inertia factor; acceleration constant c₁And c₂Is a non-negative number; r is₁And r₂Is at [01]Random numbers transformed within the range are applied to a kernel parameter optimization process by an information exchange mode of a particle swarm optimization algorithm, the solved kernel parameters theta (sigma, l, beta) are brought back into the model to obtain a dimension reduction model, the extracted characteristic parameters are sent into the dimension reduction model to obtain hidden parameters, and the hidden parameters are dimension reduced data;

(5) and (3) analyzing a dimension reduction result: and carrying out visual display on the data subjected to the dimensionality reduction.

2. The kernel function-based audio feature signal dimension reduction method according to claim 1, wherein: the audio acquisition is performed by an audio acquisition device, and the audio acquisition device sets the sampling frequency, the number of sampling channels and the quantization precision when acquiring the audio signals.

3. The kernel function-based audio feature signal dimension reduction method according to claim 1, wherein: the audio signal pre-processing comprises the steps of:

(1) filtering the collected audio signal x (n) by adopting a rectangular window function w (n) to obtain a signal y_a(n) wherein

(2) For the filtered signal y_a(n) pre-emphasis processing is carried out by using a difference method to obtain a signal y_b(n) wherein y_b(n) y (n) - α y (n-1), α being a pre-emphasis coefficient and generally having a value close to 1;

(3) processing the pre-emphasis to obtain a signal y_b(n) dividing the frame into a plurality of voice frames, and partially overlapping the frames, wherein the overlapped part is called frame shift.

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