QoE prediction model for mobile video telephony

Abstract

Interactive online video applications, such as video telephony, are known for their vulnerability to network condition. With the increasing usage of hand-held wireless mobile devices, which are capable of capturing and processing good quality videos, combined with the flexibility in an end-user movements have added new challenging factors for application providers and network operators. These factors affect the perceived video quality of mobile video telephony applications, unlike conventional video telephony over desktop computers. We investigate this impact on video quality of mobile video telephony in varying network conditions and end-users movement scenarios. Based on 312 live traces, we quantitatively derive the correlation between the perceived video quality and the network Quality of Service (QoS) and user mobility. With the results, we develop a Quality of Experience (QoE) prediction model for mobile video telephony using Support Vector Regression techniques. The prediction models display ≈ 0.8 pearson correlation with experimental data. Our methodology and findings can be used to guide the video telephony application providers and network operators to work towards satisfying end-user experience.

Appendix A: Support vector regression

Support Vector Regression (SVR), is a machine learning tool proposed in [3]. We discuss the linear case followed by non-linear SVR algorithm.

Suppose the training data set is as following

$$ S = \{(\mathbf{x_{i}}, y_{i}) | i = 1, 2, 3, ...., m \} $$

(8)

where real-valued inputs x _i ∈R ⁿ, and target y ∈ 𝔑. The objective function is to find function f that returns the best fit i.e. f : 𝔑ⁿ → 𝔑 The linear regression function f is given as

$$ f(\mathbf{x}) = <\mathbf{\omega},\mathbf{x}> + b $$

(9)

where b ∈ 𝔑 and ω ∈ 𝔑ⁿ. To avoid over-fitting, a regularization term is introduced to have small ω and can be formulated as the convex optimization problem minimizing the euclidean norm i.e.

$$\begin{array}{@{}rcl@{}} {\text{minimize}} & &\qquad\qquad\qquad \frac{1}{2} \parallel\mathbf{\omega} \parallel^{2} \\ \text{subject to} & &\qquad\qquad\qquad y_{i} - <\mathbf{\omega},\mathbf{x}> - b \leq \varepsilon \\ & &\qquad\qquad\qquad - y_{i} + <\mathbf{\omega},\mathbf{x}> + b \leq \varepsilon \end{array} $$

The convex optimization problem may not be feasible if the errors are more than ε. Thus, any point outside the ε region contributes to the cost of the function.

SVR introduces slack variables, ξ _i and $\xi ^{*}_{i}$ to cope up with not feasible constraints. The convex optimization can be defined as

$$\begin{array}{@{}rcl@{}} {\text{minimize}} & &\qquad\qquad\qquad \frac{1}{2} \parallel \mathbf{\omega} \parallel^{2} + C \sum\limits_{i = 1}^{m} (\xi_{i} + \xi_{i}^{*}) \end{array} $$

(10)

$$\begin{array}{@{}rcl@{}} \text{subject to} & & \qquad\qquad\qquad\xi_{i}, \xi_{i}^{*} \geq 0 \end{array} $$

(11)

$$\begin{array}{@{}rcl@{}} & & \qquad\qquad\qquad y_{i} - <\mathbf{\omega},\mathbf{x}> - b \leq \varepsilon \end{array} $$

(12)

$$\begin{array}{@{}rcl@{}} & & \qquad\qquad\qquad- y_{i} + <\mathbf{\omega},\mathbf{x}> + b \leq \varepsilon \end{array} $$

(13)

where C is a constant known as penalty factor. It consists the trade-off between smaller ω values and ε-insensitive loss function given as

$$|\xi|_{\varepsilon} = \left\{ \begin{array}{ll} 0 & : {\text{if }} |\xi| \leq \varepsilon\\ | \xi | - \varepsilon & : {\text{otherwise}} \end{array} \right. $$

The (13) is the Primal form and handles inequality constraints directly. The dual form obtained by constructing a Lagrange function and taking partial derivative w.r.t. primal variables is given as-

$$\begin{array}{@{}rcl@{}} {\text{maximize}} & &\qquad\qquad\qquad \frac{1}{2} \sum\limits_{i,j=1}^{n} (\alpha_{i} - \alpha_{i}^{*}) (\alpha_{j} - \alpha_{j}^{*}) <\mathbf{x}_{i},\mathbf{x}_{j}>\end{array} $$

(14)

$$\begin{array}{@{}rcl@{}} & &\qquad\qquad\qquad- \varepsilon \sum\limits_{i = 1}^{n} (\alpha_{i} + \alpha_{i}^{*}) + \sum\limits_{i = 1}^{n} y_{i} (\alpha_{i} - \alpha_{i}^{*}) \end{array} $$

(15)

$$\begin{array}{@{}rcl@{}} {\text{subject to}} & &\qquad\qquad\qquad\sum\limits_{i = 1}^{n} (\alpha_{i} - \alpha_{i}^{*}) = 0 \end{array} $$

(16)

$$\begin{array}{@{}rcl@{}} & &\qquad\qquad\qquad\alpha_{i}, \alpha_{i}^{*} \in [0,C] \end{array} $$

(17)

where $\alpha _{i}, \alpha _{i}^{*}$ are Lagrange multipliers. The steps for partial derivative can be looked upon in [1]. Interestingly, the partial derivative also gives following equation:

$$ \mathbf{\omega} = \sum\limits_{i=1}^{n} (\alpha_{i} - \alpha_{i}^{*}) \mathbf{x_{i}}. $$

(18)

Hence, the SVR linear regression reduces to

$$ f(\mathbf{x}) = \sum\limits_{i = 1}^{n} (\alpha_{i} - \alpha_{i}^{*}) <\mathbf{x_{i}}, \mathbf{x}> + b $$

(19)

The (9)–(19) discussed so far are simple cases when SVR algorithm is used for a linear function. SV algorithm can be made non-linear by simply substituting every instance of x with Φ(x). The approach becomes infeasible when x is mapped to higher-dimensions. Using kernel method, explicit substitution of x with Φ(x) is avoided. The kernel function is given as -

$$ <{\Phi}(\mathbf{x_{i}}),{\Phi}(\mathbf{x})> = K(\mathbf{x_{i}}, \mathbf{x}) $$

(20)

The commonly used kernel functions are polynomial kernels: K(x,y)=(x ^T y+1)^d and radial basis function (RBF) kernels: $K(x, y) = exp\left (\frac {-||x - y||^{2}}{2 \sigma ^{2}}\right )$ . Hence, from (19) and (20), the solution function can be written as

$$ f(\mathbf{x}) = \sum\limits_{i = 1}^{n} (\alpha_{i} - \alpha_{i}^{*}) K(\mathbf{x_{i}},\mathbf{x}) + b $$

(21)