Content Popularity Prediction in Fog-RANs: A Clustered Federated Learning Based Approach

1) Local popularity prediction: The content request pattern reflects the user-content interaction, and the hidden representations of users and contents are responsible for the interaction [16]. In order to learn the hidden representations of local users and contents which are helpful to capture user-content interaction, DCNN model is introduced to produce deep latent features of local users and contents from initial features constructed by neighbor selection. Then, the request probability can be predicted by merging the deep latent features of local users and contents. To distinguish regional variations of local popularity, CFL is employed to specialize the model parameters of DCNN of each F-AP by grouping F-APs with similar regional types into the same cluster. Bandwidth resource can also be saved because only model parameters need to be transmitted in CFL. The local popularity in each F-AP is the integration of the predicted request probability and the activity levels of local users.

2) Mobile popularity prediction: Due to the random mobility of mobile users as well as privacy reasons, in order to predict the mobile popularity in a given F-AP, user preference learning is implemented independently by each mobile user in an offline manner. With all the currently associated mobile users sending the request probability predicted via user preference and content information, mobile popularity of contents in a given F-AP can be obtained.

3) Popularity integration: The content popularity in a given F-AP can be obtained by integrating the content popularities in terms of local users and mobile users. By monitoring the request records of local users as well as the user mobility of mobile users, the content popularity can be dynamically updated to maximize the cache hit rate.

The procedure of local popularity prediction consists of the following three steps: neighbor selection based feature construction, DCNN model construction and CFL based model specialization.

1) Neighbor selection based feature construction: To construct initial features of local users or contents, it is meaningful to take the information of users with similar preference or the information of contents requested by similar users into account [17]. For example, if a user prefers to movies which are favored mostly by teenagers, then the user’s feature may be relevant to the information of teenagers. Therefore, we adopt a similarity computation method enhanced by inverse request frequency of users (IRFU) and inverse request frequency of contents (IRFC) to select neighbor set [18].

Based on Euclidean distance, the similarity between two local users enhanced by IRFU can be computed by the rating of contents they both have requested according to [18]. Defined as the logarithmic transformation of the ratio of the total users to the users who have requested a certain content, IRFU reflects the discrimination of contents when computing the similarity between two local users. By utilizing IRFC of users, the similarity between two contents in a given F-AP can be computed analogously. Given similarities within the scope of a given F-AP $m$, the neighbor set $\mathcal{N}(l_{u}^{m})$ of $l_{u}^{m}$ and $\mathcal{N}^{m}(i)$ of content $i$ are selected from the top $T$ most similar neighbors respectively.

In order to incorporate neighbor information with self information, we propose to generate initial features via information integration. Let $\bm{\xi}_{u}^{m}\in[0,1]^{d_{U}}$ and $\bm{\zeta}_{i}\in[0,1]^{d_{I}}$ denote the information vectors of user $l_{u}^{m}$ and content $i$ respectively, where $d_{U}$ is the dimension of user information space and $d_{I}$ is the dimension of content information space. The initial feature vector $\bm{x}_{u}^{m}$ of user $l_{u}^{m}$ is computed as the weighted sum of the self information vector and the average information vector of neighbor set:

where $w_{\mathcal{N}}$ denotes the weight factor of self information in initial features. The initial feature vector $\bm{\chi}_{i}^{m}$ of content $i$ in F-AP $m$ is computed in a similar way:

2) DCNN model construction: Given initial features of local users and contents, a DCNN model is leveraged to learn the hidden representations by producing deep latent features in a given F-AP. Motivated by [19], two feature transforming functions are constructed in DCNN to produce deep latent features of local users and contents respectively. Let $F_{U}:\mathbb{R}^{d_{U}}\mapsto\mathbb{R}^{H}$ and $F_{I}:\mathbb{R}^{d_{I}}\mapsto\mathbb{R}^{H}$ denote the feature transforming functions for local users and contents respectively. The deep latent features of local user $l_{u}^{m}$ and content $i$ in F-AP $m$ can be computed as $F_{U}(\bm{x}_{u}^{m},\Theta_{U}^{m})$ and $F_{I}(\bm{\chi}_{i}^{m},\Theta_{I}^{m})$, where $\Theta_{U}^{m}$ and $\Theta_{I}^{m}$ denote the parameters of the feature transforming functions in F-AP $m$. Let $\hat{p}_{u,i}^{m}$ denote the request probability of local user $l_{u}^{m}$ for content $i$. Then, it can be predicted by the inner product of the deep latent features as follows:

We introduce the multilayer perceptron (MLP) as the feature transforming function in DCNN model, which is effective to learn the hidden representaions between input and output. Compared with the latent features generated from the observed request data [9], deep latent features generated from initial features contain the hidden representations, which contributes to capturing the user-content interaction.

Let $\mathcal{A}^{m}=\left\{(\bm{x}_{u}^{m},\bm{\chi}_{i}^{m},y_{u,i}^{m}),l_{u}^{m}\in\mathcal{L}^{m},i\in\mathcal{I}\right\}$ denote the set of training samples of F-AP $m$, where $y_{u,i}^{m}$ is the binary request label. $y_{u,i}^{m}=1$ if local user $l^{m}_{u}$ has requested content $i$, otherwise $y_{u,i}^{m}=0$. The binary cross entropy (BCE) loss is utilized as the loss function for the optimization of parameters, which can be expressed as follows:

The DCNN model is trained by adjusting the parameters $\Theta_{U}^{m}$ and $\Theta_{I}^{m}$ through Adam optimizer with learning rate decaying.

As the predicted request probability above is essentially the probability conditional on a sended request, it is necessary to take user activity level into account [20]. The activity level of local user $l^{m}_{u}$ (i.e., the probability that local user $l^{m}_{u}$ sends a request) is defined as $s^{m}_{u}=\left|R^{m}_{u}\right|/\sum_{l_{v}^{m}\in\mathcal{L}^{m}}\left|R^{m}_{v}\right|$, where $\left|R^{m}_{u}\right|$ is the number of requests of local user $l_{u}^{m}$. According to the theory of total probability, local popularity of content $i$ in F-AP $m$ can be expressed as:

3) CFL based model specialization: With training data stored in F-APs in a distributed manner, computational tasks for training a single global model can be distributed from the cloud server to F-APs via conventional FL [21]. Moreover, only model parameters need to be transmitted to the cloud server instead of all the training data, resulting in tremendous bandwidth resource savings. However, due to the diverse regional types of F-APs, local popularity in different F-APs varies. For example, users served by F-APs located near stadium are more likely to request contents related with sports, while users located at school tend to request educational contents. In this situation, only one single global model obtained from conventional FL can hardly predict local popularity accurately, as all the F-APs with incongruent data distributions are treated equally.

In order to solve the aforementioned problem with incongruent data distributions, CFL is adopted [22]. CFL not only retains the advantage of saving bandwidth resource, but also adaptively splits up F-APs with incongruent data distributions into separated clusters without the prior knowledge of cluster number. Thus, F-APs with similar regional types (i.e., similar data distributions) can benefit from one another’s training data in the same cluster, arriving at more specialized models with a higher accuracy.

Let $\Phi=\left\{\phi_{1},\phi_{2},\dots,\phi_{g},\dots,\phi_{G}\right\}$ denote the final clustering result generated by CFL, where $\phi_{g}$ is a cluster containing at least one F-AP. The clustering result $\Phi$ can be obtained after $G-1$ valid bipartitions. Let $\theta$ denote the parameter of DCNN model. CFL will recursively split up F-APs and optimize model parameters in a top-down way. In the beginning, CFL is applied in the initial set of F-APs $\mathcal{M}$ with initial model parameter $\theta_{\mathcal{M}}$. Then, CFL will perform FL according to Algorithm 1 with $\phi\equiv\mathcal{M}$, where $\varepsilon_{1}$ is the coefficient of FL stopping criteria.

After FL has converged, the FL solution $\theta^{*}_{\mathcal{M}}$ of $\mathcal{M}$ can be obtained. Then, the following clustering criteria is evaluated:

where $\varepsilon_{2}$ is the coefficient of the clustering criteria. If the clustering criteria is satisfied in $\mathcal{M}$, all F-APs are thought to be sufficiently close to their optimal model parameters. CFL terminates and $\theta^{*}_{\mathcal{M}}$ will serve as the solution for every F-AP in $\mathcal{M}$. If not satisfied, F-APs in $\mathcal{M}$ are thought to be incongruent and the pairwise cosine similarity $\alpha$ will be computed in $\mathcal{M}$ by utilizing F-APs’ model weight updates:

Given the pairwise similarity, the cloud server will split up the F-APs in $\mathcal{M}$ into two sub-clusters by minimizing the maximum similarity between F-APs from different sub-clusters:

Then, F-APs will aggregate their model parameters within the newly seperated clusters by averaging their model weight updates. Let $\phi(m)$ denote the cluster containing F-AP $m$. Then, the aggregation operation can be expressed as:

If any F-AP has not converged to its optimal model parameter, CFL will be recursively reapplied in each of the two sub-clusters based on their own updated model parameters $\theta_{\phi_{1}}$ and $\theta_{\phi_{2}}$ seperately. When none of the sub-clusters violates the clustering criteria in (7), all clusters of the congruent F-APs $\Phi$ have been identified, and each F-AP will obtain a more specialized DCNN model with a higher accuracy. The detailed procedure of CFL based model specialization is presented in Algorithm 2.

Corresponding to the content information vector $\bm{\zeta}_{i}\in[0,1]^{d_{I}}$, let $\bm{a}_{u}=[a_{u1},a_{u2},\dots,a_{ud_{I}}]^{T}$ denote the user preference vector of mobile user $k_{u}$, which represents the preference for different content information. The learning process of user preference will be carried out independently by mobile users.

For mobile user $k_{u}$, the set of training samples $\mathcal{B}_{u}=\left\{(\bm{\zeta}_{i},y_{u,i}),i\in\mathcal{I}\right\}$ is extracted from its local request records, where $y_{u,i}$ is the binary request label. $y_{u,i}=1$ if mobile user $k_{u}$ has requested content $i$, otherwise $y_{u,i}=0$. Let $\hat{q}_{u,i}$ denote the probability that mobile user $k_{u}$ has requested content $i$, which can be predicted based on content information and user preference as follows:

Given the predicted $\hat{q}_{u,i}$, the negative log-likelihood of $y_{u,i}$ is formulated as follows:

The “Follow The (Proximally) Regularized Leader”(FTRL-Proximal) algorithm is adopted to obtain the user preference of mobile users by minimizing $\ell(\bm{a}_{u})$ in an offline manner [4], and the user preference will be periodically updated when $\ell(\bm{a}_{u})$ exceeds a certain threshold.

Due to privacy reasons, F-APs cannot access historical request records of mobile users. Without loss of generality, we assume the activity levels of mobile users in an F-AP are the same. Let $\mathcal{K}^{m}\subseteq\mathcal{K}$ denote the set of mobile users currently associated with F-AP $m$. All the currently associated mobile users only need to send the predicted request probability to the F-AP, which also contributes to the saving of bandwidth resource. Then, the predicted mobile popularity of content $i$ in F-AP $m$ can be computed as the average request probability of the currently associated mobile users:

In order to eliminate the differences between local popularity and mobile popularity, local popularity and mobile popularity of all the contents will be normalized respectively in each F-AP as follows: $\hat{P}_{i}^{m}\leftarrow\hat{P}_{i}^{m}/\sum_{j\in\mathcal{I}}\hat{P}_{j}^{m}$ and $\hat{Q}_{i}^{m}\leftarrow\hat{Q}_{i}^{m}/\sum_{j\in\mathcal{I}}\hat{Q}_{j}^{m}$. Then, the predicted popularity $\hat{pop}_{i}^{m}$ of content $i$ in F-AP $m$ can be calculated to be:

where $w_{m}$ is defined as the ratio of the currently associated mobile users to the total users in F-AP $m$ for the purpose of tackling the varying number of mobile users caused by user mobility. By the integration of local and mobile popularities, both user mobility and regional variations of content popularity are properly considered in our proposed content popularity prediction policy.

According to the above descriptions, the proposed popularity prediction policy not only dynamically updates the predicted content popularity by monitoring the request records of local users as well as the user mobility of mobile users, but also significantly reduces communication overhead.