## 3 The Proposed Method
### Multi-Way Local Attentive Learning  
Deep learning models are trained to approximate the underlying probability distribution of sample input-output pairs (or the underlying function) by updating the values of model parameters repeatedly with sample exposure. The model parameters have no explicit bearing on the parameters of empirical path loss models. or their values cannot be explicitly determined. The parameters of empirical models for the path loss in urban scenarios include those associated with rooftop-to-street diffraction and scatter loss, T-R separation, and differences between building height, etc. The 3D LAMS images are proposed to represent these parameters implicitly, such that the 3D CNN model, trained with the multi-way partitioning scheme, can approximate the underlying path loss function. We propose the Multi-way Local Attentive Learning algorithm to enhance the performance of the basic training algorithm for the CNN, by presenting the training data in minibatches sampled according to the inherent organization, such as associated PCIs, distances and relative angles. In conventional training approaches, such as stochastic gradient descent, the entire training data set is partitioned into multiple, possibly overlapping, subsets of samples called a minibatch \(\mathbf{\mathcal{B}}\) to evaluate the estimate of the gradient over the entire training set:  
\[\mathbf{g}=\frac{1}{m^{\prime}}\
abla_{\theta}\sum_{i=1}^{m^{\prime}}L\Big{(}x^{ (i)},y^{(i)},\theta\Big{)} \tag{1}\]  
where \(\mathbf{\mathcal{B}}=\Big{\{}\mathbf{x^{(1)},\ldots,\mathbf{x^{(m^{\prime})}}}\Big{\}}\) is the minibatch of size \(m^{\prime}\) drawn uniformly. We generalize this notion of minibatch, such that the minibatches are not generated by random sampling but, instead, by some data set partitioning scheme based on the values of training data attributes, i.e., \(\mathbf{\mathcal{B}_{p}}=\Big{\{}\mathbf{x_{p}}^{(1)},\ldots,\mathbf{x_{p}}^{(m^{\prime})} \Big{\}}\), \(\mathbf{1}{\leq}p{\leq}P\), where \(P\) represents the number of minibatches generated by a particular partition scheme. If we can have \(L\) partitioning schemes over the entire sample data set, the set of minibatches comprises \(\mathbb{B}_{l}=\{\mathbf{\mathcal{B}_{1}},\mathbf{\mathcal{B}_{2}},\ldots,\mathbf{\mathcal{ B}_{l}}\}\), \(\mathbf{1}\leq I\leq L\). Since each minibatch is made up of sample data set within a range of values with respect to a particular attribute, a CNN is expected to pay higher attention on certain features during the training. The gradient can be approximately estimated using the randomly sampled minibatch and the optimization process based on this estimation is called stochastic gradient descent. Although the stochastic gradient descent ensures unbiased and computationally efficient learning, it cannot exploit the inherent partitions which can help learning by providing additional information specific to each partition. Hence, we propose to take advantage of inherent partitions whenever available instead of using randomly sampled minibatches. One advantage of this approach is that these partitions can be obtained in multiple ways based on a number of attributes of the training data. The number of features learned can increase as the number of partitions increase. This idea can be explained by the human  
Figure 3: The input of FC Network. analogy where students learn not only by different courses (subjects) but also by different grades, even for the same subject. In multi-way local attentive learning, the entire training data set is partitioned into minibatches by the multi-way partitioning schemes, based on different attributes, and model parameters are trained using these minibatches. Several variants of this approach can be implemented, for instance, with respect to the order of minibatches used. Either a single model can be trained on all partitions, or an individual model can be trained on each partitioning scheme and then combined into a single model in the final stage. The proposed method is summarized in Algorithm 2 in detail.