## 3 Analysis Methods
### Measuring Migration of Scholars' Research Interests  
Building on the meaningful semantic space and mHealth article labels obtained from the previous steps, we aim to examine how scholars' research interests evolve after they  
Figure 3: Flowchart of the hierarchical topic clustering process.  
completed in the mHTI program. Instead of simply measuring changes in the number of mHealth publications, we leverage the rich information in the semantic space to detect shifts in scholars' research topics. Specifically, we examine whether or not the scholars move toward the regions of the semantic space where mHealth articles are concentrated.  
To achieve this, we first model the probability distribution of mHealth articles in the semantic space using kernel methods. For computational convenience, we perform this estimation directly in the two-dimensional semantic space used for visualization. We use a Gaussian kernel with a bandwidth of 0.8. The kernel density estimate (KDE) at a point \(\mathbf{x}\) in the semantic space is given by  
\[f(\mathbf{x})=\frac{1}{nh^{d}}\sum_{i=1}^{n}K\bigg{(}\frac{\mathbf{x}-\mathbf{ x}_{i}}{h}\bigg{)},\]  
where \(n\) is the number of mHealth articles, \(h=0.8\) is the bandwidth, \(d=2\) is the dimensionality of the semantic space, and \(K(\cdot)\) is the Gaussian kernel function defined as  
\[K(\mathbf{u})=\frac{1}{\sqrt{2\pi}}\exp\biggl{(}-\frac{1}{2}\|\mathbf{u}\|^{2} \biggr{)}.\]  
Next, we represent each scholar's research interests as an average vector of the embeddings of their published articles. For a scholar with \(m\) articles, their average research interest vector \(\bar{\mathbf{v}}\) is computed as  
\[\bar{\mathbf{v}}=\frac{1}{m}\sum_{j=1}^{m}\mathbf{v}_{j},\]  
where \(\mathbf{v}_{j}\) is the embedding vector of the \(j\)-th article. We define the year of participation in the mHTI training as year 0 and calculate the average research interest vector for each scholar over three-year intervals. Specifically, we compute the average interest vector for the three years following training (interval \((0,3]\)).  
Finally, we determine whether the scholars' average research interests shift toward the regions of the semantic space with higher mHealth probability density. For each scholar, we compute the difference vector \(\Delta\mathbf{v}\) between their post-training average vector \(\bar{\mathbf{v}}_{\text{post}}\) and their pretraining average vector \(\bar{\mathbf{v}}_{\text{pre}}\):  
\[\Delta\mathbf{v}=\bar{\mathbf{v}}_{\text{post}}-\bar{\mathbf{v}}_{\text{pre}}.\]  
We then evaluate whether this difference vector results in a movement toward the regions of higher mHealth probability density. Specifically, we calculate the change in probability density between the pretraining average vector \(\bar{\mathbf{v}}_{\text{pre}}\) and the post-training average vector \(\bar{\mathbf{v}}_{\text{post}}\). The change in probability density \(\Delta f\) is given by:  
\[\Delta f=f(\bar{\mathbf{v}}_{\text{post}})-f(\bar{\mathbf{v}}_{\text{pre}}),\]  
where \(f(\mathbf{x})\) is the mHealth probability density function estimated using the kernel method. A positive value of \(\Delta f\) indicates that the scholar's research interests have shifted toward the regions of the semantic space with higher mHealth density. This approach allows us to assess the impact of mHTI on scholars' research trajectories.