## 5 Expertise Retrieval
### Measuring Similarity Between Mobile Apps' Descriptions
#### 5.1.2 App Description Similarity Setup
\begin{table}
\begin{tabular}{c p{284.5 pt}} \hline \hline
**Query** & \multicolumn{2}{c}{**Used Descriptions**} \\ \hline \multirow{4}{*}{\(q_{1}\)} & Fitness application that’s used to keep track of your physical fitness data, daily calorie count, invite friends to work out together and ultimately get healthy. Features involve: Measures daily fitness, Graphical Statistics, Record Daily Food Activity, Invite Friends by sharing location [81]. \\ \hline \multirow{4}{*}{\(q_{2}\)} & Crosswords is an application that lets you enjoy crossword puzzles from a number of online sources. It can also load puzzles in the popular Across Lie puzzle format. It checks your answers, provides hints, or shows the solution when you get stuck. Saves your progress. Adaptive layout adjusts to screen size, Panable and zoomable grid helps you see puzzle on small screens [82]. \\ \hline \multirow{4}{*}{\(q_{3}\)} & Matematica vera is a mobile app, that helps children get familiar with the basics of mathematics. It features a list of games where the user is presented with a number of mathematical tasks like addition, subtraction, multiplication or division. For each of them, several answers are shown. By selecting the correct answer user goes to the next task, selecting the incorrect one increases errors count and shuffles possible answers. Additionally, the app features a game creator where user can define their games [83]. \\ \hline \multirow{4}{*}{\(q_{4}\)} & OpenCryptofolio is a cryptocurrency portfolio manager capable of handling multiple portfolios, showing chart data on portfolio performance and live value in BTC and major fats, exporting/importing portfolio data, as well as displaying all major cryptocurrencies live trading data and historical performance chart [84]. \\ \hline \multirow{4}{*}{\(q_{5}\)} & CodeEdit is a code editor built by the community, for the community, written entirely and unapologetically for macOS. Features include syntax highlighting, code completion, project find and replace, snippets, terminal, task running, debugging, git integration, code review, extensions, and more [85]. \\ \hline \multirow{4}{*}{\(q_{6}\)} & It is an image editing app with simple, easy support for image manipulation. Features include: adding images, adding stickers, adding text with option to change its color, drawing on image with option to change its color, its size and erasing, scaling and rotating views, deleting views, saving photo after editing, undo after adding views, transforms by flipping, rotating and resizing [86]. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected open-source application descriptions from GitHub. category = Education description = a description about a mathematics educational app for kids \(q_{4}:\) role = users and developers category = Finance description = a description about cryptocurrency portfolio manager app \(q_{5}:\) role = users and developers category = Developer Tools description = a description about a code editor app \(q_{6}:\) role = developers category = All description = a description about an image-editing app The similarity between the embeddings that are generated using pre-trained SBERT and Doc2 Vec models for the app descriptions is calculated using cosine similarity which is a commonly used similarity measure [87]. Given two embedding vectors \(x\) and \(y\) with dimension \(m\), the formula for cosine similarity is as follows:  
\[Cosine(x,y)=\frac{\sum_{i=1}^{m}x_{i}*y_{i}}{\sqrt{\sum_{i=1}^{m}x_{i}^{2}}\sqrt {\sum_{i=1}^{m}y_{i}^{2}}}\]  
Cosine similarity values range from \(-1\) to \(1\). When the vectors \(x\) and \(y\) have the same orientation, it means the angle in between them is equal to \(0\) and the cosine similarity \(cos\) (\(\theta\)) = 1. Having a cosine similarity equal to \(1\) indicates that the two vectors are similar or even identical. When the two vectors \(x\) and \(y\) are orthogonal this means the angle is \(90^{\circ}\) and that the cosine similarity \(cos\) (\(\theta\)) = 0 which means that the vectors are unrelated.