# User Mobility Modeling in Crowdsourcing Application to Prevent Inference Attacks
## 4 Proposed Approach
### Preliminaries  
**Definition 1**. : _Mobility Graph is a structured directed graph that represents the historical location data of a user in crowdsourcing application. Formally, our Mobility Graph \(G\) is represented as follows:  
Figure 2: Flow of the proposed approach. \[G=(\mathcal{V},\mathcal{E},\mathcal{M},\mathcal{W},f_{\mathcal{W}},f_{\mathcal{M}})\] _where:_ * \(\mathcal{V}=\{v_{1},v_{2},...,v_{n}\}\) _is a set of vertices. Each vertex_ \(v_{i}\) _represents a significant location defined as a specific location frequently visited by a user and uniquely identified (e.g., IUIIDs, system-specific codes, or addresses)._ * \(\mathcal{E}=\{e_{1},e_{2},...,e_{n}\}\) _is a set of edges, where each edge_ \(e_{i}=(s,t)\) _represents a relation between two locations, with_ \(s\) _(source) and_ \(t\) _(target) being vertices in_ \(\mathcal{V}\)_._ * \(\mathcal{M}\) _is a set of contextual metadata elements designed to enrich the understanding of_ \(\mathcal{V}\) _and_ \(\mathcal{E}\) _in a graph. These elements encapsulate a variety of contextual details related to significant locations and their connections, extending insights beyond simple geographical or categorical data. The diversity and richness of_ \(\mathcal{M}\) _facilitate sophisticated analyses and interpretations, enabling nuanced interactions and informed decisions. Each metadata value_ \(m\) _is represented as a key-value pair as follows:_ \[m=\langle attribute:value\rangle\] _where_ * _attribute (string): The key (attribute) is a string that denotes the name of the metadata component (such as \"name\" or \"address\")._ * _value: The value (value) is the specific information corresponding to the attribute, which can vary in type._ _It is worthy to note that some standard metadata components such as name, address, coordinates, and category play a crucial role in providing a comprehensive and unified understanding of each significant location. They enable efficient data processing, facilitate accurate geolocation, enhance searchability, and support semantic querying across different systems and applications. The following are the standard metadata components along with their descriptions:_ * _Name (string): The significant location official or commonly used name. Examples include \"Eiffel Tower\" and \"Central Park\"._ * _Address (string): The physical location of the significant location, including street address, city, state, and country. An example is \"5 Avenue Anatole France, 75007 Paris, France\"._ * _Coordinates (C): Geographical coordinates that delineate the significant locations boundaries. These can form simple shapes or complex polygons, offering a precise geographical footprint (cf. Definition 2)._ * _Category (string[]): A hierarchical structure describing the category of the significant location (cf. Definition 3)._ * \(\mathcal{W}\) _is a set of numeric values representing weights._ * \(f_{\mathcal{W}}:\mathcal{E}\rightarrow\mathcal{P}(\mathcal{W})\) _is a weighting function that maps each edge_ \(e\) _in the set of edges_ \(\mathcal{E}\) _to the following statistics attribute_ \(S\)_, offering a detailed characterization of the relationship between two significant locations:_ \[S=\langle ts,td,f_{s},st,dt\rangle\] _where_ * _ts (integer): Denotes the time segment during which the movement occurs, offering a time-bound context to the frequency and duration of trips._ * _td (integer): Classifies the movements based on the type of day, such as weekdays, weekends, or holidays, adding a layer of temporal classification to the analysis._ * _fs (integer): Denotes the frequency of visits between_ \(s\) _and_ \(t\) _within a given time frame_ \(ts\)_, highlighting the regularity or irregularity of these movements._ * _st (integer): Represents the duration of the user's stay at location_ \(s\) _before departing to location_ \(t\) _at_ \(ts\) _and_ \(td\)_, respectively.__dt (double): Represents the average duration of travel from_ \(s\) _to_ \(t\)_, providing a temporal measurement of the movement.