# CoreTemp: Coreset Sampled Templates for Multimodal Mobile Biometrics
## 4 Methods  
### Overview  
Figure 1 depicts the overall pipeline for open-set authentication with CoreTemp: coreset-reduced templates. We follow the legacy of previous works [9; 16] with a notable benchmark for acquiring extracted signals. Specifically, we take the \(x-y\) coordinates, the pressure, and the area information of the point of contact from the touchscreen; the linear speed in \(x\), \(y\), and \(z\) directions from the accelerometer; and the angular speed pivoting around \(x\), \(y\), and \(z\) directions from the gyroscope. Noting that each sensor operates according to its clock cycle, an additional timestamp of sensory reading per sensor is added to compensate for the timely discrepancies.  
Finally, the raw readings are converted to a concatenated touchstroke signal. A sliding window technique with a window size of \(T_{w}\) and an overlap of \(T_{o}\) is utilized to convert the signals to more refined, discrete samples. Thus, assuming the frequency of the sensors as \(f\) and the data from the touchscreen, accelerometer, and gyroscope as \(S_{t}\), \(S_{a}\), and \(S_{g}\), we now derive a discrete user sample \(X=\{S_{t},S_{a},S_{g}\}\in\mathbb{R}^{(|S_{t}|+|S_{a}|+|S_{g}|+3)\cdot(f\cdot T _{w})}\). Note that 3 stands for the auxiliary timestamp information.  
Suppose a pretrained model \(f(\cdot)\) has been pretrained upon a general, favorably large-scale pretraining dataset; we first discuss the enrollment and authentication procedures. In the enrollment phase of OSA, the genuine user's signals forwarded through \(f(\cdot)\) are taken as a template. Here, we observe that employing the entire set of templates will likely be impractical in realistic schemes. Observing that nearest neighbor distance functions as a strong foundation for calculating similarity scores, we propose performing a minimax facility location coreset selection on the raw template (as discussed in Section 3.2), where the resulting CoreTemp is an excerpt of user-representative behavioral signals. Consequently, the distilled CoreTemp is stored in the user's device and compared against claimants' signals.  
During authentication, the input signals from a claimant are likewise processed into discrete samples and forwarded through \(f(\cdot)\). Subsequently, the comparison against CoreTemp utilizing the nearest neighbor yields a similarity score, where the claimant is accepted or rejected according to such a score and a threshold value, following the legacy of OSA.  
Moreover, we present the feasibility of identification with now reduced templates, adopting nearest neighbor distance as the similarity score to identity each, as further described in Section 4.2.  
Similarly, during enrollment and identification, the genuine user's touchstrokes are processed through \(f(\cdot)\), where the coreset-reduced template is tagged with its identity. With  
Figure 1: A pipeline of (**a**) authentication and (**b**) identification with CoreTemp.  
multiple independently coreset-reduced templates registered in the system, a claimant's sample is compared against each coreset, where the identity revealing the closest nearest neighbor distance is chosen as the user.  
Importantly, we do not make any presumptions about the claimant's identity; without the loss of generality, it is supposed to be disjoint from the identities of the pretraining dataset.