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Figure 3
An illustration of the three types of negative examples. (a) xa represents an anchor example and xp is a positive example. Two arcs in dashed lines, both centered at xa, are used to divide the embedding space into three areas. The inner arc has a radius of [\|f(x_{i}^{a})-f(x_{i}^{p})\|_{2}^{2}], whereas the outer arc has a radius that is larger by a margin of α. Negative examples will possess three difficulty levels in model training based on the area where they are situated. It is considered a hard negative example if it is located within the inner arc, where [\|f(x_{i}^{a})-f(x_{i}^{n})\|_{2}^{2}<\|f(x_{i}^{a})-f(x_{i}^{p})\|_{2}^{2}]. On the contrary, it is considered an easy negative example when it goes outside the outer arc, where [\|f(x_{i}^{a})-f(x_{i}^{n})\|_{2}^{2}-\|f(x_{i}^{a})-f(x_{i}^{p})\|_{2}^{2}>\alpha]. Lastly, it becomes a semi-hard negative example when it resides in the area bound between the two arcs. Moreover, the loss function results in [{\cal L} = \alpha] and [{\cal L} = 0] when [x^{n}_{\rm {semi-hard}}] is on the inner arc and outer arc, respectively. Our model training will pull [x^{n}_{\rm {semi-hard}}] close to the outer arc as much as possible, namely minimizing the loss. (b) Illustration of possible semi-hard scenarios when two unique single-particle samples are involved.

IUCrJ
Volume 10| Part 5| September 2023| Pages 568-578
ISSN: 2052-2525
https://doi.org/10.1107/S2052252523006115