Kepler Missions single-band photometry suffers from astrophysical false positives, the most common of background eclipsing binaries (BEBs) and companion transiting planets (CTPs). Multi-color photometry can reveal the color-dependent depth feature of
false positives and thus exclude them. In this work, we aim to estimate the fraction of false positives that are unable to be classified by Kepler alone but can be identified with their color-dependent depth feature if a reference band (z, Ks and TESS) were adopted in follow-up observation. We build up physics-based blend models to simulate multi-band signals of false positives. Nearly 65-95% of the BEBs and more than 80% of the CTPs that host a Jupiter-size planet will show detectable depth variations if the reference band can achieve a Kepler-like precision. Ks band is most effective in eliminating BEBs exhibiting any depth sizes, while z and TESS band prefer to identify giant candidates and their identification rates are more sensitive to photometric precision. Provided the radius distribution of planets transiting the secondary star in binary systems, we derive formalism to calculate the overall identification rate for CTPs. By comparing the likelihood distribution of the double-band depth ratio for BEB and planet models, we calculate the false positive probability (FPP) for typical Kepler candidates. Additionally, we show that the FPP calculation helps distinguish the planet candidates host star in an unresolved binary system. The analysis framework of this paper can be easily adapted to predict the multi-color photometry yield for other transit surveys, especially for TESS.
The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of synthesized data, an
d the identified subspaces tend to control image attributes globally (i.e., manipulating an attribute causes the change of an entire image). By contrast, this work introduces low-rank subspaces that enable more precise control of GAN generation. Concretely, given an arbitrary image and a region of interest (e.g., eyes of face images), we manage to relate the latent space to the image region with the Jacobian matrix and then use low-rank factorization to discover steerable latent subspaces. There are three distinguishable strengths of our approach that can be aptly called LowRankGAN. First, compared to analytic algorithms in prior work, our low-rank factorization of Jacobians is able to find the low-dimensional representation of attribute manifold, making image editing more precise and controllable. Second, low-rank factorization naturally yields a null space of attributes such that moving the latent code within it only affects the outer region of interest. Therefore, local image editing can be simply achieved by projecting an attribute vector into the null space without relying on a spatial mask as existing methods do. Third, our method can robustly work with a local region from one image for analysis yet well generalize to other images, making it much easy to use in practice. Extensive experiments on state-of-the-art GAN models (including StyleGAN2 and BigGAN) trained on various datasets demonstrate the effectiveness of our LowRankGAN.
