Recommender systems have shown great potential to solve the information explosion problem and enhance user experience in various online applications. To tackle data sparsity and cold start problems in recommender systems, researchers propose knowledge graphs (KGs) based recommendations by leveraging valuable external knowledge as auxiliary information. However, most of these works ignore the variety of data types (e.g., texts and images) in multi-modal knowledge graphs (MMKGs). In this paper, we propose Multi-modal Knowledge Graph Attention Network (MKGAT) to better enhance recommender systems by leveraging multi-modal knowledge. Specifically, we propose a multi-modal graph attention technique to conduct information propagation over MMKGs, and then use the resulting aggregated embedding representation for recommendation. To the best of our knowledge, this is the first work that incorporates multi-modal knowledge graph into recommender systems. We conduct extensive experiments on two real datasets from different domains, results of which demonstrate that our model MKGAT can successfully employ MMKGs to improve the quality of recommendation system.

We present complexity of the Galactic outer disc by fitting the stellar volume densities of the red giant branch stars with a two-disc component model. The discs are confirmed to extend to R ∼ 19 kpc. The radial density profile of the discs shows two breaks at R ∼ 11 and ∼ 14 kpc, respectively, which separate the radial profile into three segments with different scale lengths of 2.12 ± 0.26, 1.18 ± 0.08, and 2.72 kpc at R < 11, 11 ≤ R ≤ 14, and R > 14 kpc, respectively. The first break is likely due to the sudden drop in the radial profile of the thin disc, which may be an evidence of the radial migration. Beyond 14 kpc, the thick disc becomes prominent and the transition from thin to thick disc leads to the second break. This implies that the geometrically defined thick disc is more radially extended than the thin disc. This is also supported by the larger scale length of the thick disc than that of the thin disc. Meanwhile, the scale height of the thicker component increases from 0.637 +0.056 −0.036 at R = 8 to 1.284 +0.086 −0.079 kpc at R = 19 kpc, showing an intensive flared disc. Moreover, rich substructures are displayed in the residuals of the stellar density. Among them, the substructures D14 + 2.0 and O14 − 1.5 show a north-south asymmetry, which can be essentially explained by southward shifting of the thick disc. However, no significant overdensity is found for the Monoceros ring. Finally, the thick disc shows a ripple-like feature with unclear origin at 9 < R < 10.5 kpc.

We present a statistical method to derive the stellar density profiles of the Milky Way from spectroscopic survey data, taking into account selection effects. We assume that the selection function of the spectroscopic survey is based on photometric colors and magnitudes and possibly altered during observations and data reductions. Then the underlying selection function for a line-of-sight can be well recovered by comparing the distribution of the spectroscopic stars in a color-magnitude plane with that of the photometric dataset. Subsequently, the stellar density profile along a line-of-sight can be derived from the spectroscopically measured stellar density profile multiplied by the selection function. The method is validated using Galaxia mock data with two different selection functions. We demonstrate that the derived stellar density profiles well reconstruct the true ones not only for the full targets, but also for the sub-populations selected from the full dataset. Finally, the method is applied to map the density profiles for the Galactic disk and halo, respectively, using the LAMOST RGB stars. The Galactic disk extends to about R = 19 kpc, where the disk still contributes about 10% to the total stellar surface density. Beyond this radius, the disk smoothly transitions to the halo without any truncation, bending, or broken. Moreover, no over-density corresponding to the Monoceros ring is found in the Galactic anti-center direction. The disk shows moderate north-south asymmetry at radii larger than 12 kpc. On the other hand, the R-Z tomographic map directly shows that the stellar halo is substantially oblate within a Galactocentric radius of 20 kpc and gradually becomes nearly spherical beyond 30 kpc.