  Vertical federated learning (VFL) is a promising category of federated
learning for the scenario where data is vertically partitioned and distributed
among parties. VFL enriches the description of samples using features from
different parties to improve model capacity. Compared with horizontal federated
learning, in most cases, VFL is applied in the commercial cooperation scenario
of companies. Therefore, VFL contains tremendous business values. In the past
few years, VFL has attracted more and more attention in both academia and
industry. In this paper, we systematically investigate the current work of VFL
from a layered perspective. From the hardware layer to the vertical federated
system layer, researchers contribute to various aspects of VFL. Moreover, the
application of VFL has covered a wide range of areas, e.g., finance,
healthcare, etc. At each layer, we categorize the existing work and explore the
challenges for the convenience of further research and development of VFL.
Especially, we design a novel MOSP tree taxonomy to analyze the core component
of VFL, i.e., secure vertical federated machine learning algorithm. Our
taxonomy considers four dimensions, i.e., machine learning model (M),
protection object (O), security model (S), and privacy-preserving protocol (P),
and provides a comprehensive investigation.
