  Anomaly detection (AD) has attracted considerable attention in both academia
and industry. Due to the lack of anomalous data in many practical cases, AD is
usually solved by first modeling the normal data pattern and then determining
if data fit this model. Generative models (GMs) seem a natural tool to achieve
this purpose, which learn the normal data distribution and estimate it using a
probability density function (PDF). However, some works have observed the ideal
performance of such GM-based AD methods. In this paper, we propose a new
perspective on the ideal performance of GM-based AD methods. We state that in
these methods, the implicit assumption that connects GMs'results to AD's goal
is usually implausible due to normal data's multi-peaked distribution
characteristic, which is quite common in practical cases. We first
qualitatively formulate this perspective, and then focus on the Gaussian
mixture model (GMM) to intuitively illustrate the perspective, which is a
typical GM and has the natural property to approximate multi-peaked
distributions. Based on the proposed perspective, in order to bypass the
implicit assumption in the GMM-based AD method, we suggest integrating the
Discriminative idea to orient GMM to AD tasks (DiGMM). With DiGMM, we establish
a connection of generative and discriminative models, which are two key
paradigms for AD and are usually treated separately before. This connection
provides a possible direction for future works to jointly consider the two
paradigms and incorporate their complementary characteristics for AD.
