Many methods based on sparse and low-rank representation been developed along
with guarantees of correct outlier detection. Self-representation states that a
point in a subspace can always be expressed as a linear combination of other
points in the subspace. A suitable Markov Chain can be defined on the
self-representation and it allows us to recognize the difference between
inliers and outliers. However, the reconstruction error of self-representation
that is still informative to detect outlier detection, is neglected.Inspired by
the gradient boosting, in this paper, we propose a new outlier detection
framework that combines a series of weak "outlier detectors" into a single
strong one in an iterative fashion by constructing multi-pass
self-representation. At each stage, we construct a self-representation based on
elastic-net and define a suitable Markov Chain on it to detect outliers. The
residual of the self-representation is used for the next stage to learn the
next weaker outlier detector. Such a stage will repeat many times. And the
final decision of outliers is generated by the previous all results.
Experimental results on image and speaker datasets demonstrate its superiority
with respect to state-of-the-art sparse and low-rank outlier detection methods.

本文提出了一种新的异常检测框架，使用多次自表示构建弱异常检测器，利用弹性网络和马尔可夫链在每个阶段构建自表示，实现梯度提升，将多个弱检测器结合成一个强检测器，可应用于图像和讲者数据库中的异常检测问题，并取得了优异的实验效果。

级联子空间聚类用于异常检测

Cascade Subspace Clustering for Outlier Detection

To make accurate inferences in an interactive setting, an agent must not
confuse passive observation of events with having intervened to cause those
events. The do operator formalises interventions so that we may reason about
their effect. Yet there exist pareto optimal mathematical formalisms of general
intelligence in an interactive setting which, presupposing no explicit
representation of intervention, make maximally accurate inferences. We examine
one such formalism. We show that in the absence of an operator, an intervention
can still be represented by a variable. Furthermore, the need to explicitly
represent interventions in advance arises only because we presuppose
abstractions. The aforementioned formalism avoids this and so, initial
conditions permitting, representations of relevant causal interventions will
emerge through induction. These emergent abstractions function as
representations of one`s self and of any other object, inasmuch as the
interventions of those objects impact the satisfaction of goals. We argue (with
reference to theory of mind) that this explains how one might reason about
one's own identity and intent, those of others, of one`s own as perceived by
others and so on. In a narrow sense this describes what it is to be aware, and
is a mechanistic explanation of aspects of consciousness.

该研究探讨了在交互环境下，如何从正确的干预行为进行推理，并证明了在没有操作符的情况下，一个干预仍然可以被表示为变量，进而提出了一种去除预设抽象的形式化方法，透过归纳左右的抽象层次逐渐增加，直到能够代表自我和他人的干预效应，从而实现对意图与自我认知的推理。这种方法也被认为是对意识产生影响的机械解释。