183 research outputs found
Kernel Spectral Clustering and applications
In this chapter we review the main literature related to kernel spectral
clustering (KSC), an approach to clustering cast within a kernel-based
optimization setting. KSC represents a least-squares support vector machine
based formulation of spectral clustering described by a weighted kernel PCA
objective. Just as in the classifier case, the binary clustering model is
expressed by a hyperplane in a high dimensional space induced by a kernel. In
addition, the multi-way clustering can be obtained by combining a set of binary
decision functions via an Error Correcting Output Codes (ECOC) encoding scheme.
Because of its model-based nature, the KSC method encompasses three main steps:
training, validation, testing. In the validation stage model selection is
performed to obtain tuning parameters, like the number of clusters present in
the data. This is a major advantage compared to classical spectral clustering
where the determination of the clustering parameters is unclear and relies on
heuristics. Once a KSC model is trained on a small subset of the entire data,
it is able to generalize well to unseen test points. Beyond the basic
formulation, sparse KSC algorithms based on the Incomplete Cholesky
Decomposition (ICD) and , , Group Lasso regularization are
reviewed. In that respect, we show how it is possible to handle large scale
data. Also, two possible ways to perform hierarchical clustering and a soft
clustering method are presented. Finally, real-world applications such as image
segmentation, power load time-series clustering, document clustering and big
data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms
Selective review of offline change point detection methods
This article presents a selective survey of algorithms for the offline
detection of multiple change points in multivariate time series. A general yet
structuring methodological strategy is adopted to organize this vast body of
work. More precisely, detection algorithms considered in this review are
characterized by three elements: a cost function, a search method and a
constraint on the number of changes. Each of those elements is described,
reviewed and discussed separately. Implementations of the main algorithms
described in this article are provided within a Python package called ruptures
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