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M. Andrecut
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We combine K-means clustering with the least-squares kernel classification method. K-means clustering is used to extract a set of representative vectors for each class. The least-squares kernel method uses these representative vectors as a training set for the classification task. We show that this combination of unsupervised and supervised learning algorithms performs very well, and we illustrate this approach using the MNIST dataset
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As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and consequently, kernel mean matching (KMM) has become an important method for knowledge discovery and novelty detection in kernel machines. Furthermore, the existing KMM methods have focused on concrete learning frameworks. In this work, a novel approach to adaptive matching of kernel means is proposed, and selected data with high importance are adopted to achieve calculation efficiency with optimization. In addition, scalable learning can be conducted in proposed method as a generalized solution to matching of appended data. The experimental results on a wide variety of real-world data sets demonstrate the proposed method is able to give outstanding performance compared with several state-of-the-art methods, while calculation efficiency can be preserved.
$k$-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, $k$-means algorithm suffers from relatively poor performance on the dataset containing heavy-tailed data or outliers. Besides, standard $k$-means algorithm also has relatively weak stability, $i.e.$ its results have a large variance, which reduces its credibility. In this paper, we propose a robust and stable $k$-means variant, dubbed the $t$-$k$-means, as well as its fast version to alleviate those problems. Theoretically, we derive the $t$-$k$-means and analyze its robustness and stability from the aspect of the loss function and the expression of the clustering center, respectively. Extensive experiments are also conducted, which verify the effectiveness and efficiency of the proposed method. The code for reproducing main results is available at url{https://github.com/THUYimingLi/t-k-means}.
We present a simple heuristic algorithm for efficiently optimizing the notoriously hard minimum sum-of-squares clustering problem, usually addressed by the classical k-means heuristic and its variants. The algorithm, called recombinator-k-means, is very similar to a genetic algorithmic scheme: it uses populations of configurations, that are optimized independently in parallel and then recombined in a next-iteration population batch by exploiting a variant of the k-means++ seeding algorithm. An additional reweighting mechanism ensures that the population eventually coalesces into a single solution. Extensive tests measuring optimization objective vs computational time on synthetic and real-word data show that it is the only choice, among state-of-the-art alternatives (simple restarts, random swap, genetic algorithm with pairwise-nearest-neighbor crossover), that consistently produces good results at all time scales, outperforming competitors on large and complicated datasets. The only parameter that requires tuning is the population size. The scheme is rather general (it could be applied even to k-medians or k-medoids, for example). Our implementation is publicly available at https://github.com/carlobaldassi/RecombinatorKMeans.jl.
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of producing block-diagonal biclusters. We provide a new formulation of the biclustering problem based on the idea of minimizing the empirical clustering risk. We develop and prove a consistency result with respect to the empirical clustering risk. Since the optimization problem is combinatorial in nature, finding the global minimum is computationally intractable. In light of this fact, we propose a simple and novel algorithm that finds a local minimum by alternating the use of an adapted version of the k-means clustering algorithm between columns and rows. We evaluate and compare the performance of our algorithm to other related biclustering methods on both simulated data and real-world gene expression data sets. The results demonstrate that our algorithm is able to detect meaningful structures in the data and outperform other competing biclustering methods in various settings and situations.
This article briefly introduced Arthur and Vassilvitshiis work on textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in the textbf{k-means++} algorithm.
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