Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the individuality and commonality of multi-view data can be leveraged to generate high-quality and diverse clusterings. To this end, we propose a novel multi-view multiple clustering (MVMC) algorithm. MVMC first adapts multi-view self-representation learning to explore the individuality encoding matrices and the shared commonality matrix of multi-view data. It additionally reduces the redundancy (i.e., enhancing the individuality) among the matrices using the Hilbert-Schmidt Independence Criterion (HSIC), and collects shared information by forcing the shared matrix to be smooth across all views. It then uses matrix factorization on the individual matrices, along with the shared matrix, to generate diverse clusterings of high-quality. We further extend multiple co-clustering on multi-view data and propose a solution called multi-view multiple co-clustering (MVMCC). Our empirical study shows that MVMC (MVMCC) can exploit multi-view data to generate multiple high-quality and diverse clusterings (co-clusterings), with superior performance to the state-of-the-art methods.

If you want to determine the optimal number of clusters in your analysis, you're faced with an overwhelming number of (mostly subjective) choices. Note that there's no "best" method, no "correct" k, and there isn't even a consensus as to the definition of what a "cluster" is. With that said, this picture focuses on three popular methods that should fit almost every need: Silhouette, Elbow, and Gap Statistic.

Tree-based machine learning models such as random forests, decision trees, and gradient boosted trees are the most popular non-linear predictive models used in practice today, yet comparatively little attention has been paid to explaining their predictions. Here we significantly improve the interpretability of tree-based models through three main contributions: 1) The first polynomial time algorithm to compute optimal explanations based on game theory. 2) A new type of explanation that directly measures local feature interaction effects. 3) A new set of tools for understanding global model structure based on combining many local explanations of each prediction. We apply these tools to three medical machine learning problems and show how combining many high-quality local explanations allows us to represent global structure while retaining local faithfulness to the original model. These tools enable us to i) identify high magnitude but low frequency non-linear mortality risk factors in the general US population, ii) highlight distinct population sub-groups with shared risk characteristics, iii) identify non-linear interaction effects among risk factors for chronic kidney disease, and iv) monitor a machine learning model deployed in a hospital by identifying which features are degrading the model's performance over time. Given the popularity of tree-based machine learning models, these improvements to their interpretability have implications across a broad set of domains.

Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it's still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we consider diverse clusterings embedded in different subspaces, and analyze the embedding subspaces to shed light into the structure of each clustering. To this end, we provide a two-stage approach called MISC (Multiple Independent Subspace Clusterings). In the first stage, MISC uses independent subspace analysis to seek multiple and statistical independent (i.e. non-redundant) subspaces, and determines the number of subspaces via the minimum description length principle. In the second stage, to account for the intrinsic geometric structure of samples embedded in each subspace, MISC performs graph regularized semi-nonnegative matrix factorization to explore clusters. It additionally integrates the kernel trick into matrix factorization to handle non-linearly separable clusters. Experimental results on synthetic datasets show that MISC can find different interesting clusterings from the sought independent subspaces, and it also outperforms other related and competitive approaches on real-world datasets.

The data points in machine learning are often real human beings. There is legitimate concern that traditional machine learning algorithms that are blind to this fact may inadvertently exacerbate problems of bias and injustice in society [25]. Motivated by concerns ranging from the granting of bail in the legal system to the quality of recommender systems, researchers have devoted considerable effort to developing fair algorithms for the canonical supervised learning tasks of classification and regression [13, 28, 20, 27, 34, 11, 30, 35, 26, 18, 21]. We extend this work to a canonical problem in unsupervised learning: centroid clustering. In centroid clustering, we want to partition data into k clusters by choosing k "centers" and then matching points to one of the centers.

Abstract--In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. In [12] a novel RBF network with the multi-kernel is proposed to obtain an optimized and I. INTRODUCTION The unknown centres of the multikernels The RBF neural networks have shown excellent performance are determined by an improved k-means clustering in a number of problems of practical interest. An orthogonal least squares (OLS) algorithm is reservoirs of brine are analyzed for physicochemical properties used to determine the remaining parameters. The convergence of the ACA is analyzed by the [3] the RBF kernel is used to predict the pressure gradient Lyapunov criterion. In the context of nuclear physics, RBF Cognitive Radial Basis Function network (McRBFN) and its has been effectively used to model the stopping power data Projection based Learning (PBL) referred to as PBL-McRBFN of materials as in [4].

Clustering aims to separate observed data into different categories. The performance of popular clustering models relies on the sample-to-sample similarity. However, the pairwise similarity is prone to be corrupted by noise or outliers and thus deteriorates the subsequent clustering. A high-order relationship among samples-to-samples may elaborate the local manifold of the data and thus provide complementary information to guide the clustering. However, few studies have investigated the connection between high-order similarity and usual pairwise similarity. To fill this gap, we first define a high-order tensor similarity to exploit the samples-to-samples affinity relationship. We then establish the connection between tensor similarity and pairwise similarity, proving that the decomposable tensor similarity is the Kronecker product of the usual pairwise similarity and the non-decomposable tensor similarity is generalized to provide complementary information, which pairwise similarity fails to regard. Finally, the high-order tensor similarity and pairwise similarity (IPS2) were integrated collaboratively to enhance clustering performance by enjoying their merits. The proposed IPS2 is shown to perform superior or competitive to state-of-the-art methods on synthetic and real-world datasets. Extensive experiments demonstrated that tensor similarity is capable to boost the performance of the classical clustering method.

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would take additional analysis effort such as identifying clusters and understanding their characteristics. While there are many automatic methods (e.g., density-based clustering methods) to identify clusters, effective methods for understanding a cluster's characteristics are still lacking. A cluster can be mostly characterized by its distribution of feature values. Reviewing the original feature values is not a straightforward task when the number of features is large. To address this challenge, we present a visual analytics method that effectively highlights the essential features of a cluster in a DR result. To extract the essential features, we introduce an enhanced usage of contrastive principal component analysis (cPCA). Our method can calculate each feature's relative contribution to the contrast between one cluster and other clusters. With our cPCA-based method, we have created an interactive system including a scalable visualization of clusters' feature contributions. We demonstrate the effectiveness of our method and system with case studies using several publicly available datasets.

Finite mixture model is an important branch of clustering methods and can be applied on data sets with mixed types of variables. However, challenges exist in its applications. First, it typically relies on the EM algorithm which could be sensitive to the choice of initial values. Second, biomarkers subject to limits of detection (LOD) are common to encounter in clinical data, which brings censored variables into finite mixture model. Additionally, researchers are recently getting more interest in variable importance due to the increasing number of variables that become available for clustering. To address these challenges, we propose a Bayesian finite mixture model to simultaneously conduct variable selection, account for biomarker LOD and obtain clustering results. We took a Bayesian approach to obtain parameter estimates and the cluster membership to bypass the limitation of the EM algorithm. To account for LOD, we added one more step in Gibbs sampling to iteratively fill in biomarker values below or above LODs. In addition, we put a spike-and-slab type of prior on each variable to obtain variable importance. Simulations across various scenarios were conducted to examine the performance of this method. Real data application on electronic health records was also conducted.

"Feint Attack", as a new type of APT attack, has become the focus of attention. It adopts a multi-stage attacks mode which can be concluded as a combination of virtual attacks and real attacks. Under the cover of virtual attacks, real attacks can achieve the real purpose of the attacker, as a result, it often caused huge losses inadvertently. However, to our knowledge, all previous works use common methods such as Causal-Correlation or Cased-based to detect outdated multi-stage attacks. Few attentions have been paid to detect the "Feint Attack", because the difficulty of detection lies in the diversification of the concept of "Feint Attack" and the lack of professional datasets, many detection methods ignore the semantic relationship in the attack. Aiming at the existing challenge, this paper explores a new method to solve the problem. In the attack scenario, the fuzzy clustering method based on attribute similarity is used to mine multi-stage attack chains. Then we use a few-shot deep learning algorithm (SMOTE&CNN-SVM) and bidirectional Recurrent Neural Network model (Bi-RNN) to obtain the "Feint Attack" chains. "Feint Attack" is simulated by the real attack inserted in the normal causal attack chain, and the addition of the real attack destroys the causal relationship of the original attack chain. So we used Bi-RNN coding to obtain the hidden feature of "Feint Attack" chain. In the end, our method achieved the goal to detect the "Feint Attack" accurately by using the LLDoS1.0 and LLDoS2.0 of DARPA2000 and CICIDS2017 of Canadian Institute for Cybersecurity.