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Joint clustering and dimensionality reduction methods are a promising solution to clustering due to its scalability to high-dimensional data. Some methods leverage trace ratio criterion and attain clusters by borrowing the K-means algorithm. However, trace ratio criterion has no close-formed solution for the discriminative projection matrix and the K-means algorithm has a limited capacity to handle the many-cluster problem. In this paper, Coordinate Descent Optimized Trace Difference model (CDOTD) is proposed for joint clustering and feature extraction. Formulating the objective function as a direct trace difference criterion containing a balance parameter, CDOTD harmonizes between-cluster scatter maximization and within-cluster scatter minimization by the balance parameter. Using the direct trace difference criterion, CDOTD can straightforward solve for the discriminative projection matrix and avoid obtaining a poor discriminative projection matrix in the iterative manner when a bad cluster start is given. CDOTD uses the coordinate descent method for clustering optimization, improving the ability to address the many-cluster problem. Extensive experiments show that CDOTD has achieved significant performance improvements compared to previous trace ratio criterion related joint clustering and feature extraction methods, and also outperformed other clustering methods in most cases. • A joint clustering and feature extraction model named CDOTD is proposed. • It ensures both favorable clustering performance and high running efficiency. • It improves the ability to address many cluster data clustering cases. • Extensive experiments have demonstrated the success of CDCTD. [ABSTRACT FROM AUTHOR]

• We present the first dissimilarity-based random forest-clustering approach. • The approach works only with distances, thus appropriate for non-vectorial objects. • The approach works also with non-metric dissimilarities. • We present a novel unsupervised RF variant working only with dissimilarities. In this paper we present a novel Random Forest Clustering approach, called Dissimilarity Random Forest Clustering (DisRFC) , which requires in input only pairwise dissimilarities. Thanks to this characteristic, the proposed approach is appliable to all those problems which involve non-vectorial representations, such as strings, sequences, graphs or 3D structures. In the proposed approach, we first train an Unsupervised Dissimilarity Random Forest (UD-RF), a novel variant of Random Forest which is completely unsupervised and based on dissimilarities. Then, we exploit the trained UD-RF to project the patterns to be clustered in a binary vectorial space, where the clustering is finally derived using fast and effective K-means procedures. In the paper we introduce different variants of DisRFC, which are thoroughly and positively evaluated on 12 different problems, also in comparison with alternative state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

• We propose a three-stage clustering framework based on the pre-computed k nearest neighbors matrix. • A CD metric is developed in this paper to quantify the possibility of each data point as a boundary point. • The BS strategy completes the allocation of labels by shrinking the boundary points inwards. Locating the centers before assigning clustering labels is a traditional routine of clustering methods, which also limits the development of new clustering ideas. In this paper, we achieve the clustering task by firstly identifying the boundary points in the feature space, and then we shrink the boundary points to allocate the un-clustered points. Concretely, we propose a Centroid Drift (CD) metric and a Boundary Shrinkage (BS) strategy to detect boundary points in the feature space and allocate labels for un-clustered points, respectively. Both the CD and BS are closely related to the pre-computed k-nearest neighbor matrix, contributing to the decrease of algorithm parameters. Moreover, the common problems of noise points and non-uniform density distribution of data points in clustering task can also be alleviated with our proposed large value suppression and normalization of k-nearest neighbor distance techniques. The experiments on synthetic datasets, real-world face image datasets and hyperspectral images demonstrate the superiorities of our proposed clustering framework. [ABSTRACT FROM AUTHOR]

• Review of the most commonly used distance measures in machine learning • Analysis of their main properties, applications and key aspects to consider • The similarity analysis shows a high degree of correlation between all the measures • Evaluation of classification and clustering performance, noise tolerance and runtime • Canberra distance shows the best overall performance and the highest tolerance to noise Many machine learning and data mining tasks are based on distance measures, so a large amount of literature addresses this aspect somehow. Due to the broad scope of the topic, this paper aims to provide an overview of the use of these measures in the most common machine learning problems, pointing out those aspects to consider to choose the most appropriate measure for a particular task. For this purpose, the most recent works addressing the subject were reviewed and seven of the most commonly used measures were analyzed, investigating in detail their main properties and applications. Different experiments were carried out to study their relationships and compare their performance. The degradation of the results in the presence of noise was also considered, as well as the execution time required by each measure. [ABSTRACT FROM AUTHOR]

• In this paper, an object-based clustering validity index with densities referred to as OCVD is proposed. This index uses densities of clusters to capture the exclusive contribution of each data object in both separation and compactness of clusters. • OCVD is superior to many existing clustering validity indices that capture the properties of clusters by using representative statistics such as mean, variance, diameter, etc. The reason is that those indices might not perform well in capturing the whole characteristics of clusters with arbitrary shapes but OCVD is well capable of doing so. • Although there are some existing density-based validity indices, studies show that they have problems such as poor performance on clusters with arbitrary shapes which are not necessarily perfectly separated and poor performance due to relying only on some representative data objects in clusters. Clustering validity indices are typically used as tools to find the correct number of clusters in a data set and/or to evaluate the quality of the clusters formed by clustering algorithms. Clustering validity indices measure separation and compactness of clusters. Typically, when applying a clustering algorithm, the input includes the number of clusters. After applying the algorithm with several different numbers of clusters, we determine the number of clusters to be the one with the best validity index. There are two types of clustering validity indices: external indices that are supervised, and internal indices that are unsupervised. The focus of this paper is on internal validity indices. Some existing internal validity indices capture the properties of the clusters by using representative statistics such as mean, variance, diameter, etc., however, these do not perform well when clusters have arbitrary shapes. One approach to overcome this issue is to use the density of the data objects in each cluster. That provides the advantage of capturing the full characteristics of the cluster which is most beneficial when there are clusters with arbitrary shapes. In the literature, a few density-based clustering validity indices have been proposed. However, some of them show poor performance when the clusters are not perfectly separated. Some others perform poorly because they use only representative objects from each cluster instead of all objects. The contribution of this paper is an internal validity index named the object-based clustering validity index with densities (OCVD). OCVD is a single number that averages the density-based contribution of individual data objects to both separation and compactness of clusters. The methodology behind calculating the density-based contributions of the objects is kernel density estimation. We show through several experiments that OCVD performs well in detecting the correct number of clusters in data sets with different cluster shapes including arbitrary shapes. [ABSTRACT FROM AUTHOR]

• Possibilistic c-means (PCM) clustering by incorporating the sparsity idea with feature weights is further studied. • We propose two approaches that make the PCM clustering with the least absolute shrinkage and selection operator (Lasso), called S-PCM1 and S-PCM2. • Synthetic and real data sets are used to compare the proposed S-PCM1 and S-PCM2 with some existing algorithms. • Experimental results and comparisons demonstrate the good effectiveness and usefulness of the proposed S-PCM1 and S-PCM2 algorithms. Krishnapuram and Keller first proposed possibilistic c-means (PCM) clustering in 1993. Afterward, PCM was widely studied with various extensions. The PCM algorithm and its extensions always treat feature components under equal importance, but, in real applications, different features may better have different weights. Recently, Yang and Benjamin in 2021 proposed a feature-weighted PCM clustering with feature reduction. Although Yang and Benjamin (2021) can reduce feature dimensions, it still encounters the curse of dimensionality for high dimensional data. One possible way to address this problem is to conduct a sparse clustering technique. In this paper, we further study the PCM clustering by incorporating the idea of sparsity with different feature weights. We propose two approaches that use the PCM clustering with the least absolute shrinkage and selection operator (Lasso). The first one is the sparse PCM subject to a Lasso constraint of feature weights, called S-PCM1. The second is the sparse PCM by adding a Lasso penalty term of feature weights in the objective function, called S-PCM2. We show that S-PCM1 and S-PCM2 are theoretically the same, and both can induce sparsity in features, but they use different procedures in algorithms. Synthetic and real data sets are used to compare S-PCM1 and S-PCM2 with some existing sparsity clustering algorithms. Experimental results and comparisons demonstrate the effectiveness and usefulness of the proposed S-PCM1 and S-PCM2 clustering algorithms. [ABSTRACT FROM AUTHOR]

• Propose a new data-dependent similarity measure based on probability mass called MP-Similarity which is invariant to data representations (units/scales used to measure/express data features). • Apply MP-Similarity in the Density Peak Clustering (DPC) algorithm to overcome its two main issues: (i) inability to detect clusters with varying densities; and (ii) sensitive to the units/scales used to measure/express data. • Demonstrate the effectiveness and robustness of the proposed MP-Similarity in DPC by comparing its performance against widely used existing data-independent (distance-based and data-dependent measures in a wide range of datasets with diverse characteristics. Density Peak Clustering (DPC) is a popular state-of-the-art clustering algorithm, which requires pairwise (dis)similarity of data objects to detect arbitrary shaped clusters. While it is shown to perform well for many applications, DPC remains: (i) not robust for datasets with clusters having different densities, and (ii) sensitive to the change in the units/scales used to represent data. These drawbacks are mainly due to the use of the data-independent similarity measure based on the Euclidean distance. In this paper, we address these issues by proposing an effective data-dependent similarity measure based on Probability Mass , which we call MP-Similarity , and by incorporating it in DPC to create MP-DPC, a data-dependent variant of DPC. We evaluate and compare MP-DPC against diverse baselines using several clustering metrics and datasets. Our experiments demonstrate that: (a) MP-DPC produces better clustering results than DPC using the Euclidean distance and existing data-dependent similarity measures; (b) MP-Similarity coupled with Shared-Nearest-Neighbor-based density metric in DPC further enhances the quality of clustering results; and (c) unlike DPC with existing data-independent and data-dependent similarity measures, MP-DPC is robust to the change in the units/scales used to represent data. Our findings suggest that MP-Similarity provides a more viable solution for DPC in datasets with unknown distribution or units/scales of features, which is often the case in many real-world applications. [ABSTRACT FROM AUTHOR]

• A novel hypergraph based semi-supervised SNMF method is proposed for image clustering. • A new hypergraph based pairwise constraints propagation algorithm is presented. • The proposed method is analysed in terms of convergence, supervisory information, and computational complexity. • Extensive experiments confirm the effectiveness of the proposed method in clustering applications. Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been shown to be a significant method for both linear and nonlinear data clustering applications. Nevertheless, existing SNMF-based methods only adopt a simple graph to construct the similarity matrix, and cannot fully use the limited supervised information for the construction of the similarity matrix. To overcome the drawbacks of previous SNMF-based methods, a new semi-supervised SNMF-based method called hypergraph based semi-supervised SNMF (HSSNMF), is proposed in this paper for image clustering. Specifically, HSSNMF adopts a predefined hypergraph to build a similarity matrix for capturing the high-order relationships of samples. By exploiting a new hypergraph based pairwise constraints propagation (HPCP) algorithm, HSSNMF propagates the pairwise constraints of the limited data points to the entire data points, which can make full use of the limited supervised information and construct a more informative similarity matrix. Using the multiplicative updating algorithm, a discriminative assignment matrix can then be obtained by solving the optimization problem of HSSNMF. Moreover, analyses of the convergence, supervisory information, and computational complexity of HSSNMF are presented. Finally, extensive clustering experiments have been conducted on six real-world image datasets, and the experimental results have demonstrated the superiority of HSSNMF while compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Kernelized concept factorization (KCF) has shown its advantage on handling data with nonlinear structures; however, the kernels involved in the existing KCF-based methods are empirically predefined, which may compromise the performance. In this paper, we propose semi-supervised adaptive kernel concept factorization (SAKCF), which integrates the data representation and kernel learning into a unified model to make the two learning processes adapt to each other. SAKCF extends traditional KCF in a semi-supervised manner, which encourages the high-dimensional representation to be consistent with both the limited supervisory and local geometric information. Besides, an alternating iterative algorithm is proposed to solve the resulting constrained optimization problem. Experimental results on six real-world data sets verify the effectiveness and advantages of our SAKCF over state-of-the-art methods when applied on the clustering task. [ABSTRACT FROM AUTHOR]

• We discuss the problems of existing clustering algorithms in dealing with real-world data. • We present a method to determine the involved parameter adaptively in our algorithm. • By improving the density peak algorithm, our approach works well with data of Gaussian distribution and avoids cluster merging. • In experiments on real-world data, our algorithm without parameter dependence generates comparable results to those with parameter tuning. While many clustering algorithms have been published, existing algorithms are often afflicted by some problems in processing real-world data. We present an algorithm to deal with two of these problems in this paper. First, the majority of clustering algorithms depend on one or more parameters. Second, some algorithms are not suitable for clusters of Gaussian distribution, whereas clusters of many real datasets are of Gaussian distribution approximately. Our algorithm generates clusters sequentially, and each cluster is obtained by expanding an initial cluster. The initial cluster is extracted with the dominant set algorithm, and we study the correlation between the pairwise data similarity matrix and clustering result to determine the involved scaling parameter adaptively. In expanding the initial cluster, we improve the density peak algorithm so that the expansion will not cross the boundary between two clusters, and the involved density parameter has little influence on clustering results. In our algorithm, the cluster expansion enables our algorithm to work well with clusters of Gaussian distribution, and two involved parameters can be fixed or determined adaptively. Our algorithm goes a step forward in parameter-free clustering for real-world data, and it is shown to perform better than or comparably to some commonly used algorithms with parameters in experiments with synthetic datasets composed of Gaussian clusters and real datasets. [ABSTRACT FROM AUTHOR]

• A novel density peaks clustering algorithm called BC-DPC is proposed based on mutual nearest neighbor and connectivity, which can quickly find the correct cluster centers and obtain satisfactory clustering results. • A new definition of density is proposed, which can elimilate the density difference among different clusters and accurately estimate the density of the data points. • This algorithm fully considers the density change and connectivity between data points when calculating the relative distance. This makes the domino effect can be avoided in the clustering process. • The algorithm proposes a novel fast search strategy, which is used to calculate relative distance of data points. This strategy makes the efficiency of the proposed algorithm greatly improved. • The performance of the proposed algorithm is compared to DPC and five improved DPC in synthetic, UCI, and image datasets. • The experimental results show the effectiveness and the efficiency of the proposed algorithm. Density peaks clustering (DPC) algorithm regards the density peaks as the potential cluster centers, and assigns the non-center point into the cluster of its nearest higher-density neighbor. Although DPC can discover clusters with arbitrary shapes, it has some limitations. On the one hand, the density measure of DPC fails to eliminate the density difference among different clusters, which affects the accuracy of recognizing cluster center. On the other hand, the nearest higher-density point is determined without considering connectivity, which leads to continuously clustering errors. Therefore, DPC fails to obtain satisfactory clustering results on datasets with great density difference among clusters. In order to eliminate these limitations, a novel DPC algorithm based on balance density and connectivity (BC-DPC) is proposed. First, the balance density is proposed to eliminate the density difference among different clusters to accurately recognize cluster centers. Second, the connectivity between a data point and its nearest higher-density point is guaranteed by mutual nearest neighbor relationship to avoid continuously clustering errors. Finally, a fast search strategy is proposed to find the nearest higher-density point. The experimental results on synthetic, UCI, and image datasets demonstrate the efficiency and effectiveness of the proposed algorithm in this paper. [ABSTRACT FROM AUTHOR]

• Propose three noise-robust mechanisms to address the noise generation problem in classic oversampling algorithms: adopting an advanced clustering algorithm, designing adaptive embedding to generate samples, and implementing a safe boundary to enlarge class boundaries. • Propose the heterogeneous distance metric to better cluster mixed-type data along with dedicated approaches to avoid generating groundless samples with categorical variables. • Adapted decomposition strategy extends solution for binary imbalanced data to the multi-class setting. Moreover, better placement of new samples are provided. • Experiments on the standard datasets validate the effectiveness of the proposed data. The class imbalance problem is characterized by an unequal data distribution in which majority classes have a greater number of data samples than minority classes. Oversampling methods generate samples for minority classes to balance the data distribution. However, the generated minority samples may overlap with majority samples, resulting in noise. In this paper, we propose a noise-robust oversampling algorithm for mixed-type and multi-class imbalanced data. Our proposed noise-robust designs include an algorithm to eliminate noise within clusters of data samples, adaptive embedding to generate samples safely, and a safe boundary for enlarging class boundaries. The heterogeneous distance metric and adapted decomposition strategy render our noise-robust algorithm suitable for mixed-type and multi-class imbalanced data. Experimental results on 20 benchmark datasets demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Data distribution alignment and clustering-based self-training are two feasible solutions to tackle unsupervised domain adaptation (UDA) on person re-identification (re-ID). Most existing alignment-based methods solely learn the source domain decision boundaries and align the data distribution of the target domain to the source domain, thus the re-ID performance on the target domain completely depends on the shared decision boundaries and how well the alignment is performed. However, two domains can hardly be precisely aligned because of the label space discrepancy of two domains, resulting in poor target domain re-ID performance. Although clustering-based self-training approaches could learn independent decision boundaries on the pseudo-labelled target domain data, they ignore both the accurate ID-related information of the labelled source domain data and the underlying relations between two domains. To fully exploit the source domain data to learn discriminative target domain ID-related features, in this paper, we propose a novel cross-domain alignment method in the homogeneous distance space, which is constructed by the newly designed stair-stepping alignment (SSA) matcher. Such alignment method can be integrated into both alignment-based framework and clustering-based framework. Extensive experiments validate the effectiveness of our proposed alignment method in these two frameworks. We achieve superior performance when the proposed alignment module is integrated into the clustering-based framework. Codes will be available at: http://github.com/Dingyuan-Zheng/HDS. [ABSTRACT FROM AUTHOR]

• A new non-negative matrix factorization decomposition model is proposed. • A new non-negative matrix factorization method, calledFeature Nonlinear Transformation Non-Negative Matrix Factorization with Kullback-Leibler Divergence (FNTNMF-KLD) is proposed. • New iterative update rules for basis matrix and feature matrix are derived strictly. • A proof of algorithm convergence is provided. • There are higher accuracies in object recognition and clustering. This paper introduces a Feature Nonlinear Transformation Non-Negative Matrix Factorization with Kullback-Leibler Divergence (FNTNMF-KLD) for extracting the nonlinear features of a matrix in standard NMF. This method uses a nonlinear transformation to act on the feature matrix for constructing a NMF model based on the objective function of Kullback-Leibler Divergence, and the Taylor series expansion and the Newton iteration formula of solving root are used to obtain the iterative update rules of the basis matrix and the feature matrix. Experimental results show that the proposed method obtains the nonlinear features of data matrix in a more efficient way. In object recognition and clustering tasks, better accuracy can be achieved over some typical NMF methods. [ABSTRACT FROM AUTHOR]

• The limitation of the exploitation efficiency in existing reinforcement learning methods is analyzed in detail. • Clustering is combined into the experience replay by a divide-and-conquer framework to improve the exploitation efficiency. • Our experience replay can sufficiently replay all kinds of transitions in the current training with low time consumption. • A new reinforcement learning method is proposed to implement our experience replay. Reinforcement learning is a useful tool for training an agent to effectively achieve the desired goal in the sequential decision-making problem. It trains the agent to make decision by exploiting the experience in the transitions resulting from the different decisions. To exploit this experience, most reinforcement learning methods replay the explored transitions by uniform sampling. But in this way, it is easy to ignore the last explored transitions. Another way to exploit this experience defines the priority of each transition by the estimation error in training and then replays the transitions according to their priorities. But it only updates the priorities of the transitions replayed at the current training time step, thus the transitions with low priorities will be ignored. In this paper, we propose a clustering experience replay, called CER, to effectively exploit the experience hidden in all explored transitions in the current training. CER clusters and replays the transitions by a divide-and-conquer framework based on time division as follows. Firstly, it divides the whole training process into several periods. Secondly, at the end of each period, it uses k -means to cluster the transitions explored in this period. Finally, it constructs a conditional probability density function to ensure that all kinds of transitions will be sufficiently replayed in the current training. We construct a new method, TD3 _ CER, to implement our clustering experience replay on TD3. Through the theoretical analysis and experiments, we illustrate that our TD3 _ CER is more effective than the existing reinforcement learning methods. The source code can be downloaded from https://github.com/grcai/CER-Master. [ABSTRACT FROM AUTHOR]

• By regarding multi-view learning as a natural choice to address feature heterogeneity in federated setting, we present a novel federated multi-view learning method based on orthogonal matrix factorization due to its extensibility and lower costs. • By allowing each node with the flexibility to address its subproblem approximately, the proposed optimization algorithm is able to handle communication variability associated with node heterogeneity. • We further provide convergence guarantees for the proposed algorith that also take the communication variability into consideration and provide insight into the implementation performance. • Empirical study shows encouraging results of our model in comparison to several state-of-the-art algorithms, as we illustrate through simulations on benchmark federated multi-view datasets. Multi-view learning aims to explore a global common structure shared by different views collected from multiple individual sources. The nascent field of federated learning tries to learn a global model over distributed networks of devices. This paper shows that multi-view learning is naturally suited to address the feature heterogeneity of the federated setting. We propose a novel model, namely robust federated multi-view learning (FedMVL), which is considered in the following formulation: given a dataset with M views, it is required to train machine learning models while the M views are distributed across M devices or nodes. Considering the unique challenges like stragglers and fault tolerance in federated setting, we derive an iterative federated optimization algorithm that allows each node with the flexibility to approximately address its subproblem. To the best of our knowledge, our model for the first time considers the issues including high communication cost, fault tolerance, and stragglers for distributed multi-view learning. The proposed model also achieves encouraging performance on clustering task compared to closely related methods, as we illustrate through simulations on several real-world datasets. [ABSTRACT FROM AUTHOR]

• Efficient kNN search based on feature learning, clustering, and adaptive k values. • Several proposals to automatically optimize the search parameters. • Comprehensive experimentation with 10 datasets of different typology and size. • Results demonstrate that the proposal outperforms state-of-the-art methods. The k -Nearest Neighbor (k NN) algorithm is widely used in the supervised learning field and, particularly, in search and classification tasks, owing to its simplicity, competitive performance, and good statistical properties. However, its inherent inefficiency prevents its use in most modern applications due to the vast amount of data that the current technological evolution generates, being thus the optimization of k NN-based search strategies of particular interest. This paper introduces the caKD+ algorithm, which tackles this limitation by combining the use of feature learning techniques, clustering methods, adaptive search parameters per cluster, and the use of pre-calculated K-Dimensional Tree structures, and results in a highly efficient search method. This proposal has been evaluated using 10 datasets and the results show that caKD+ significantly outperforms 16 state-of-the-art efficient search methods while still depicting such an accurate performance as the one by the exhaustive k NN search. [ABSTRACT FROM AUTHOR]

• A novel non-parametric clustering algorithm based on the concept of divide-and-merge. • Ability to discover both convex and non-convex shaped clusters. • Ability to discover clusters different in densities. • Ability to detect and remove outliers/noise in the data. • Usability for high dimensional data and easily tunable or fixed hyperparameters. In this paper, a novel non-parametric clustering algorithm which is based on the concept of divide-and-merge is proposed. The proposed algorithm is based on two primary phases, after data cleaning: (i) the Division phase and (ii) the Merging phase. In the initial phase of division, the data is divided into an optimized number of small sub-clusters utilizing all the dimensions of the data. In the second phase of merging, the small sub-clusters obtained as a result of division are merged according to an advanced statistical metric to form the actual clusters in the data. The proposed algorithm has the following merits: (i) ability to discover both convex and non-convex shaped clusters, (ii) ability to discover clusters different in densities, (iii) ability to detect and remove outliers/noise in the data (iv) easily tunable or fixed hyperparameters (v) and its usability for high dimensional data. The proposed algorithm is extensively tested on 20 benchmark datasets including both, the synthetic and the real datasets and is found better/competing to the existing state-of-the-art parametric and non-parametric clustering algorithms. [ABSTRACT FROM AUTHOR]

• A taxonomy and comprehensive survey of Few-Shot Learning (FSL) is illustrated. • Unsupervised FSL eliminates the dependency on annotations of source dataset in vanilla FSL. • Our unsupervised FSL method C2FPS-ML explores coarseto fine pseudo supervisions for optimizing meta-task sampling. • A comprehensive experimental evaluation of C2FPS-ML is conducted. • C2FPS-ML is competitive with other state-of-the-art Unsupervised FSL methods. • C2FPS-ML achieves the higher training efficiency than that of the related methods. Few-Shot Learning (FSL) is a challenging and practical learning pattern, aiming to solve a target task which has only a few labeled examples. Currently, the field of FSL has made great progress, but largely in the supervised setting, where a large auxiliary labeled dataset is required for offline training. However, the unsupervised FSL (UFSL) problem where the auxiliary dataset is fully unlabeled has been seldom investigated despite of its significant value. This paper focuses on the more general and challenging UFSL problem and presents a novel method named Coarse-to-Fine Pseudo Supervision-guided Meta-Learning (C2FPS-ML) for unsupervised few-shot object classification. It first obtains prior knowledge from an unlabeled auxiliary dataset during unsupervised meta-training, and then use the prior knowledge to assist the downstream few-shot classification task. Coarse-to-Fine Pseudo Supervisions in C2FPS-ML aim to optimize meta-task sampling process in unsupervised meta-training stage which is one of the dominant factors for improving the performance of meta-learning based FSL algorithms. Human can learn new concepts progressively or hierarchically following the coarse-to-fine manners. By simulating this human's behaviour, we develop two versions of C2FPS-ML for two different scenarios: one is natural object dataset and another one is other kinds of dataset (e.g. , handwritten character dataset). For natural object dataset scenario, we propose to exploit the potential hierarchical semantics of the unlabeled auxiliary dataset to build a tree-like structure of visual concepts. For another scenario, progressive pseudo supervision is obtained by forming clusters in different similarity aspects and is represented by a pyramid-like structure. The obtained structure is applied as the supervision to construct meta-tasks in meta-training stage, and prior knowledge from the unlabeled auxiliary dataset is learned from the coarse-grained level to the fine-grained level. The proposed method sets the new state of the art on the gold-standard mini ImageNet and achieves remarkable results on Omniglot while simultaneously increases efficiency. [ABSTRACT FROM AUTHOR]

• Properties that help solve the clustering users dilemma. • Weighted properties formally differentiate clustering methods. • A formal classification highlights advantages of center-based clustering techniques. This paper makes a major step towards addressing a long-standing challenge in cluster analysis, known as the user's dilemma , which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this challenge relies on the identification of succinct, user-friendly properties that capture formal differences amongst clustering techniques. While helpful for gaining insight into the nature of clustering paradigms, there is a theory-practice gap that has so far limited the utility of this approach: Formal properties typically highlight advantages of classical linkage-based algorithms, while practical experience shows that center-based methods are preferable for many applications. We present simple new properties that delineate core differences between common clustering paradigms and overcome this theory-practice gap. The properties we present give a formal understanding of the advantages of center-based approaches for some applications and insight into when different clustering paradigms should be used. These properties address how sensitive algorithms are to changes in element frequencies, which we capture in a generalized setting where every element is associated with a real-valued weight. To complement extensive formal analysis, we discuss how these properties can be applied in practice. [ABSTRACT FROM AUTHOR]

• Fuzzy c-means (FCM) clustering had been extended for handling multi-view data. • We propose a novel multi-view FCM (MVFCM) clustering algorithm with view and feature weights based on collaborative learning, called Co-FW-MVFCM. • The proposed Co-FW-MVFCM contains a two-step schema that includes a local step and a collaborative step. • The Co-FW-MVFCM can give feature reduction to exclude redundant feature components during clustering processes. • Comparisons among Co-FW-MVFCM and existing MVFCM algorithms actually demonstrate the effectiveness and usefulness of Co-FW-MVFCM. Fuzzy c-means (FCM) clustering had been extended for handling multi-view data with collaborative idea. However, these collaborative multi-view FCM treats multi-view data under equal importance of feature components. In general, different features should take different weights for clustering real multi-view data. In this paper, we propose a novel multi-view FCM (MVFCM) clustering algorithm with view and feature weights based on collaborative learning, called collaborative feature-weighted MVFCM (Co-FW-MVFCM). The Co-FW-MVFCM contains a two-step schema that includes a local step and a collaborative step. The local step is a single-view partition process to produce local partition clustering in each view, and the collaborative step is sharing information of their memberships between different views. These two steps are then continuing by an aggregation way to get a global result after collaboration. Furthermore, the embedded feature-weighted procedure in Co-FW-MVFCM can give feature reduction to exclude redundant/irrelevant feature components during clustering processes. Experiments with several data sets demonstrate that the proposed Co-FW-MVFCM algorithm can completely identify irrelevant feature components in each view and that, additionally, it can improve the performance of the algorithm. Comparisons of Co-FW-MVFCM with some existing MVFCM algorithms are made and also demonstrated the effectiveness and usefulness of the proposed Co-FW-MVFCM clustering algorithm. [ABSTRACT FROM AUTHOR]