Tensor decompositions have been successfully applied to multidimensional data recovery. However, classical tensor decompositions are not suitable for emerging spatio-irregular multidimensional data (i.e., spatio-irregular tensor), whose spatial domain is non-rectangular, e.g., spatial transcriptomics data from bioinformatics and semantic units from computer vision. By using preprocessing (e.g., zero-padding or element-wise 0-1 weighting), the spatio-irregular tensor can be converted to a spatio-regular tensor and then classical tensor decompositions can be applied, but this strategy inevitably introduces bias information, leading to artifacts. How to design a tensor-based method suitable for emerging spatio-irregular tensors is an imperative challenge. To address this challenge, we propose a learnable transform-assisted tensor singular value decomposition (LTA-TSVD) for spatio-irregular tensor recovery, which allows us to leverage the intrinsic structure behind the spatio-irregular tensor. Specifically, we design a learnable transform to project the original spatio-irregular tensor into its latent spatio-regular tensor, and then the latent low-rank structure is captured by classical TSVD on the resulting regular tensor. Empowered by LTA-TSVD, we develop spatio-irregular low-rank tensor completion (SIR-LRTC) and spatio-irregular tensor robust principal component analysis (SIR-TRPCA) models for the spatio-irregular tensor imputation and denoising respectively, and we design corresponding solving algorithms with theoretical convergence. Extensive experiments including the spatial transcriptomics data imputation and hyperspectral image denoising show SIR-LRTC and SIR-TRPCA are superior performance to competing approaches and benefit downstream applications.

Multi-view subspace clustering (MVSC) separates the data with multiple views into multiple clusters, and each cluster corresponds to one certain subspace. Existing tensor-based MVSC methods construct self-representation subspace coefficient matrices of all views as a tensor, and introduce the tensor nuclear norm (TNN) to capture the complementary information hidden in different views. The key assumption is that the data samples of each subspace must be sufficient for subspace representation. This work proposes a nonconvex latent transformed low-rank tensor representation framework for MVSC. To deal with the insufficient sample problem, we study the latent low-rank representation in the multi-view case to supplement underlying observed samples. Moreover, we propose to use data-driven transformed TNN (TTNN), resulting from the intrinsic structure of multi-view samples, to preserve the consensus and complementary information in the transformed domain. Meanwhile, the proposed unified nonconvex low-rank tensor representation framework can better learn the high correlation among different views. To resolve the proposed nonconvex optimization model, we propose an effective algorithm under the framework of the alternating direction method of multipliers and theoretically prove that the iteration sequences converge to the critical point. Experiments on various datasets showcase outstanding performance.

In recommendation systems, cold-start user recommendation is a challenging problem, where precise recommendations are required for users who have not appeared before. Several existing cold-start user recommendation models adopt domain adaptation to extract information from auxiliary source domains to assist the recommendations on the target domain. In this article, we propose that the cold-start user recommendation problem can be formulated by the heterogeneous domain adaption approach. We determine a transformation of user features, e.g., user social relations and historical interactions between warm users and their interested items, into a latent space so that the loss function is set by user feature reconstruction and by feature and distribution matching in the heterogeneous domains. The resulting optimization problem can be solved by matrix eigendecomposition, and the cold-start users’ preferences can thus be obtained. We also extend the proposed model using neural networks. We perform extensive experiments on several real-world datasets, and the results in terms of Precision, Recall, NDCG, and Hit Rate verify the effectiveness of the proposed model.

Hypergraphs can represent higher-order relations among objects. Traditional hypergraph neural networks involve node-edge-node transform, leading to high computational cost and timing. The main aim of this article is to propose a new sampling technique for learning with hypergraph neural networks. The core idea is to design a layer-wise sampling scheme for nodes and hyperedges to approximate the original hypergraph convolution. We rewrite hypergraph convolution in the form of double integral and leverage Monte Carlo to achieve a discrete and consistent estimator. In addition, we use importance sampling and finally derive feasible probability mass functions for both nodes and hyperedges in consideration of variance reduction, based on some assumptions. Notably, the proposed sampling technique allows us to handle large-scale hypergraph learning, which is not feasible with traditional hypergraph neural networks. Experiment results demonstrate that our proposed model keeps a good balance between running time and prediction accuracy.

User preferences behind users' decision-making processes are highly diverse and may range from lower-level concepts with more specific intentions and higher-level concepts with more general intentions. In this case, user preferences tend to be expressed hierarchically. However, learning such intentions with different levels from user behaviors is challenging, and remains largely neglected by the existing literature. Meanwhile, user behavior data tends to be sparse because of the limited user response and the vast combinations of users and items, which results in cold-start problems with unclear user intentions. In this paper, we propose a mixture intention neural stochastic process (MINSP), a new view of the stochastic processes family using a general meta-learning mechanism and mixture strategy for robust recommendation with hierarchical preferences modeling. By considering the recommendation process for each user as a stochastic process, MINSP defines distributions over functions and is capable of rapid adaptation to different users. To capture the user's intention on different levels, an iterative additive algorithm is proposed that minimizes the approximation error by backfitting the residuals of previous approximations. In this case, the induced tree intention hierarchies serve as an aggregated structured representation of the whole preference, summarizing the gist for convenient navigation and better generalization. Furthermore, we theoretically analyze the generalization error bound of the proposed MINSP to guarantee the model performance. Empirical results show that our approach can achieve substantial improvement over the state-of-the-art baselines in terms of recommendation performance, and obtain an interpretable hierarchical intention structure.

Heterogeneous Information Network(HIN) collective classification aims to classify one type of node, which is associated with multiple types of nodes through multiple types of relations. Previous studies have revealed that exploiting the relative importance of relation types is quite useful for improving node classification performance. We propose a Tensor-based Markov chain (T-Mark) model to improve the nodes classification accuracy by predicting the labels for unlabeled nodes and the importance ranking of relationship types automatically and simultaneously. Specifically, we build two tensor equations according to the HIN structure and content similarities among nodes of both labeled and unlabeled data. Consequently, We solve the semi-supervised T-Mark model by using an iterative process until obtaining two stationary distributions for labels and relation types. Experimental results on several real-world datasets demonstrate the effectiveness of T-Mark.

Multi-source domain adaptation (MSDA) aims to leverage the knowledge in multiple source domains to assist the prediction in a target domain, where the source and target domains have different data distributions. This paper presents a MSDA model to investigate both domain discrepancy and domain relevance, whose interactions are also exploited to gradually refine the learning performance. Particularly, the proposed model contains two components, i.e., feature spaces learning and transferred weights learning. The former one minimizes the domain discrepancy and the latter one evaluates the domain relevance. Experimental results on several real-world datasets demonstrate the effectiveness of the proposed model.

Domain adaptation aims at extracting knowledge from auxiliary source domains to assist the learning task in a target domain. Since the distributions of the source and target domains are different, directly using source data to build a classifier for the target domain may hamper the classification performance on the target data. In this paper, we propose to find a feature subset that is both transferable and discriminative, so that both the domain discrepancy and the classification loss measured on the selected features can be reduced. To achieve this, we formulate a new sparse learning model that is able to jointly reduce the domain discrepancy and select informative features for classification. Extensive experiments on real-world data sets demonstrate the effectiveness of the proposed method.

In this article, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed rank matrices can be expensive as the singular value decomposition is required. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by the alternating projections onto the tangent spaces of the fixed rank matrices manifold and the nonnegative matrix manifold, converge linearly to a point in the intersection of the two manifolds where the convergent point is sufficiently close to optimal solutions. This convergence result based inexact projection onto the manifold is new and is not studied in the literature. Numerical examples in data clustering, pattern recognition and hyperspectral data analysis are given to demonstrate that the performance of the proposed method is better than that of nonnegative matrix factorization methods in terms of computational time and accuracy.

This article presents a novel model named Adversarial Auto-encoder Domain Adaptation to handle the recommendation problem under cold-start settings. Specifically, we divide the hypergraph into two hypergraphs, i.e., a positive hypergraph and a negative one. Below, we adopt the cold-start user recommendation for illustration. After achieving positive and negative hypergraphs, we apply hypergraph auto-encoders to them to obtain positive and negative embeddings of warm users and items. Additionally, we employ a multi-layer perceptron to get warm and cold-start user embeddings called regular embeddings. Subsequently, for warm users, we assign positive and negative pseudo-labels to their positive and negative embeddings, respectively, and treat their positive and regular embeddings as the source and target domain data, respectively. Then, we develop a matching discriminator to jointly minimize the classification loss of the positive and negative warm user embeddings and the distribution gap between the positive and regular warm user embeddings. In this way, warm users’ positive and regular embeddings are connected. Since the positive hypergraph maintains the relations between positive warm user and item embeddings, and the regular warm and cold-start user embeddings follow a similar distribution, the regular cold-start user embedding and positive item embedding are bridged to discover their relationship. The proposed model can be easily extended to handle the cold-start item recommendation by changing inputs. We perform extensive experiments on real-world datasets for both cold-start user and cold-start item recommendations. Promising results in terms of precision, recall, normalized discounted cumulative gain, and hit rate verify the effectiveness of the proposed method.

Social relations between users have been proven to be a good type of auxiliary information to improve the recommendation performance. However, it is a challenging issue to sufficiently exploit the social relations and correctly determine the user preference from both social and rating information. In this article, we propose a unified Bayesian Additive Matrix Approximation model (BAMA), which takes advantage of rating preference and social network to provide high-quality recommendation. The basic idea of BAMA is to extract social influence from social networks, integrate them to Bayesian additive co-clustering for effectively determining the user clusters and item clusters, and provide an accurate rating prediction. In addition, an efficient algorithm with collapsed Gibbs Sampling is designed to inference the proposed model. A series of experiments were conducted on six real-world social datasets. The results demonstrate the superiority of the proposed BAMA by comparing with the state-of-the-art methods from three views, all users, cold-start users, and users with few social relations. With the aid of social information, furthermore, BAMA has ability to provide the explainable recommendation.

Multi-source domain adaptation is a challenging topic in transfer learning, especially when the data of each domain are represented by different kinds of features, i.e., Multi-source Heterogeneous Domain Adaptation (MHDA). It is important to take advantage of the knowledge extracted from multiple sources as well as bridge the heterogeneous spaces for handling the MHDA paradigm. This article proposes a novel method named Multiple Graphs and Low-rank Embedding (MGLE), which models the local structure information of multiple domains using multiple graphs and learns the low-rank embedding of the target domain. Then, MGLE augments the learned embedding with the original target data. Specifically, we introduce the modules of both domain discrepancy and domain relevance into the multiple graphs and low-rank embedding learning procedure. Subsequently, we develop an iterative optimization algorithm to solve the resulting problem. We evaluate the effectiveness of the proposed method on several real-world datasets. Promising results show that the performance of MGLE is better than that of the baseline methods in terms of several metrics, such as AUC, MAE, accuracy, precision, F1 score, and MCC, demonstrating the effectiveness of the proposed method.

Hypergraphs have shown great power in representing high-order relations among entities, and lots of hypergraph-based deep learning methods have been proposed to learn informative data representations for the node classification problem. However, most of these deep learning approaches do not take full consideration of either the hyperedge information or the original relationships among nodes and hyperedges. In this article, we present a simple yet effective semi-supervised node classification method named Hypergraph Convolution on Nodes-Hyperedges network, which performs filtering on both nodes and hyperedges as well as recovers the original hypergraph with the least information loss. Instead of only reducing the cross-entropy loss over the labeled samples as most previous approaches do, we additionally consider the hypergraph reconstruction loss as prior information to improve prediction accuracy. As a result, by taking both the cross-entropy loss on the labeled samples and the hypergraph reconstruction loss into consideration, we are able to achieve discriminative latent data representations for training a classifier. We perform extensive experiments on the semi-supervised node classification problem and compare the proposed method with state-of-the-art algorithms. The promising results demonstrate the effectiveness of the proposed method.

Heterogeneous Information Network (HIN) collecitve classification studies the problem of predicting labels for one type of nodes in a HIN which contains multiple types of nodes multiple types of links among them. Previous studies have revealed that exploiting relative importance of links is quite useful to improve node classification performance as connected nodes tend to have similar labels. Most existing approaches exploit the relative importance of links either by directly counting the number of connections among nodes or by learning the weight of each type of link from labeled data only. However, these approaches either neglect the importance of types of links to the class labels or may lead to overfitting problem. We propose aTensor-basedMarkov chain (T-Mark) approach, which is able to automatically and simultaneously predict the labels for unlabeled nodes and give the relative importance of types of links that actually improve the classification accuracy. Specifically, we build two tensor equations by using the HIN and features of nodes from both labeled and unlabeled data. A Markov chain-based model is proposed and it is solved by an iterative process to obtain the stationary distributions. Theoretical analyses of the existence and uniqueness of such probability distributions are given. Extensive experimental results demonstrate that T-Mark is able to achieve superior performance in the comparison and obtain reasonable relative importance of links.

One of the main challenges in multi-source domain adaptation is how to reduce the domain discrepancy between each source domain and a target domain, and then evaluate the domain relevance to determine how much knowledge should be transferred from different source domains to the target domain. However, most prior approaches barely consider both discrepancies and relevance among domains. In this paper, we propose an algorithm, called Iterative Refinement based on Feature Selection and the Wasserstein distance (IRFSW), to solve semi-supervised domain adaptation with multiple sources. Specifically, IRFSW aims to explore both the discrepancies and relevance among domains in an iterative learning procedure, which gradually refines the learning performance until the algorithm stops. In each iteration, for each source domain and the target domain, we develop a sparse model to select features in which the domain discrepancy and training loss are reduced simultaneously. Then a classifier is constructed with the selected features of the source and labeled target data. After that, we exploit optimal transport over the selected features to calculate the transferred weights. The weight values are taken as the ensemble weights to combine the learned classifiers to control the amount of knowledge transferred from source domains to the target domain. Experimental results validate the effectiveness of the proposed method.

Domain adaptation aims at extracting knowledge from auxiliary source domains to assist the learning task in a target domain. In classification problems, since the distributions of the source and target domains are different, directly using source data to build a classifier for the target domain may hamper the classification performance on the target data. Fortunately, in many tasks, there can be some features that are transferable, i.e., the source and target domains share similar properties. On the other hand, it is common that the source data contain noisy features which may degrade the learning performance in the target domain. This issue, however, is barely studied in existing works. In this paper, we propose to find a feature subset that is transferable across the source and target domains. As a result, the domain discrepancy measured on the selected features can be reduced. Moreover, we seek to find the most discriminative features for classification. To achieve the above goals, we formulate a new sparse learning model that is able to jointly reduce the domain discrepancy and select informative features for classification. We develop two optimization algorithms to address the derived learning problem. Extensive experiments on real-world data sets demonstrate the effectiveness of the proposed method.

Domain adaptation aims at improving the performance of learning tasks in a target domain by leveraging the knowledge extracted from a source domain. To this end, one can perform knowledge transfer between these two domains. However, this problem becomes extremely challenging when the data of these two domains are characterized by different types of features, i.e., the feature spaces of the source and target domains are different, which is referred to as heterogeneous domain adaptation (HDA). To solve this problem, we propose a novel model called Knowledge Preserving and Distribution Alignment (KPDA), which learns an augmented target space by jointly minimizing information loss and maximizing domain distribution alignment. Specifically, we seek to discover a latent space, where the knowledge is preserved by exploiting the Laplacian graph terms and reconstruction regularizations. Moreover, we adopt the Maximum Mean Discrepancy to align the distributions of the source and target domains in the latent space. Mathematically, KPDA is formulated as a minimization problem with orthogonal constraints, which involves two projection variables. Then, we develop an algorithm based on the Gauss–Seidel iteration scheme and split the problem into two subproblems, which are solved by searching algorithms based on the Barzilai–Borwein (BB) stepsize. Promising results demonstrate the effectiveness of the proposed method.

Due to leveraging social relationships between users as well as their past social behavior, social recommendation becomes a core component in recommendation systems. Most existing social recommendation methods only consider direct social relationships among users (e.g., explicit and observed social relations). Recently, researchers proved that indirect social relationships can be effective to improve the recommendation quality when users only have few social connections, because it can identify the user interesting group even though the users have no observed social connection. In the literature, separate two-stage methods are studied, but they cannot explicitly capture the natural relationship between indirect social relations and latent user/item factors. In this paper, the main contribution is to propose a new joint recommendation model taking advantage of the Indirect Social Relations detection and Matrix Factorization collaborative filtering on social network and rating behavior information, which is called as InSRMF. In our work, the user latent factors can simultaneously and seamlessly capture user's personal preferences and social group characteristics. To optimize the InSRMF model, we develop a parallel graph vertex programming algorithm for efficiently handling large scale social recommendation data. Experiments based on four real-world datasets (Ciao, Epinions, Douban and Yelp) are conducted to demonstrate the performance of the proposed model. The experimental results have shown that InSRMF has ability to mine the proper indirect social relations and improve the recommendation performance compared with the testing methods in the literature, especially on the users with few social neighbors, Near-cold-start Users, Pure-cold-start Users and Long-tail Items.

Multi-source domain adaptation has received considerable attention due to its effectiveness of leveraging the knowledge from multiple related sources with different distributions to enhance the learning performance. One of the fundamental challenges in multi-source domain adaptation is how to determine the amount of knowledge transferred from each source domain to the target domain. To address this issue, we propose a new algorithm, called Domain-attention Conditional Wasserstein Distance (DCWD), to learn transferred weights for evaluating the relatedness across the source and target domains. In DCWD, we design a new conditional Wasserstein distance objective function by taking the label information into consideration to measure the distance between a given source domain and the target domain. We also develop an attention scheme to compute the transferred weights of different source domains based on their conditional Wasserstein distances to the target domain. After that, the transferred weights can be used to reweight the source data to determine their importance in knowledge transfer. We conduct comprehensive experiments on several real-world data sets, and the results demonstrate the effectiveness and efficiency of the proposed method.

With the quick development of social websites, there are more opportunities to have different media types (such as text, image, video, etc.) describing the same topic from large-scale heterogeneous data sources. To efficiently identify the inter-media correlations for multimedia retrieval, unsupervised cross-modal hashing (UCMH) has gained increased interest due to the significant reduction in computation and storage. However, most UCMH methods assume that the data from different modalities are well paired. As a result, existing UCMH methods may not achieve satisfactory performance when partially paired data are given only. In this article, we propose a new-type of UCMH method called robust unsupervised cross-modal hashing ( RUCMH ). The major contribution lies in jointly learning modal-specific hash function, exploring the correlations among modalities with partial or even without any pairwise correspondence, and preserving the information of original features as much as possible. The learning process can be modeled via a joint minimization problem, and the corresponding optimization algorithm is presented. A series of experiments is conducted on four real-world datasets (Wiki, MIRFlickr, NUS-WIDE, and MS-COCO). The results demonstrate that RUCMH can significantly outperform the state-of-the-art unsupervised cross-modal hashing methods, especially for the partially paired case, which validates the effectiveness of RUCMH.

In this article, we study the problem of online heterogeneous transfer learning, where the objective is to make predictions for a target data sequence arriving in an online fashion, and some offline labeled instances from a heterogeneous source domain are provided as auxiliary data. The feature spaces of the source and target domains are completely different, thus the source data cannot be used directly to assist the learning task in the target domain. To address this issue, we take advantage of unlabeled co-occurrence instances as intermediate supplementary data to connect the source and target domains, and perform knowledge transition from the source domain into the target domain. We propose a novel online heterogeneous transfer learning algorithm called O nline H eterogeneous K nowledge T ransition (OHKT) for this purpose. In OHKT, we first seek to generate pseudo labels for the co-occurrence data based on the labeled source data, and then develop an online learning algorithm to classify the target sequence by leveraging the co-occurrence data with pseudo labels. Experimental results on real-world data sets demonstrate the effectiveness and efficiency of the proposed algorithm.

In this paper, we study relations ranking and object classification for multi-relational data where objects are interconnected by multiple relations. The relations among objects should be exploited for achieving a good classification. While most existing approaches exploit either by directly counting the number of connections among objects or by learning the weight of each relation from labeled data only. In this paper, we propose an algorithm, TensorRRCC, which is able to determine the ranking of relations and the labels of objects simultaneously. Our basic idea is that highly ranked relations within a class should play more important roles in object classification, and class membership information is important for determining a ranking quality over the relations w.r.t. a specific learning task. TensorRRCC implements the idea by modeling a Markov chain on transition probability graphs from connection and feature information with both labeled and unlabeled objects and propagates the ranking scores of relations and relevant classes of objects. An iterative progress is proposed to solve a set of tensor equations to obtain the stationary distribution of relations and objects. We compared our algorithm with current collective classification algorithms on two real-world data sets and the experimental results show the superiority of our method.

Multi-label classification deals with the problem where each example is associated with multiple class labels. Since the labels are often dependent to other labels, exploiting label dependencies can significantly improve the multi-label classification performance. The label dependency in existing studies is often given as prior knowledge or learned from the labels only. However, in many real applications, such prior knowledge may not be available, or labeled information might be very limited. In this paper, we propose a new algorithm, called Ml-Forest , to learn an ensemble of hierarchical multi-label classifier trees to reveal the intrinsic label dependencies. In Ml-Forest, we construct a set of hierarchical trees, and develop a label transfer mechanism to identify the multiple relevant labels in a hierarchical way. In general, the relevant labels at higher levels of the trees capture more discriminable label concepts, and they will be transferred into lower level children nodes that are harder to discriminate. The relevant labels in the hierarchy are then aggregated to compute label dependency and make the final prediction. Our empirical study shows encouraging results of the proposed algorithm in comparison with the state-of-the-art multi-label classification algorithms under Friedman test and post-hoc Nemenyi test.

Heterogeneous transfer learning has been proposed as a new learning strategy to improve performance in a target domain by leveraging data from other heterogeneous source domains where feature spaces can be different across different domains. In order to connect two different spaces, one common technique is to bridge feature spaces by using some co-occurrence data. For example, annotated images can be used to build feature mapping from words to image features, and then applied on text-to-image knowledge transfer. However, in practice, such co-occurrence data are often from Web, e.g. Flickr, and generated by users. That means these data can be sparse and contain personal biases. Directly building models based on them may fail to provide reliable bridge. To solve these aforementioned problems, in this paper, we propose a novel algorithm named Mixed-Transfer. It is composed of three components, that is, a cross domain harmonic function to avoid personal biases, a joint transition probability graph of mixed instances and features to model the heterogeneous transfer learning problem, a random walk process to simulate the label propagation on the graph and avoid the data sparsity problem. We conduct experiments on 171 real-world tasks, showing that the proposed approach outperforms four state-of-the-art heterogeneous transfer learning algorithms.

The main aim of this paper is to develop a community discovery scheme in a multi-dimensional network for data mining applications. In online social media, networked data consists of multiple dimensions/entities such as users, tags, photos, comments, and stories. We are interested in finding a group of users who interact significantly on these media entities. In a co-citation network, we are interested in finding a group of authors who relate to other authors significantly on publication information in titles, abstracts, and keywords as multiple dimensions/entities in the network. The main contribution of this paper is to propose a framework (MultiComm)to identify a seed-based community in a multi-dimensional network by evaluating the affinity between two items in the same type of entity (same dimension)or different types of entities (different dimensions)from the network. Our idea is to calculate the probabilities of visiting each item in each dimension, and compare their values to generate communities from a set of seed items. In order to evaluate a high quality of generated communities by the proposed algorithm, we develop and study a local modularity measure of a community in a multi-dimensional network. Experiments based on synthetic and real-world data sets suggest that the proposed framework is able to find a community effectively. Experimental results have also shown that the performance of the proposed algorithm is better in accuracy than the other testing algorithms in finding communities in multi-dimensional networks.

The problem of multilabel classification has attracted great interest in the last decade, where each instance can be assigned with a set of multiple class labels simultaneously. It has a wide variety of real-world applications, e.g., automatic image annotations and gene function analysis. Current research on multilabel classification focuses on supervised settings which assume existence of large amounts of labeled training data. However, in many applications, the labeling of multilabeled data is extremely expensive and time consuming, while there are often abundant unlabeled data available. In this paper, we study the problem of transductive multilabel learning and propose a novel solution, called Trasductive Multilabel Classification (TraM), to effectively assign a set of multiple labels to each instance. Different from supervised multilabel learning methods, we estimate the label sets of the unlabeled instances effectively by utilizing the information from both labeled and unlabeled data. We first formulate the transductive multilabel learning as an optimization problem of estimating label concept compositions. Then, we derive a closed-form solution to this optimization problem and propose an effective algorithm to assign label sets to the unlabeled instances. Empirical studies on several real-world multilabel learning tasks demonstrate that our TraM method can effectively boost the performance of multilabel classification by using both labeled and unlabeled data.

In this paper, we propose a framework HAR to study the hub and authority scores of objects, and the relevance scores of relations in multi-relational data for query search. The basic idea of our framework is to consider a random walk in multi-relational data, and study in such random walk, limiting probabilities of relations for relevance scores, and of objects for hub scores and authority scores. The main contribution of this paper is to (i) propose a framework (HAR) that can compute the hub, authority and relevance scores by solving limiting probabilities arising from multi-relational data, and can incorporate input query vectors to handle query-specific search; (ii) show existence and uniqueness of such limiting probabilities so that they can be used for query search effectively; and (iii) develop an iterative algorithm to solve a set of tensor (multivariate polynomial) equations to obtain such probabilities. Extensive experimental results on TREC and DBLP data sets suggest that the proposed method is very effective in obtaining relevant results to the querying inputs. In the comparison, we find that the performance of HAR is better than those of HITS, SALSA and TOPHITS.

The main aim of this paper is to design a co-ranking scheme for objects and relations in multi-relational data. It has many important applications in data mining and information retrieval. However, in the literature, there is a lack of a general framework to deal with multi-relational data for co-ranking. The main contribution of this paper is to (i) propose a framework (MultiRank) to determine the importance of both objects and relations simultaneously based on a probability distribution computed from multi-relational data; (ii) show the existence and uniqueness of such probability distribution so that it can be used for co-ranking for objects and relations very effectively; and (iii) develop an efficient iterative algorithm to solve a set of tensor (multivariate polynomial) equations to obtain such probability distribution. Extensive experiments on real-world data suggest that the proposed framework is able to provide a co-ranking scheme for objects and relations successfully. Experimental results have also shown that our algorithm is computationally efficient, and effective for identification of interesting and explainable co-ranking results.

In this paper, we present an agglomerative fuzzy $k$-means clustering algorithm for numerical data, an extension to the standard fuzzy $k$-means algorithm by introducing a penalty term to the objective function to make the clustering process not sensitive to the initial cluster centers. The new algorithm can produce more consistent clustering results from different sets of initial clusters centers. Combined with cluster validation techniques, the new algorithm can determine the number of clusters in a data set, which is a well known problem in $k$-means clustering. Experimental results on synthetic data sets (2 to 5 dimensions, 500 to 5000 objects and 3 to 7 clusters), the BIRCH two-dimensional data set of 20000 objects and 100 clusters, and the WINE data set of 178 objects, 17 dimensions and 3 clusters from UCI, have demonstrated the effectiveness of the new algorithm in producing consistent clustering results and determining the correct number of clusters in different data sets, some with overlapping inherent clusters.

This paper presents a new k-means type algorithm for clustering high-dimensional objects in sub-spaces. In high-dimensional data, clusters of objects often exist in subspaces rather than in the entire space. For example, in text clustering, clusters of documents of different topics are categorized by different subsets of terms or keywords. The keywords for one cluster may not occur in the documents of other clusters. This is a data sparsity problem faced in clustering high-dimensional data. In the new algorithm, we extend the k-means clustering process to calculate a weight for each dimension in each cluster and use the weight values to identify the subsets of important dimensions that categorize different clusters. This is achieved by including the weight entropy in the objective function that is minimized in the k-means clustering process. An additional step is added to the k-means clustering process to automatically compute the weights of all dimensions in each cluster. The experiments on both synthetic and real data have shown that the new algorithm can generate better clustering results than other subspace clustering algorithms. The new algorithm is also scalable to large data sets.

Recent studies suggest that projected clusters with extremely low dimensionality exist in many real datasets. A number of projected clustering algorithms have been proposed in the past several years, but few can identify clusters with dimensionality lower than 10% of the total number of dimensions, which are commonly found in some real datasets such as gene expression profiles. In this paper we propose a new algorithm that can accurately identify projected clusters with relevant dimensions as few as 5% of the total number of dimensions. It makes use of a robust objective function that combines object clustering and dimension selection into a single optimization problem. The algorithm can also utilize domain knowledge in the form of labeled objects and labeled dimensions to improve its clustering accuracy. We believe this is the first semi-supervised projected clustering algorithm. Both theoretical analysis and experimental results show that by using a small amount of input knowledge, possibly covering only a portion of the underlying classes, the new algorithm can be further improved to accurately detect clusters with only 1% of the dimensions being relevant. The algorithm is also useful in getting a target set of clusters when there are multiple possible groupings of the objects.

In high-dimensional data, clusters can exist in subspaces that hide themselves from traditional clustering methods. A number of algorithms have been proposed to identify such projected clusters, but most of them rely on some user parameters to guide the clustering process. The clustering accuracy can be seriously degraded if incorrect values are used. Unfortunately, in real situations, it is rarely possible for users to supply the parameter values accurately, which causes practical difficulties in applying these algorithms to real data. In this paper, we analyze the major challenges of projected clustering and suggest why these algorithms need to depend heavily on user parameters. Based on the analysis, we propose a new algorithm that exploits the clustering status to adjust the internal thresholds dynamically without the assistance of user parameters. According to the results of extensive experiments on real and synthetic data, the new method has excellent accuracy and usability. It outperformed the other algorithms even when correct parameter values were artificially supplied to them. The encouraging results suggest that projected clustering can be a practical tool for various kinds of real applications.

This paper presents an empirical study on the visual method for cluster validation based on the Fastmap projection. The visual cluster validation method attempts to tackle two clustering problems in data mining: to verify partitions of data created by a clustering algorithm; and to identify genuine clusters from data partitions. They are achieved through projecting objects and clusters by Fastmap to the 2D space and visually examining the results by humans. A Monte Carlo evaluation of the visual method was conducted. The validation results of the visual method were compared with the results of two internal statistical cluster validation indices, which shows that the visual method is in consistence with the statistical validation methods. This indicates that the visual cluster validation method is indeed effective and applicable to data mining applications.