Existing federated clustering methods typically assume that either all clients supply the same type of single-modal/multi-modal data, or that different clients provide various modalities describing the same object. However, a prevalent real-world scenario involves clients contributing data from diverse and unrelated modalities. Addressing the challenge of uncovering clustering patterns from such heterogeneous modality data distributed across distinct clients is crucial. In this paper, we propose a novel cross-modal feature decoupling-based mixed federated clustering model. To address client heterogeneity, we introduce a cross-modal feature decoupling module for each client, designed to decouple modality-agnostic and modality-specific features through distinct encoders.Only the modality-agnostic encoder parameters and clustering centers of each client are transmitted to the server. This enables the server to aggregate various modality-agnostic encoders, effectively discovering the global clustering structure while avoiding interference from modality-specific noise. Moreover, we develop a global consistent complementary clustering module to integrate the complementary clustering centers from various clients. The global clustering centers are then dispatched back to clients to guide and calibrate their local clustering models. Experimental results on three public datasets show the superiority of the proposed model compared to classic federated clustering methods.

A significant challenge for Graph Neural Networks (GNNs) lies in accurately performing node classification tasks on heterophilous graphs. Traditional GNN models, which largely rely on the assumption of homophily, often struggle under heterophilous conditions due to the inherent low-pass filtering nature during message-passing among neighboring nodes. Motivated by these limitations, our research explores the dendritic structures found in real neurons, which dynamically amplify and inhibit signals. We demonstrate how the biophysical properties of dendrites enable GNNs to adaptively modulate the Dirichlet energy of graph representations based on the specific context, providing a theoretical justification for integrating neural dendrites into GNNs to improve learning on heterophilous graphs. In this work, we introduce the GDendrite framework, which dynamically adjusts GNN's output response to the various contexts. Our empirical studies, conducted across 13 homophilous and heterophilous benchmark datasets, show that our framework significantly enhances the performance of traditional GNNs in heterophilous settings and outperforms state-of-the-art models in most cases.

Abstract Entity alignment (EA) aims at identifying equivalent entity pairs across different knowledge graphs (KGs) that refer to the same real-world identity. It has been a compelling but challenging task that requires the integration of heterogeneous information from different KGs to expand the knowledge coverage and enhance inference abilities. To circumvent the shortage of prior seed alignments provided for training, recent EA models utilize pseudo-labeling strategies to iteratively add unaligned entity pairs predicted with high confidence to the seed alignments for model training. However, the adverse impact of confirmation bias during pseudo-labeling has been largely overlooked, thus hindering entity alignment performance. To systematically combat confirmation bias, we propose a new Unified Pseudo-Labeling framework for Entity Alignment (UPL-EA) that explicitly alleviates pseudo-labeling errors to boost the performance of entity alignment. UPL-EA achieves this goal through two key innovations: (1) Optimal Transport (OT)-based pseudo-labeling uses discrete OT modeling as an effective means to determine entity correspondences and reduce erroneous matches across two KGs. An effective criterion is derived to infer pseudo-labeled alignments that satisfy one-to-one correspondences; (2) Parallel pseudo-label ensembling refines pseudo-labeled alignments by combining predictions over multiple models independently trained in parallel. The ensembled pseudo-labeled alignments are thereafter used to augment seed alignments to reinforce subsequent model training for alignment inference. The effectiveness of UPL-EA in eliminating pseudo-labeling errors is both theoretically supported and experimentally validated. Our extensive results and in-depth analyses demonstrate the superiority of UPL-EA over 15 competitive baselines and its utility as a general pseudo-labeling framework for entity alignment.

Graph Neural Networks (GNNs) have become a cornerstone in multivariate time series forecasting by addressing the challenge of modeling inter-series dependencies often overlooked by traditional temporal approaches. However, real-world temporal dependencies (inter- and intra-dependencies) are inherently intertwined, making it difficult to treat them as separate processes. Recent pure graph paradigms attempt to capture these dependencies holistically by transforming time series into fully connected graphs. While effective, these methods suffer from prohibitive computational complexity O (( NT ) 2 ), limiting their scalability for large-scale data and long-term forecasting. To address these challenges, we propose UFGTime, a novel framework that leverages spectral signals to construct a "spectral-variate graph," embedding multivariate temporal dependencies in a compact spectral representation and modeling inter- and intra-signal connections through frequency similarities. Empowered by our proposed graph framelet message-passing function, UFGTime efficiently aggregates global information, avoids over-smoothing, and achieves near-linear complexity O ( kNT ). Extensive experiments on diverse datasets demonstrate that UFG-Time consistently outperforms state-of-the-art baselines, offering a scalable, accurate, and resource-efficient pure graph solution for multivariate time series forecasting.

Graph Transformers have demonstrated outstanding performance across various graph-based applications. Despite their success, applying them to large-scale graphs presents significant scalability challenges, limiting their practical use in industrial environments. Recent studies have attempted to overcome this challenge by focusing on the spatial domain of graphs, leading to the development of various scalable models. However, these approaches neglect the spectral characteristics of graphs, which are crucial for adaptively extracting information from full-frequency bands based on the graph’s inherent properties. As a result, existing scalable Graph Transformers tend to rely heavily on low-frequency features, overlooking valuable mid- and high-frequency information. This article proposes the Graph Filter Transformer (GFformer), a framework designed to effectively extract full-frequency information from large-scale graphs. Unlike existing Graph Transformers, GFformer integrates graph filters into the Transformer architecture, thereby enhancing its ability to model both structural and frequency-related properties. Utilizing the proposed Spectral Token Converter (ST-converter), GFformer generates a unique spectral token sequence for each node by incorporating features from diverse frequencies that act as tokens. This design enables the independent learning of node representations in parallel and supports mini-batch training with flexible batch sizes, making GFformer highly scalable. ST-converter employs spectral graph filters, including low-, mid-, and high-pass filters, to extract features serving as tokens. Consequently, each sequence encompasses features from various frequencies, enabling GFformer to capture comprehensive frequency information effectively. Extensive experiments on datasets of varying scales, including both homophilic and heterophilic graphs, consistently demonstrate that GFformer outperforms existing representative methods.

Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with various geometric structures interwoven. However, existing Temporal Knowledge Graph Completion (TKGC) methods either model TKGs in a single space or neglect the heterogeneity of different curvature spaces, thus constraining their capacity to capture these intricate geometric structures. In this paper, we propose a novel Integrating Multi-curvature shared and specific Embedding (IME) model for TKGC tasks. Concretely, IME models TKGs into multi-curvature spaces, including hyperspherical, hyperbolic, and Euclidean spaces. Subsequently, IME incorporates two key properties, namely space-shared property and space-specific property. The space-shared property facilitates the learning of commonalities across different curvature spaces and alleviates the spatial gap caused by the heterogeneous nature of multi-curvature spaces, while the space-specific property captures characteristic features. Meanwhile, IME proposes an Adjustable Multi-curvature Pooling (AMP) approach to effectively retain important information. Furthermore, IME innovatively designs similarity, difference, and structure loss functions to attain the stated objective. Experimental results clearly demonstrate the superior performance of IME over existing state-of-the-art TKGC models.

Long Document Classification (LDC) has attracted great attention in Natural Language Processing and achieved considerable progress owing to the large-scale pre-trained language models. In spite of this, as a different problem from the traditional text classification, LDC is far from being settled. Long documents, such as news and articles, generally have more than thousands of words with complex structures. Moreover, compared with flat text, long documents usually contain multi-modal content of images, which provide rich information but not yet being utilized for classification. In this article, we propose a novel cross-modal method for long document classification, in which multiple granularity feature shifting networks are proposed to integrate the multi-scale text and visual features of long documents adaptively. Additionally, a multi-modal collaborative pooling block is proposed to eliminate redundant fine-grained text features and simultaneously reduce the computational complexity. To verify the effectiveness of the proposed model, we conduct experiments on the Food101 dataset and two constructed multi-modal long document datasets. The experimental results show that the proposed cross-modal method outperforms the single-modal text methods and defeats the state-of-the-art related multi-modal baselines.

The goal of mixed-modality clustering, which differs from typical multi-modality/view clustering, is to divide samples derived from various modalities into several clusters. This task has to solve two critical semantic gap problems: i) how to generate the missing modalities without the pairwise-modality data; and ii) how to align the representations of heterogeneous modalities. To tackle the above problems, this paper proposes a novel mixedmodality clustering model, which integrates the missing-modality generation and the heterogeneous modality alignment into a unified framework. During the missing-modality generation process, a bidirectional mapping is established between different modalities, enabling generation of preliminary representations for the missing-modality using information from another modality. Then the intra-modality bipartite graphs are constructed to help generate better missing-modality representations by weighted aggregating existing intra-modality neighbors. In this way, a pairwise-modality representation for each sample can be obtained. In the process of heterogeneous modality alignment, each modality is modelled as a graph to capture the global structure among intra-modality samples and is aligned against the heterogeneous modality representations through the adaptive heterogeneous graph matching module. Experimental results on three public datasets show the effectiveness of the proposed model compared to multiple state-of-the-art multi-modality/view clustering methods.

To date, various neural methods have been proposed for causal effect estimation based on observational data, where a default assumption is the same distribution and availability of variables at both training and inference (i.e., runtime) stages. However, distribution shift (i.e., domain shift) could happen during runtime, and bigger challenges arise from the impaired accessibility of variables. This is commonly caused by increasing privacy and ethical concerns, which can make arbitrary variables unavailable in the entire runtime data and imputation impractical. We term the co-occurrence of domain shift and inaccessible variablesruntime domain corruption, which seriously impairs the generalizability of a trained counterfactual predictor. To counter runtime domain corruption, we subsume counterfactual prediction under the notion of domain adaptation. Specifically, we upper-bound the error w.r.t. the target domain (i.e., runtime covariates) by the sum of source domain error and inter-domain distribution distance. In addition, we build an adversarially unified variational causal effect model, named VEGAN, with a novel two-stage adversarial domain adaptation scheme to reduce the latent distribution disparity between treated and control groups first, and between training and runtime variables afterwards. We demonstrate that VEGAN outperforms other state-of-the-art baselines on individual-level treatment effect estimation in the presence of runtime domain corruption on benchmark datasets.

The global economic losses caused by credit card fraud are enormous and continuously increasing. Effective and accurate fraud detection has become a crucial task in recent years. Prior approaches can achieve good detection performance under certain conditions. However, these existing methods lack the robustness and scalability to deal with real-world credit card transactional datasets containing a large number of missing values. In this paper, we propose a Feature Importance-based Weighted Graph Neural Network (FIW-GNN) as an effective, stable, and practical solution for credit card fraud detection. First, we propose a method to construct a heterogeneous graph designed for credit card transactional datasets. Next, based on the architecture of the relational graph convolutional network, a feature importance-based method is employed to assign edge weights. Finally, we evaluate the effectiveness of FIW-GNN on two benchmark datasets. The experimental results demonstrate that FIW-GNN outperforms the state-of-the-art baselines in all selected evaluation metrics.

Data similarity computation is a fundamental research topic which underpins many high-level applications based on similarity measures. However, the exact similarity computation has become daunting in large-scale real-world scenarios. Currently, MinHash is a popular technique for efficiently estimating the Jaccard similarity of binary sets and, furthermore, weighted MinHash is utilized to estimate the generalized Jaccard similarity of weighted sets. This review focuses on categorizing and discussing the existing works of weighted MinHash algorithms. Also, we have developed a Python toolbox for the algorithms, and released it in our github.

The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.

The reverse k nearest neighbors (RkNN) query is a prominent yet time-consuming spatial query used in facility siting, influential domain analysis, potential customer analysis, etc. Its aim is to identify all points that consider the query point as one of their k closest points. However, when k is relatively large (e.g. k = 1000), existing RkNN techniques often struggle to provide acceptable response times (within a few seconds). To address this issue, we propose a verification approach called conic section discriminance (CSD). This method serves to determine whether points belong to the RkNN set. With CSD, only a small fraction of candidates require costly k nearest neighbors (kNN) queries for verification, while the rest can be rapidly verified with O(1) complexity. Furthermore, we propose a Voronoi-based candidate generation approach to curtail the candidate set size. By leveraging the VoR-tree structure, we integrate these two approaches to form a novel RkNN algorithm named CSD-RkNN. A comprehensive set of experiments is conducted to compare CSD-RkNN with Slice as the state-of-the-art RkNN algorithm, and VR-RkNN as the original RkNN algorithm on VoR-tree. The results indicate that CSD-RkNN consistently outperforms the other two algorithms, especially when k is relatively large.

Knowledge Graph Completion (KGC) aims at inferring missing entities or relations by embedding them in a low-dimensional space. However, most existing KGC methods generally fail to handle the complex concepts hidden in triplets, so the learned embeddings of entities or relations may deviate from the true situation. In this article, we propose a novel M ulti- c oncept R epresentation L earning (McRL) method for the KGC task, which mainly consists of a multi-concept representation module, a deep residual attention module, and an interaction embedding module. Specifically, instead of the single-feature representation, the multi-concept representation module projects each entity or relation to multiple vectors to capture the complex conceptual information hidden in them. The deep residual attention module simultaneously explores the inter- and intra-connection between entities and relations to enhance the entity and relation embeddings corresponding to the current contextual situation. Moreover, the interaction embedding module further weakens the noise and ambiguity to obtain the optimal and robust embeddings. We conduct the link prediction experiment to evaluate the proposed method on several standard datasets, and experimental results show that the proposed method outperforms existing state-of-the-art KGC methods.

With the powerful learning ability of deep convolutional networks, deep clustering methods can extract the most discriminative information from individual data and produce more satisfactory clustering results. However, existing deep clustering methods usually ignore the relationship between the data. Fortunately, the graph convolutional network can handle such relationships, opening a new research direction for deep clustering. In this paper, we propose a cross-attention based deep clustering framework, named Cross-Attention Fusion based Enhanced Graph Convolutional Network (CaEGCN), which contains four main modules: the cross-attention fusion module which innovatively concatenates the Content Auto-encoder module (CAE) relating to the individual data and Graph Convolutional Auto-encoder module (GAE) relating to the relationship between the data in a layer-by-layer manner, and the self-supervised model that highlights the discriminative information for clustering tasks. While the cross-attention fusion module fuses two kinds of heterogeneous representation, the CAE module supplements the content information for the GAE module, which avoids the over-smoothing problem of GCN. In the GAE module, two novel loss functions are proposed that reconstruct the content and relationship between the data, respectively. Finally, the self-supervised module constrains the distributions of the middle layer representations of CAE and GAE to be consistent. Experimental results on different types of datasets prove the superiority and robustness of the proposed CaEGCN.

Conventional Knowledge Graph Completion (KGC) methods typically map entities and relations to a unified space through the shared mapping matrix, and then interact with entities and relations to infer the missing items in the knowledge graph. Although this shared mapping matrix considers the suitability of all triplets, it neglects the specificity of each triplet. To solve this problem, we dynamically learn one information distributor for each triplet to exchange its specific information. In this paper, we propose a novel Triplet Distributor Network (TDN) for the knowledge graph completion task. Specifically, we adaptively learn one Triplet Distributor (TD) for each triplet to assist the interaction between the entity and relation. Furthermore, on the basis of TD, we creatively design the information exchange layer to dynamically propagate the information of the entity and relation, thus mutually enhancing entity and relation representations. Except for several commonly-used knowledge graph datasets, we still implement the link prediction task on the social-relational and medical datasets to test the proposed method. Experimental results demonstrate that the proposed method performs better than existing state-of-the-art KGC methods. The source codes of this paper are available athttps://github.com/TDNfor Knowledge Graph Completion.git.

Collaborative filtering is a central task in a broad range of recommender systems. As traditional methods train latent variables for user/item individuals under a transductive setting, it requires re-training for out-of-sample inferences. Inductive matrix completion (IMC) solves this problem by learning transformation functions upon engineered features, but it sacrifices model expressiveness and highly depends on feature qualities. In this paper, we propose Geometric Inductive Matrix Completion (GIMC) by introducing hyperbolic geometry and a unified message passing scheme into this generic task. The proposed method is the earliest attempt utilizing capacious hyperbolic space to enhance the capacity of IMC. It is the first work defining continuous explicit feedback prediction within non-Euclidean space by introducing hyperbolic regression for vertex interactions. This is also the first to provide comprehensive evidence that edge semantics can significantly improve recommendations, which is ignored by previous works. The proposed method outperforms the state-of-the-art algorithms with less than 1% parameters compared to its transductive counterparts. Extensive analysis and ablation studies are conducted to reveal the design considerations and practicability for a positive impact to the research community.

Data similarity (or distance) computation is a fundamental research topic which underpins many high-level applications based on similarity measures in machine learning and data mining. However, in large-scale real-world scenarios, the exact similarity computation has become daunting due to “3V” nature (volume, velocity and variety) of big data. In this case, the hashing techniques have been verified to efficiently conduct similarity estimation in terms of both theory and practice. Currently, MinHash is a popular technique for efficiently estimating the Jaccard similarity of binary sets and furthermore, weighted MinHash is generalized to estimate the generalized Jaccard similarity of weighted sets. This review focuses on categorizing and discussing the existing works of weighted MinHash algorithms. In this review, we mainly categorize the weighted MinHash algorithms into quantization-based approaches, “active index”-based ones and others, and show the evolution and inherent connection of the weighted MinHash algorithms, from the integer weighted MinHash ones to the real-valued weighted MinHash ones. Also, we have developed a Python toolbox for the algorithms, and released it in our github. We experimentally conduct a comprehensive study of the standard MinHash algorithm and the weighted MinHash ones in the similarity estimation error and the information retrieval task.

Locality preserving projection (LPP) is a dimensionality reduction algorithm preserving the neighhorhood graph structure of data. However, the conventional LPP is sensitive to outliers existing in data. This article proposes a novel low-rank LPP model called LR-LPP. In this new model, original data are decomposed into the clean intrinsic component and noise component. Then the projective matrix is learned based on the clean intrinsic component which is encoded in low-rank features. The noise component is constrained by theℓ1-norm which is more robust to outliers. Finally, LR-LPP model is extended to LR-FLPP in which low-dimensional feature is measured by F-norm. LR-FLPP will reduce aggregated error and weaken the effect of outliers, which will make the proposed LR-FLPP even more robust for outliers. The experimental results on public image databases demonstrate the effectiveness of the proposed LR-LPP and LR-FLPP.

Linear discriminant analysis (LDA) is a well-known supervised method for dimensionality reduction in which the global structure of data can be preserved. The classical LDA is sensitive to the noises, and the projection direction of LDA cannot preserve the main energy. This article proposes a novel feature extraction model with l 2,1 norm constraint based on LDA, termed as RALDA. This model preserves within-class local structure in the latent subspace according to the label information. To reduce information loss, it learns a projection matrix and an inverse projection matrix simultaneously. By introducing an implicit variable and matrix norm transformation, the alternating direction multiple method with updating variables is designed to solve the RALDA model. Moreover, both computational complexity and weak convergence property of the proposed algorithm are investigated. The experimental results on several public databases have demonstrated the effectiveness of our proposed method.

Dimensionality reduction is widely used to deal with high-dimensional data. As a famous dimensionality reduction method, principal component analysis (PCA) aiming at finding the low dimension feature of original data has made great successes, and many improved PCA algorithms have been proposed. However, most algorithms based on PCA only consider the linear correlation of data features. In this article, we propose a novel dimensionality reduction model called maximally correlated PCA based on deep parameterization learning (MCPCADP), which takes nonlinear correlation into account in the deep parameterization framework for the purpose of dimensionality reduction. The new model explores nonlinear correlation by maximizing Ky-Fan norm of the covariance matrix of nonlinearly mapped data features. A new BP algorithm for model optimization is derived. In order to assess the proposed method, we conduct experiments on both a synthetic database and several real-world databases. The experimental results demonstrate that the proposed algorithm is comparable to several widely used algorithms.

Restricted Boltzmann machine (RBM) is a famous model for feature extraction and can be used as an initializer for neural networks. When applying the classic RBM to multidimensional data such as 2D/3D tensors, one needs to vectorize such as high-order data. Vectorizing will result in dimensional disaster and valuable spatial information loss. As RBM is a model with fully connected layers, it requires a large amount of memory. Therefore, it is difficult to use RBM with high-order data on low-end devices. In this article, to utilize classic RBM on tensorial data directly, we propose a new tensorial RBM model parameterized by the tensor train format (TTRBM). In this model, both visible and hidden variables are in tensorial form, which are connected by a parameter matrix in tensor train format. The biggest advantage of the proposed model is that TTRBM can obtain comparable performance compared with the classic RBM with much fewer model parameters and faster training process. To demonstrate the advantages of TTRBM, we conduct three real-world applications, face reconstruction, handwritten digit recognition, and image super-resolution in the experiments.

Clustering is one of the fundamental topics in data mining and pattern recognition. As a prospective clustering method, the subspace clustering has made considerable progress in recent researches, e.g., sparse subspace clustering (SSC) and low rank representation (LRR). However, most existing subspace clustering algorithms are designed for vectorial data from linear spaces, thus not suitable for high-dimensional data with intrinsic non-linear manifold structure. For high-dimensional or manifold data, few research pays attention to clustering problems. The purpose of clustering on manifolds tends to cluster manifold-valued data into several groups according to the mainfold-based similarity metric. This article proposes an extended LRR model for manifold-valued Grassmann data that incorporates prior knowledge by minimizing partial sum of singular values instead of the nuclear norm, namely Partial Sum minimization of Singular Values Representation (GPSSVR). The new model not only enforces the global structure of data in low rank, but also retains important information by minimizing only smaller singular values. To further maintain the local structures among Grassmann points, we also integrate the Laplacian penalty with GPSSVR. The proposed model and algorithms are assessed on a public human face dataset, some widely used human action video datasets and a real scenery dataset. The experimental results show that the proposed methods obviously outperform other state-of-the-art methods.

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. Tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model's dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Dimensionality reduction has been considered as one of the most significant tools for data analysis. In general, supervised information is helpful for dimensionality reduction. However, in typical real applications, supervised information in multiple source tasks may be available, while the data of the target task are unlabeled. An interesting problem of how to guide the dimensionality reduction for the unlabeled target data by exploiting useful knowledge, such as label information, from multiple source tasks arises in such a scenario. In this paper, we propose a new method for dimensionality reduction in the transfer learning setting. Unlike traditional paradigms where the useful knowledge from multiple source tasks is transferred through distance metric, our proposal firstly converts the dimensionality reduction problem into integral regression problems in parallel. Gaussian process is then employed to learn the underlying relationship between the original data and the reduced data. Such a relationship can be appropriately transferred to the target task by exploiting the prediction ability of the Gaussian process model and inventing different kinds of regularizers. Extensive experiments on both synthetic and real data sets show the effectiveness of our method.