ABSTRACT Image segmentation serves as a fundamental task in computer vision and image analysis, holding critical application value in key domains such as medical imaging analysis and autonomous driving. However, traditional active contour models still face three major challenges in practical applications: noise interference, intensity inhomogeneity and complex background effects. To address these issues, this study proposes an improved active contour model based on a probability density function. Through innovative redefinition of local statistical features (mean and variance), the model achieves precise modelling of image intensity distribution and constructs a robust energy functional framework driven by the probability density function. This improvement delivers three key advantages: (1) significantly enhanced robustness to noise and intensity inhomogeneity; (2) improved boundary detection capability; and (3) guaranteed convergence of the energy functional to global optima. To further optimize performance, we introduce a dual mechanism incorporating both length penalty and distance regularization terms, effectively maintaining the geometric accuracy and numerical stability of evolving curves. Experimental results demonstrate that the new model not only accurately segments noisy and intensity‐inhomogeneous images while avoiding local optima, but also exhibits outstanding performance in medical image processing, with both robustness and segmentation accuracy significantly surpassing those of comparison algorithms. The code is available at: https://github.com/MXC646964/Demo_ACM_PDF .

The trade-off between expressiveness and interpretability remains a core challenge when building human-centric models for classification and decision-making. While symbolic rules offer interpretability, they often lack expressiveness, whereas neural networks excel in performance but are known for being black boxes. This paper shows a combination of Large Language Models (LLMs) and symbolic programs can bridge this gap. In the proposed LLM-based Symbolic Programs (LSPs), the pretrained LLM with natural language prompts provides a massive set of interpretable modules that can transform raw input into natural language concepts. Symbolic programs then integrate these modules into interpretable decision rules. To train LSPs, we develop a divide-and-conquer approach to incrementally build the program from scratch, where the learning process of each step is guided by LLMs. To evaluate the effectiveness of LSPs in extracting interpretable and accurate knowledge from data, we introduce IL-Bench, a collection of diverse tasks, including both synthetic and real-world scenarios across different modalities. Empirical results demonstrate LSP's superior performance compared to traditional neurosymbolic programs and vanilla automatic prompt tuning methods. Moreover, as the knowledge learned by LSP is a combination of natural language descriptions and symbolic rules, it is easily transferable to humans (interpretable), and other LLMs, and generalizes well to out-of-distribution samples. Our code and benchmark will be released for future research.

Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the updates depending on how the two LoRA factors are scaled or rotated. This deficiency leads to inefficient learning and sub-optimal solutions in practice. This paper introduces LoRA-RITE, a novel adaptive matrix preconditioning method for LoRA optimization, which can achieve transformation invariance and remain computationally efficient. We provide theoretical analysis to demonstrate the benefit of our method and conduct experiments on various LLM tasks with different models including Gemma 2B, 7B, and mT5-XXL. The results demonstrate consistent improvements against existing optimizers. For example, replacing Adam with LoRA-RITE during LoRA fine-tuning of Gemma-2B yielded 4.6% accuracy gain on Super-Natural Instructions and 3.5% accuracy gain across other four LLM benchmarks (HellaSwag, ArcChallenge, GSM8K, OpenBookQA).

This work proposes the Lattice Boltzmann Model (LBM) to learn real-world pixel dynamicity for visual tracking. LBM decomposes visual representations into dynamic pixel lattices and solves pixel motion states through collision-streaming processes. Specifically, the high-dimensional distribution of the target pixels is acquired through a multilayer predict-update network to estimate the pixel positions and visibility. The predict stage formulates lattice collisions among the spatial neighborhood of target pixels and develops lattice streaming within the temporal visual context. The update stage rectifies the pixel distributions with online visual representations. Compared with existing methods, LBM demonstrates practical applicability in an online and real-time manner, which can efficiently adapt to real-world visual tracking tasks. Comprehensive evaluations of real-world point tracking benchmarks such as TAP-Vid and RoboTAP validate LBM's efficiency. A general evaluation of large-scale open-world object tracking benchmarks such as TAO, BFT, and OVT-B further demonstrates LBM's real-world practicality.

Pretrained large language models (LLMs) are general purpose problem solvers applicable to a diverse set of tasks with prompts. They can be further improved towards a specific task by fine-tuning on a specialized dataset. However, fine-tuning usually makes the model narrowly specialized on this dataset with reduced general in-context learning performances, which is undesirable whenever the fine-tuned model needs to handle additional tasks where no fine-tuning data is available. In this work, we first demonstrate that fine-tuning on a single task indeed decreases LLMs' general in-context learning performance. We discover one important cause of such forgetting, format specialization, where the model overfits to the format of the fine-tuned task.We further show that format specialization happens at the very beginning of fine-tuning. To solve this problem, we propose Prompt Tuning with MOdel Tuning (ProMoT), a simple yet effective two-stage fine-tuning framework that reduces format specialization and improves generalization.ProMoT offloads task-specific format learning into additional and removable parameters by first doing prompt tuning and then fine-tuning the model itself with this soft prompt attached. With experiments on several fine-tuning tasks and 8 in-context evaluation tasks, we show that ProMoT achieves comparable performance on fine-tuned tasks to standard fine-tuning, but with much less loss of in-context learning performances across a board range of out-of-domain evaluation tasks. More importantly, ProMoT can even enhance generalization on in-context learning tasks that are semantically related to the fine-tuned task, e.g. ProMoT on En-Fr translation significantly improves performance on other language pairs, and ProMoT on NLI improves performance on summarization. Experiments also show that ProMoT can improve the generalization performance of multi-task training.

Dataset Distillation is a newly emerging area that aims to distill large datasets into much smaller and highly informative synthetic ones to accelerate training and reduce storage. Among various dataset distillation methods, trajectory-matching-based methods (MTT) have achieved SOTA performance in many tasks, e.g., on CIFAR-10/100. However, due to exorbitant memory consumption when unrolling optimization through SGD steps, MTT fails to scale to large-scale datasets such as ImageNet-1K. Can we scale this SOTA method to ImageNet-1K and does its effectiveness on CIFAR transfer to ImageNet-1K? To answer these questions, we first propose a procedure to exactly compute the unrolled gradient with constant memory complexity, which allows us to scale MTT to ImageNet-1K seamlessly with $\sim 6$x reduction in memory footprint. We further discover that it is challenging for MTT to handle datasets with a large number of classes, and propose a novel soft label assignment that drastically improves its convergence. The resulting algorithm sets new SOTA on ImageNet-1K: we can scale up to 50 IPCs (Image Per Class) on ImageNet-1K on a single GPU (all previous methods can only scale to 2 IPCs on ImageNet-1K), leading to the best accuracy (only 5.9% accuracy drop against full dataset training) while utilizing only 4.2% of the number of data points - an 18.2% absolute gain over prior SOTA.

Abstract To segment noisy and multi‐target images, an active contour model based on a hybrid signed pressure force function that fuses global and local information of the image is proposed. Firstly, a local signed pressure force function is defined using the local area information of the image. Then, it is combined with the existing global grey density function to construct a new signed pressure force function. Finally, the selective binary and Gaussian filtering regularized level set are modified using the newly defined function. Extensive experiments and comparisons on both synthetic and real images demonstrate that the proposed method is robust to noise and can handle noisy and multi‐target images with high accuracy.

Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes increasingly large, condensation methods become a prominent direction for accelerating network training and reducing data storage. Despite numerous methods have been proposed in this rapidly growing field, evaluating and comparing different condensation methods is non-trivial and still remains an open issue. The quality of condensed dataset are often shadowed by many critical contributing factors to the end performance, such as data augmentation and model architectures. The lack of a systematic way to evaluate and compare condensation methods not only hinders our understanding of existing techniques, but also discourages practical usage of the synthesized datasets. This work provides the first large-scale standardized benchmark on Dataset Condensation. It consists of a suite of evaluations to comprehensively reflect the generability and effectiveness of condensation methods through the lens of their generated dataset. Leveraging this benchmark, we conduct a large-scale study of current condensation methods, and report many insightful findings that open up new possibilities for future development. The benchmark library, including evaluators, baseline methods, and generated datasets, is open-sourced to facilitate future research and application.

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where $L_2$ distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g., dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous neural network framework called Neural Stochastic Differential Equation (Neural SDE), which naturally incorporates various commonly used regularization mechanisms based on random noise injection. For regularization purposes, our framework includes multiple types of noise patterns, such as dropout, additive, and multiplicative noise, which are common in plain neural networks. We provide some theoretical analyses explaining the improved robustness of our models against input perturbations. Furthermore, we demonstrate that the Neural SDE network can achieve better generalization than the Neural ODE and is more resistant to adversarial and non-adversarial input perturbations.

Multi-stage training and knowledge transfer, from a large-scale pretraining task to various finetuning tasks, have revolutionized natural language processing and computer vision resulting in state-of-the-art performance improvements. In this paper, we develop a multi-stage influence function score to track predictions from a finetuned model all the way back to the pretraining data. With this score, we can identify the pretraining examples in the pretraining task that contribute most to a prediction in the finetuning task. The proposed multi-stage influence function generalizes the original influence function for a single model in (Koh &Liang, 2017), thereby enabling influence computation through both pretrained and finetuned models. We study two different scenarios with the pretrained embedding fixed or updated in the finetuning tasks. We test our proposed method in various experiments to show its effectiveness and potential applications.

The concept of conditional computation for deep nets has been proposed previously to improve model performance by selectively using only parts of the model conditioned on the sample it is processing. In this paper, we investigate input-dependent dynamic filter selection in deep convolutional neural networks (CNNs). The problem is interesting because the idea of forcing different parts of the model to learn from different types of samples may help us acquire better filters in CNNs, improve the model generalization performance and potentially increase the interpretability of model behavior. We propose a novel yet simple framework called GaterNet, which involves a backbone and a gater network. The backbone network is a regular CNN that performs the major computation needed for making a prediction, while a global gater network is introduced to generate binary gates for selectively activating filters in the backbone network based on each input. Extensive experiments on CIFAR and ImageNet datasets show that our models consistently outperform the original models with a large margin. On CIFAR-10, our model also improves upon state-of-the-art results.

Existing attention mechanisms are trained to attend to individual items in a collection (the memory) with a predefined, fixed granularity, e.g., a word token or an image grid. We propose area attention: a way to attend to areas in the memory, where each area contains a group of items that are structurally adjacent, e.g., spatially for a 2D memory such as images, or temporally for a 1D memory such as natural language sentences. Importantly, the shape and the size of an area are dynamically determined via learning, which enables a model to attend to information with varying granularity. Area attention can easily work with existing model architectures such as multi-head attention for simultaneously attending to multiple areas in the memory. We evaluate area attention on two tasks: neural machine translation (both character and token-level) and image captioning, and improve upon strong (state-of-the-art) baselines in all the cases. These improvements are obtainable with a basic form of area attention that is parameter free.

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by~\citezhang2018gaan.

We study the robustness verification problem of tree based models, including random forest (RF) and gradient boosted decision tree (GBDT). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches cast this verification problem into a mixed integer linear programming (MILP) problem, which finds the minimal adversarial distortion in exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles the verification problem can be cast as a max-clique problem on a multi-partite boxicity graph. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we devise an efficient verification algorithm that can give tight lower bounds on robustness of decision tree ensembles, and allows iterative improvement and any-time termination. On RF/GBDT models trained on a variety of datasets, we significantly outperform the lower bounds obtained by relaxing the MILP formulation into a linear program (LP), and are hundreds times faster than solving MILPs to get the exact minimal adversarial distortion. Our proposed method is capable of giving tight robustness verification bounds on large GBDTs with hundreds of deep trees.

In this paper, we proposed a general framework for data poisoning attacks to graph-based semi-supervised learning (G-SSL). In this framework, we first unify different tasks, goals and constraints into a single formula for data poisoning attack in G-SSL, then we propose two specialized algorithms to efficiently solve two important cases --- poisoning regression tasks under $\ell_2$-norm constraint and classification tasks under $\ell_0$-norm constraint. In the former case, we transform it into a non-convex trust region problem and show that our gradient-based algorithm with delicate initialization and update scheme finds the (globally) optimal perturbation. For the latter case, although it is an NP-hard integer programming problem, we propose a probabilistic solver that works much better than the classical greedy method. Lastly, we test our framework on real datasets and evaluate the robustness of G-SSL algorithms. For instance, on the MNIST binary classification problem (50000 training data with 50 labeled), flipping two labeled data is enough to make the model perform like random guess (around 50\% error).

Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. For advanced NLP problems, a neural language model usually consists of recurrent layers (e.g., using LSTM cells), an embedding matrix for representing input tokens, and a softmax layer for generating output tokens. For problems with a very large vocabulary size, the embedding and the softmax matrices can account for more than half of the model size. For instance, the bigLSTM model achieves state-of-the-art performance on the One-Billion-Word (OBW) dataset with around 800k vocabulary, and its word embedding and softmax matrices use more than 6GBytes space, and are responsible for over 90\% of the model parameters. In this paper, we propose GroupReduce, a novel compression method for neural language models, based on vocabulary-partition (block) based low-rank matrix approximation and the inherent frequency distribution of tokens (the power-law distribution of words). We start by grouping words into $c$ blocks based on their frequency, and then refine the clustering iteratively by constructing weighted low-rank approximation for each block, where the weights are based the frequencies of the words in the block. The experimental results show our method can significantly outperform traditional compression methods such as low-rank approximation and pruning. On the OBW dataset, our method achieved 6.6x compression rate for the embedding and softmax matrices, and when combined with quantization, our method can achieve 26x compression rate without losing prediction accuracy.

In this paper, we study the gradient boosted decision trees (GBDT) when the output space is high dimensional and sparse. For example, in multilabel classification, the output space is a $L$-dimensional 0/1 vector, where $L$ is number of labels that can grow to millions and beyond in many modern applications. We show that vanilla GBDT can easily run out of memory or encounter near-forever running time in this regime, and propose a new GBDT variant, GBDT-SPARSE, to resolve this problem by employing $L_0$ regularization. We then discuss in detail how to utilize this sparsity to conduct GBDT training, including splitting the nodes, computing the sparse residual, and predicting in sublinear time. Finally, we apply our algorithm to extreme multilabel classification problems, and show that the proposed GBDT-SPARSE achieves an order of magnitude improvements in model size and prediction time over existing methods, while yielding similar performance.

Nonlinear kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines using multiple computers. In particular, we develop a parallel block minimization framework, and demonstrate its good scalability in solving nonlinear kernel SVM and logistic regression. Our framework proceeds by dividing the problem into smaller subproblems by forming a block-diagonal approximation of the Hessian matrix. The subproblems are then solved approximately in parallel. After that, a communication efficient line search procedure is developed to ensure sufficient reduction of the objective function value by exploiting the problem structure of kernel machines. We prove global linear convergence rate of the proposed method with a wide class of subproblem solvers, and our analysis covers strongly convex and some non-strongly convex functions. We apply our algorithm to solve large-scale kernel SVM problems on distributed systems, and show a significant improvement over existing parallel solvers. As an example, on the covtype dataset with half-a-million samples, our algorithm can obtain an approximate solution with 96% accuracy in 20 seconds using 32 machines, while all the other parallel kernel SVM solvers require more than 2000 seconds to achieve a solution with 95% accuracy. Moreover, our algorithm is the first distributed kernel SVM solver that can scale to massive data sets. On the KDDB dataset (20 million samples and 30 million features), our parallel solver can compute the kernel SVM solution within half an hour using 32 machines with 640 cores in total, while existing solvers can not scale to this dataset.

Scaling kernel machines to massive data sets is a major challenge due to storage and computation issues in handling large kernel matrices, that are usually dense. Recently, many papers have suggested tackling this problem by using a low-rank approximation of the kernel matrix. In this paper, we first make the observation that the structure of shift-invariant kernels changes from low-rank to block-diagonal (without any low-rank structure) when varying the scale parameter. Based on this observation, we propose a new kernel approximation framework -- Memory Efficient Kernel Approximation (MEKA), which considers both low-rank and clustering structure of the kernel matrix. We show that the resulting algorithm outperforms state-of-the-art low-rank kernel approximation methods in terms of speed, approximation error, and memory usage. As an example, on the covtype dataset with half a million samples, MEKA takes around 70 seconds and uses less than 80 MB memory on a single machine to achieve 10% relative approximation error, while standard Nyström approximation is about 6 times slower and uses more than 400MB memory to achieve similar approximation. We also present extensive experiments on applying MEKA to speed up kernel ridge regression.

Our goal is to improve the \it training and \it prediction time of Nyström method, which is a widely-used technique for generating low-rank kernel matrix approximations. When applying the Nyström approximation for large-scale applications, both training and prediction time is dominated by computing kernel values between a data point and all landmark points. With m landmark points, this computation requires Θ(md) time (flops), where d is the input dimension. In this paper, we propose the use of a family of fast transforms to generate structured landmark points for Nyström approximation. By exploiting fast transforms, e.g., Haar transform and Hadamard transform, our modified Nyström method requires only Θ(m) or Θ(m\log d) time to compute the kernel values between a given data point and m landmark points. This improvement in time complexity can significantly speed up kernel approximation and benefit prediction speed in kernel machines. For instance, on the webspam data (more than 300,000 data points), our proposed algorithm enables kernel SVM prediction to deliver 98% accuracy and the resulting prediction time is 1000 times faster than LIBSVM and only 10 times slower than linear SVM prediction (which yields only 91% accuracy).

Matrix completion (MC) with additional information has found wide applicability in several machine learning applications. Among algorithms for solving such problems, Inductive Matrix Completion(IMC) has drawn a considerable amount of attention, not only for its well established theoretical guarantees but also for its superior performance in various real-world applications. However, IMC based methods usually place very strong constraints on the quality of the features(side information) to ensure accurate recovery, which might not be met in practice. In this paper, we propose Goal-directed Inductive Matrix Completion(GIMC) to learn a nonlinear mapping of the features so that they satisfy the required properties. A key distinction between GIMC and IMC is that the feature mapping is learnt in a supervised manner, deviating from the traditional approach of unsupervised feature learning followed by model training. We establish the superiority of our method on several popular machine learning applications including multi-label learning, multi-class classification, and semi-supervised clustering.

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within 10^-6 relative error) which achieves 96.15% prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM.

The scalability of kernel machines is a big challenge when facing millions of samples due to storage and computation issues for large kernel matrices, that are usually dense. Recently, many papers have suggested tackling this problem by using a low rank approximation of the kernel matrix. In this paper, we first make the observation that the structure of shift-invariant kernels changes from low-rank to block-diagonal (without any low-rank structure) when varying the scale parameter. Based on this observation, we propose a new kernel approximation algorithm – Memory Efficient Kernel Approximation (MEKA), which considers both low-rank and clustering structure of the kernel matrix. We show that the resulting algorithm outperforms state-of-the-art low-rank kernel approximation methods in terms of speed, approximation error, and memory usage. As an example, on the MNIST2M dataset with two-million samples, our method takes 550 seconds on a single machine using less than 500 MBytes memory to achieve 0.2313 test RMSE for kernel ridge regression, while standard Nyström approximation takes more than 2700 seconds and uses more than 2 GBytes memory on the same problem to achieve 0.2318 test RMSE.

The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basic idea of MSLP is to construct low-rank approximations of the network at multiple scales in an efficient manner. To achieve this, we propose a fast tree-structured approximation algorithm.

Matrix factorization, when the matrix has missing values, has become one of the leading techniques for recommender systems. To handle web-scale datasets with millions of users and billions of ratings, scalability becomes an important issue. Alternating Least Squares (ALS) and Stochastic Gradient Descent (SGD) are two popular approaches to compute matrix factorization. There has been a recent flurry of activity to parallelize these algorithms. However, due to the cubic time complexity in the target rank, ALS is not scalable to large-scale datasets. On the other hand, SGD conducts efficient updates but usually suffers from slow convergence that is sensitive to the parameters. Coordinate descent, a classical optimization approach, has been used for many other large-scale problems, but its application to matrix factorization for recommender systems has not been explored thoroughly. In this paper, we show that coordinate descent based methods have a more efficient update rule compared to ALS, and are faster and have more stable convergence than SGD. We study different update sequences and propose the CCD++ algorithm, which updatesrank-one factors one by one. In addition, CCD++ can be easily parallelized on both multi-core and distributed systems. We empirically show that CCD++ is much faster than ALS and SGD in both settings. As an example, on a synthetic dataset with 2 billion ratings, CCD++ is 4 times faster than both SGD and ALS using a distributed system with 20 machines.

Distribution calibration plays an important role in cross-domain learning. However, existing distribution distance metrics are not geodesic; therefore, they cannot measure the intrinsic distance between two distributions. In this paper, we calibrate two distributions by using the geodesic distance in Riemannian symmetric space. Our method learns a latent subspace in the reproducing kernel Hilbert space, where the geodesic distance between the distribution of the source and the target domains is minimized. The corresponding geodesic distance is thus equivalent to the geodesic distance between two symmetric positive definite (SPD) matrices defined in the Riemannian symmetric space. These two SPD matrices parameterize the marginal distributions of the source and target domains in the latent subspace. We carefully design an evolutionary algorithm to find a local optimal solution that minimizes this geodesic distance. Empirical studies on face recognition, text categorization, and web image annotation suggest the effectiveness of the proposed scheme.

Dimension reduction algorithms have attracted a lot of attentions in face recognition because they can select a subset of effective and efficient discriminative features in the face images. Most of dimension reduction algorithms can not well model both the intra-class geometry and interclass discrimination simultaneously. In this paper, we introduce the Discriminative Hessian Eigenmaps (DHE), a novel dimension reduction algorithm to address this problem. DHE will consider encoding the geometric and discriminative information in a local patch by improved Hessian Eigenmaps and margin maximization respectively. Empirical studies on public face database thoroughly demonstrate that DHE is superior to popular algorithms for dimension reduction, e.g., FLDA, LPP, MFA and DLA.

Is it possible to train a learning model to separate tigers from elks when we have 1) labeled samples of leopard and zebra and 2) unlabelled samples of tiger and elk at hand? Cross-domain learning algorithms can be used to solve the above problem. However, existing cross-domain algorithms cannot be applied for dimension reduction, which plays a key role in computer vision tasks, e.g., face recognition and web image annotation. This paper envisions the cross-domain discriminative dimension reduction to provide an effective solution for cross-domain dimension reduction. In particular, we propose the cross-domain discriminative Hessian Eigenmaps or CDHE for short. CDHE connects training and test samples by minimizing the quadratic distance between the distribution of the training set and that of the test set. Therefore, a common subspace for data representation can be well preserved. Furthermore, we basically expect the discriminative information used to separate leopards and zebra can be shared to separate tigers and elks, and thus we have a chance to duly address the above question. Margin maximization principle is adopted in CDHE so the discriminative information for separating different classes (e.g., leopard and zebra here) can be well preserved. Finally, CDHE encodes the local geometry of each training class (e.g., leopard and zebra here) in the local tangent space which is locally isometric to the data manifold and thus CDHE preserves the intraclass local geometry. The objective function of CDHE is not convex, so the gradient descent strategy can only find a local optimal solution. In this paper, we carefully design an evolutionary search strategy to find a better solution of CDHE. Experimental evidence on both synthetic and real word image datasets demonstrates the effectiveness of CDHE for cross-domain web image annotation and face recognition.

The regularization principals [31] lead approximation schemes to deal with various learning problems, e.g., the regularization of the norm in a reproducing kernel Hilbert space for the ill-posed problem. In this paper, we present a family of subspace learning algorithms based on a new form of regularization, which transfers the knowledge gained in training samples to testing samples. In particular, the new regularization minimizes the Bregman divergence between the distribution of training samples and that of testing samples in the selected subspace, so it boosts the performance when training and testing samples are not independent and identically distributed. To test the effectiveness of the proposed regularization, we introduce it to popular subspace learning algorithms, e.g., principal components analysis (PCA) for cross-domain face modeling; and Fisher's linear discriminant analysis (FLDA), locality preserving projections (LPP), marginal Fisher's analysis (MFA), and discriminative locality alignment (DLA) for cross-domain face recognition and text categorization. Finally, we present experimental evidence on both face image data sets and text data sets, suggesting that the proposed Bregman divergence-based regularization is effective to deal with cross-domain learning problems.