A fast weighted median algorithm based on Quickselect

Algorithm selection and hyperparameter tuning are critical steps in both academic and applied machine learning (ML). These steps are becoming increasingly delicate due to the extensive rise in the number, diversity, and distributed nature of ML resources. Multi-agent systems, when applied to the design of ML platforms, bring about several distinctive characteristics, such as scalability, flexibility, and robustness, just to name a few. This article proposes a fully automatic and collaborative agent-based mechanism for selecting distributed ML algorithms and simultaneously tuning their hyperparameters. Our method builds upon an existing agent-based hierarchical ML platform and augments its query structure to support the aforementioned functionalities without being limited to specific learning, selection, and tuning mechanisms. We have conducted theoretical assessments, formal verification, and analytical study to demonstrate the correctness, resource utilization, and computational efficiency of our technique. According to the results, our solution is algorithmically correct and exhibits linear time and space complexity in relation to the size of available resources. To further verify its correctness and demonstrate its effectiveness and flexibility across a range of algorithmic options and datasets, the article also presents a series of empirical results on a system composed of 24 algorithms and 9 datasets. The findings not only highlight the efficiency and scalability of the proposed approach, but also show its flexibility and openness to responding to the dynamic and distributed ML ecosystem.

Detecting sequences containing repetitive regions is a basic bioinformatics task with many applications. Several methods have been developed for various types of repeat detection tasks. An efficient generic method for detecting most types of repetitive sequences is still desirable. Inspired by the excellent properties and successful applications of the D2 family of statistics in comparative analyses of genomic sequences, we developed a new statistic D2R that can efficiently discriminate sequences with or without repetitive regions. Using the statistic, we developed an algorithm of linear time and space complexity for detecting most types of repetitive sequences in multiple scenarios, including finding candidate clustered regularly interspaced short palindromic repeats regions from bacterial genomic or metagenomics sequences. Simulation and real data experiments show that the method works well on both assembled sequences and unassembled short reads. The codes are available at https://github.com/XuegongLab/D2R_codes under GPL 3.0 license. Supplementary data are available at Bioinformatics online.

Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker

Large-scale eigenvector approximation via Hilbert Space Embedding Nyström

The discovery of information encoded in biological sequences is assuming a prominent role in identifying genetic diseases and in deciphering biological mechanisms. This information is usually encoded in patterns frequently occurring in the sequences, also called motifs. In fact, motif discovery has received much attention in the literature, and several algorithms have already been proposed, which are specifically tailored to deal with motifs exhibiting some kinds of regular structure. Motivated by biological observations, this paper focuses on the mining of loosely structured motifs, i.e., of more general kinds of motif where several exceptions may be tolerated in pattern repetitions. To this end, an algorithm exploiting data structures conceived to efficiently handle pattern variabilities is presented and analyzed. Furthermore, a randomized variant with linear time and space complexity is introduced, and a theoretical guarantee on its performances is proven. Both algorithms have been implemented and tested on real data sets. Despite the ability of mining very complex kinds of pattern, performance results evidence a genome-wide applicability of the proposed techniques.

The article introduces a method of finding optimal routes on raster planes. The method presented takes advantage of a new algorithm that tends to minimize a number of direction changes within a route, while steering clear of the obstacles. Two different schemes, suitable for restricted area Vessel Traffic Service (VTS) system and collision avoidance system located on the own ship are described. The VTS-oriented scheme supports VTS priority policy that may extend or override international give-way regulations. The own-ship routing scheme in a give-way situation is capable of determining the shortest safe path to the destination point. The method takes into account own ship dynamics. It has linear time and space complexities and therefore is sufficiently fast to perform real-time routing on the raster grids. Both the general method and the algorithm it uses are presented in detail in the paper. Implementation issues are also discussed.

Online kernel selection is a more complex problem compared with offline kernel selection, which intermixes training and selection at each round and requires a sublinear regret and low computational complexities. But existing online kernel selection approaches have at least linear time and space complexities at each round with respect to the number of rounds, or lack sublinear regret guarantees for an uncountably infinite number of candidate kernels. To address these issues, we propose a novel online kernel selection approach using tensor sketching, which has constant computational complexities at each round and enjoys a sublinear regret bound for an uncountably infinite number of candidate kernels. We represent the data using the tensor products and construct data sketches using the Taylor series and the Count Sketch matrices, which yields a sketched reproducing kernel Hilbert space (SRKHS). Then we update the optimal kernels and the hypotheses using online gradient descent in SRKHS. We prove that the kernel corresponding to SRKHS satisfies the reproducing property, the hypotheses in SRKHS are convex with respect to the kernel parameter, and the proposed online kernel selection approach in SRKHS enjoys a regret bound of order $O(\sqrtT )$ for an uncountably infinite number of candidate kernels, which is optimal for a convex loss function, where T is the number of rounds. By the fast Fourier transform, the hypotheses in SRKHS can be computed in a quasilinear time complexity and a logarithmic space complexity with respect to the sketch size at each round, where the sketch size is a constant. Experimental results demonstrate that our online kernel selection approach is more accurate and efficient for online kernel learning on high dimension data.

In this work, we formalize a generic fast hue-preserving histogram equalization method based on the RGB color space for image contrast enhancement and two versions of that generic process. The first method estimates a RGB 3D histogram to be equalized using R-red, G-green, and B-blue 1D histograms, while the second method employs RG, RB, and GB 2D histograms. The histogram equalization is performed using shift hue-preserving transformations, avoiding unrealistic colors. Our methods have linear time and space complexities with respect to the size of the image and do not need to apply conversions from a color space to another in order to perform the image enhancement. Such design complies with real-time applications requirements. An objective assessment comparing our methods and others is performed using a contrast measure and a color image quality measure, where the quality is established as a weighting of the naturalness and colorfulness indexes. We analyze 300 images from the dataset of the University of Berkeley. Experiments show that the value of the image contrast produced by our methods is in average 50% greater than the original image value, keeping the quality of the produced images close to the original one.

Text-to-Graph extraction aims to automatically extract information graphs consisting of mentions and types from natural language texts. Existing approaches, such as table filling and pairwise scoring, have shown impressive performance on various information extraction tasks, but they are difficult to scale to datasets with longer input texts because of their second-order space/time complexities with respect to the input length. In this work, we propose a Hybrid Span Generator (HySPA) that invertibly maps the information graph to an alternating sequence of nodes and edge types, and directly generates such sequences via a hybrid span decoder which can decode both the spans and the types recurrently in linear time and space complexities. Extensive experiments on the ACE05 dataset show that our approach also significantly outperforms state-of-the-art on the joint entity and relation extraction task.

Patient stratification or disease subtyping is crucial for precision medicine and personalized treatment of complex diseases. The increasing availability of high-throughput molecular data provides a great opportunity for patient stratification. Many clustering methods have been employed to tackle this problem in a purely data-driven manner. Yet, existing methods leveraging high-throughput molecular data often suffers from various limitations, e.g. noise, data heterogeneity, high dimensionality or poor interpretability. Here we introduced an Entropy-based Consensus Clustering (ECC) method that overcomes those limitations all together. Our ECC method employs an entropy-based utility function to fuse many basic partitions to a consensus one that agrees with the basic ones as much as possible. Maximizing the utility function in ECC has a much more meaningful interpretation than any other consensus clustering methods. Moreover, we exactly map the complex utility maximization problem to the classic K -means clustering problem, which can then be efficiently solved with linear time and space complexity. Our ECC method can also naturally integrate multiple molecular data types measured from the same set of subjects, and easily handle missing values without any imputation. We applied ECC to 110 synthetic and 48 real datasets, including 35 cancer gene expression benchmark datasets and 13 cancer types with four molecular data types from The Cancer Genome Atlas. We found that ECC shows superior performance against existing clustering methods. Our results clearly demonstrate the power of ECC in clinically relevant patient stratification. The Matlab package is available at http://scholar.harvard.edu/yyl/ecc . yunfu@ece.neu.edu or yyl@channing.harvard.edu. Supplementary data are available at Bioinformatics online.

Despite significant progress, there remain three limitations to the previous multi-view clustering algorithms. First, they often suffer from high computational complexity, restricting their feasibility for large-scale datasets. Second, they typically fuse multi-view information via one-stage fusion, neglecting the possibilities in multi-stage fusions. Third, dataset-specific hyperparameter-tuning is frequently required, further undermining their practicability. In light of this, we propose a fast multi-view clustering via ensembles (FastMICE) approach. Particularly, the concept of random view groups is presented to capture the versatile view-wise relationships, through which the hybrid early-late fusion strategy is designed to enable efficient multi-stage fusions. With multiple views extended to many view groups, three levels of diversity (w.r.t. features, anchors, and neighbors, respectively) are jointly leveraged for constructing the view-sharing bipartite graphs in the early-stage fusion. Then, a set of diversified base clusterings for different view groups are obtained via fast graph partitioning, which are further formulated into a unified bipartite graph for final clustering in the late-stage fusion. Notably, FastMICE has almost linear time and space complexity, and is free of dataset-specific tuning. Experiments on 22 multi-view datasets demonstrate its advantages in scalability (for extremely large datasets), superiority (in clustering performance), and simplicity (to be applied) over the state-of-the-art. Code available: https://github.com/huangdonghere/FastMICE.

This paper tackles the task of Few-Shot Video Object Segmentation (FSVOS), i.e., segmenting objects in the query videos with certain class specified in a few labeled support images. The key is to model the relationship between the query videos and the support images for propagating the object information. This is a many-to-many problem and often relies on full-rank attention, which is computationally intensive. In this paper, we propose a novel Domain Agent Network (DAN), breaking down the full-rank attention into two smaller ones. We consider one single frame of the query video as the domain agent, bridging between the support images and the query video. Our DAN allows a linear space and time complexity as opposed to the original quadratic form with no loss of performance. In addition, we introduce a learning strategy by combining meta-learning with online learning to further improve the segmentation accuracy. We build a FSVOS benchmark on the Youtube-VIS dataset and conduct experiments to demonstrate that our method outperforms baselines on both computational cost and accuracy, achieving the state-of-the-art performance. Code is available at https://github.com/scutpaul/DANet.

Low-rank decomposition meets kernel learning: A generalized Nyström method

Long-term time series forecasting (LTSF) is a critical task across diverse domains. Despite significant advancements in LTSF research, we identify a performance bottleneck in existing LTSF methods caused by the inadequate modeling of Temporal Dependencies within the Target (TDT). To address this issue, we propose a novel and generic temporal modeling framework, Temporal Dependency Alignment (TDAlign), that equips existing LTSF methods with TDT learning capabilities. TDAlign introduces two key innovations: 1) a loss function that aligns the change values between adjacent time steps in the predictions with those in the target, ensuring consistency with variation patterns, and 2) an adaptive loss balancing strategy that seamlessly integrates the new loss function with existing LTSF methods without introducing additional learnable parameters. As a plug-and-play framework, TDAlign enhances existing methods with minimal computational overhead, featuring only linear time complexity and constant space complexity relative to the prediction length. Extensive experiments on six strong LTSF baselines across seven real-world datasets demonstrate the effectiveness and flexibility of TDAlign. On average, TDAlign reduces baseline prediction errors by <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.47%</b> to <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9.19%</b> and change value errors by <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4.57%</b> to <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15.78%</b>, highlighting its substantial performance improvements.

Many computer vision applications can be formulated as labeling problems. However, multilabeling problems are usually very challenging to solve, especially when some ordering constraints are enforced. We solve in this paper a five-parts labeling problem proposed in [6, 7]. In this model, one wants to find an optimal labeling for an image with five possible parts: “left”, “right”, “top”, “bottom” and “center”. The geometric ordering constraints can be read naturally from the names. No previous method can solve the problem with globally optimal solutions in a linear space complexity. We propose an efficient dynamic programming based algorithm which guarantees the global optimal labeling for the five-parts model. The time complexity is O(N1.5) and the space complexity is O(N), with N being the number of pixels in the image. In practice, it runs faster than previous methods. Moreover, it works for both 4-neighborhood and 8-neighborhood settings, and can be easily parallelized for GPU.