Multi-task learning (MTL) aims to improve the performance of multiple related prediction tasks by leveraging useful information from them. Due to their flexibility and ability to reduce unknown coefficients substantially, the task-clustering-based MTL approaches have attracted considerable attention. Motivated by the idea of semisoft clustering of data, we propose a semisoft task clustering approach, which can simultaneously reveal the task cluster structure for both pure and mixed tasks as well as select the relevant features. The main assumption behind our approach is that each cluster has some pure tasks, and each mixed task can be represented by a linear combination of pure tasks in different clusters. To solve the resulting non-convex constrained optimization problem, we design an efficient three-step algorithm. The experimental results based on synthetic and real-world datasets validate the effectiveness and efficiency of the proposed approach. Finally, we extend the proposed approach to a robust task clustering problem.

One of the most fundamental data processing tasks is clustering. Here, one is given a collection of objects, a notion of similarity between those objects, and a clustering objective that scores any given partition according to how well it clusters similar objects together. The goal is then to partition the objects in a way that optimizes this clustering objective. For example, to partition the vertices of a simple graph into two clusters, one might take the clustering objective to be edge cut in the graph complement. This clustering problem is equivalent to MAX-CUT, which is known to be NP-hard [21].

K-means++ is an important algorithm to choose initial cluster centers for the k-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with near optimal running time. Given $n$ data points in $\mathbb{R}^d$, the current state-of-the-art algorithm runs in $\widetilde{O}(k )$ iterations, and each iteration takes $\widetilde{O}(nd k)$ time. The overall running time is thus $\widetilde{O}(n d k^2)$. We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total.

Abstract: We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MPRI scans. Keywords: optimal control, non-linear programming, homotopy methods, optimal path planning, concentric tube robots, stereotactic neurosurgery 1. INTRODUCTION by finding paths of connected voxels that the robot can traverse, subject to constraints on its curvature.

The diverse metabolic pathways are fundamental to all living organisms, as they harvest energy, synthesize biomass components, produce molecules to interact with the microenvironment, and neutralize toxins. While discovery of new metabolites and pathways continues, the prediction of pathways for new metabolites can be challenging. It can take vast amounts of time to elucidate pathways for new metabolites; thus, according to HMDB only 60% of metabolites get assigned to pathways. Here, we present an approach to identify pathways based on metabolite structure. We extracted 201 features from SMILES annotations, and identified new metabolites from PubMed abstracts and HMDB. After applying clustering algorithms to both groups of features, we quantified correlations between metabolites, and found the clusters accurately linked 92% of known metabolites to their respective pathways. Thus, this approach could be valuable for predicting metabolic pathways for new metabolites.

Clustering is a fundamental problem in network analysis that finds closely connected groups of nodes and separates them from other nodes in the graph, while link prediction is to predict whether two nodes in a network are likely to have a link. The definition of both naturally determines that clustering must play a positive role in obtaining accurate link prediction tasks. Yet researchers have long ignored or used inappropriate ways to undermine this positive relationship. In this article, We construct a simple but efficient clustering-driven link prediction framework(ClusterLP), with the goal of directly exploiting the cluster structures to obtain connections between nodes as accurately as possible in both undirected graphs and directed graphs. Specifically, we propose that it is easier to establish links between nodes with similar representation vectors and cluster tendencies in undirected graphs, while nodes in a directed graphs can more easily point to nodes similar to their representation vectors and have greater influence in their own cluster. We customized the implementation of ClusterLP for undirected and directed graphs, respectively, and the experimental results using multiple real-world networks on the link prediction task showed that our models is highly competitive with existing baseline models. The code implementation of ClusterLP and baselines we use are available at https://github.com/ZINUX1998/ClusterLP.

Multi-view attributed graph clustering is an important approach to partition multi-view data based on the attribute feature and adjacent matrices from different views. Some attempts have been made in utilizing Graph Neural Network (GNN), which have achieved promising clustering performance. Despite this, few of them pay attention to the inherent specific information embedded in multiple views. Meanwhile, they are incapable of recovering the latent high-level representation from the low-level ones, greatly limiting the downstream clustering performance. To fill these gaps, a novel Dual Information enhanced multi-view Attributed Graph Clustering (DIAGC) method is proposed in this paper. Specifically, the proposed method introduces the Specific Information Reconstruction (SIR) module to disentangle the explorations of the consensus and specific information from multiple views, which enables GCN to capture the more essential low-level representations. Besides, the Mutual Information Maximization (MIM) module maximizes the agreement between the latent high-level representation and low-level ones, and enables the high-level representation to satisfy the desired clustering structure with the help of the Self-supervised Clustering (SC) module. Extensive experiments on several real-world benchmarks demonstrate the effectiveness of the proposed DIAGC method compared with the state-of-the-art baselines.

The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions. This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster assignments by optimizing only a balancing term. Results on attributed graph datasets show the effectiveness of the proposed approach in terms of clustering performance and computation time.

In this paper, a new methodology is proposed that allows for the low-complexity development of neural network (NN) based equalizers for the mitigation of impairments in high-speed coherent optical transmission systems. In this work, we provide a comprehensive description and comparison of various deep model compression approaches that have been applied to feed-forward and recurrent NN designs. Additionally, we evaluate the influence these strategies have on the performance of each NN equalizer. Quantization, weight clustering, pruning, and other cutting-edge strategies for model compression are taken into consideration. In this work, we propose and evaluate a Bayesian optimization-assisted compression, in which the hyperparameters of the compression are chosen to simultaneously reduce complexity and improve performance. In conclusion, the trade-off between the complexity of each compression approach and its performance is evaluated by utilizing both simulated and experimental data in order to complete the analysis. By utilizing optimal compression approaches, we show that it is possible to design an NN-based equalizer that is simpler to implement and has better performance than the conventional digital back-propagation (DBP) equalizer with only one step per span. This is accomplished by reducing the number of multipliers used in the NN equalizer after applying the weighted clustering and pruning algorithms. Furthermore, we demonstrate that an equalizer based on NN can also achieve superior performance while still maintaining the same degree of complexity as the full electronic chromatic dispersion compensation block. We conclude our analysis by highlighting open questions and existing challenges, as well as possible future research directions.

Temporal sequences of satellite images constitute a highly valuable and abundant resource to analyze a given region. However, the labeled data needed to train most machine learning models are scarce and difficult to obtain. In this context, the current work investigates a fully unsupervised methodology that, given a sequence of images, learns a semantic embedding and then, creates a partition of the ground according to its semantic properties and its evolution over time. We illustrate the methodology by conducting the semantic analysis of a sequence of satellite images of a region of Navarre (Spain). The proposed approach reveals a novel broad perspective of the land, where potentially large areas that share both a similar semantic and a similar temporal evolution are connected in a compact and well-structured manner. The results also show a close relationship between the allocation of the clusters in the geographic space and their allocation in the embedded spaces. The semantic analysis is completed by obtaining the representative sequence of tiles corresponding to each cluster, the linear interpolation between related areas, and a graph that shows the relationships between the clusters, providing a concise semantic summary of the whole region.