Multilingual language models often perform unevenly across different languages due to limited generalization capabilities for some languages. This issue is significant because of the growing interest in making universal language models that work well for all languages. Instruction tuning with multilingual instruction-response pairs has been used to improve model performance across various languages. However, this approach is challenged by high computational costs, a lack of quality tuning data for all languages, and the "curse of multilinguality" -- the performance drop per language after adding many languages. Recent studies have found that working with datasets with few languages and a smaller number of instances can be beneficial. Yet, there exists no systematic investigation into how choosing different languages affects multilingual instruction tuning. Our study proposes a method to select languages for instruction tuning in a linguistically informed way, aiming to boost model performance across languages and tasks. We use a simple algorithm to choose diverse languages and test their effectiveness on various benchmarks and open-ended questions. Our results show that this careful selection generally leads to better outcomes than choosing languages at random. We suggest a new and simple way of enhancing multilingual models by selecting diverse languages based on linguistic features that could help develop better multilingual systems and guide dataset creation efforts. All resources, including the code for language selection and multilingual instruction tuning, are made available in our official repository at https://github.com/GGLAB-KU/ling-informed-mit enabling reproducibility and further research in this area.

Graph based semi-supervised learning is the problem of learning a labeling function for the graph nodes given a few example nodes, often called seeds, usually under the assumption that the graph's edges indicate similarity of labels. This is closely related to the local graph clustering or community detection problem of finding a cluster or community of nodes around a given seed. For this problem, we propose a novel generalization of random walk, diffusion, or smooth function methods in the literature to a convex p-norm cut function. The need for our p-norm methods is that, in our study of existing methods, we find those principled methods based on eigenvector, spectral, random walk, or linear system often have difficulty capturing the correct boundary of a target label or target cluster. In contrast, 1-norm or maxflow-mincut based methods capture the boundary, but cannot grow from small seed set; hybrid procedures that use both have many hard to set parameters.

Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in many domains including phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently popularized objective function for hierarchical clustering due to Dasgupta \cite{Dasgupta16}, namely, minimum cost hierarchical partitioning. Previous algorithms for (approximately) minimizing this objective function require linear time/space complexity. In many applications the underlying graph can be massive in size making it computationally challenging to process the graph even using a linear time/space algorithm. As a result, there is a strong interest in designing algorithms that can perform global computation using only sublinear resources (space, time, and communication).

We study the problem of clustering graphs with additional side-information of node features. The problem is extensively studied, and several existing methods exploit Graph Neural Networks to learn node representations. However, most of the existing methods focus on generic representations instead of their cluster-ability or do not scale to large scale graph datasets. In this work, we propose S3GC which uses contrastive learning along with Graph Neural Networks and node features to learn clusterable features. We empirically demonstrate that S3GC is able to learn the correct cluster structure even when graph information or node features are individually not informative enough to learn correct clusters.

In this paper, we study one challenging issue in multi-view data clustering. Instead, we assume that only a small portion of the matrices has established the correspondence in advance. Such a partially view-aligned problem (PVP) could lead to the intensive labor of capturing or establishing the aligned multi-view data, which has less been touched so far to the best of our knowledge. To solve this practical and challenging problem, we propose a novel multi-view clustering method termed partially view-aligned clustering (PVC). To be specific, PVC proposes to use a differentiable surrogate of the non-differentiable Hungarian algorithm and recasts it as a pluggable module.

With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss.

We study the k -median clustering problem for high-dimensional polygonal curves with finite but unbounded number of vertices. We tackle the computational issue that arises from the high number of dimensions by defining a Johnson-Lindenstrauss projection for polygonal curves. We analyze the resulting error in terms of the Fr\'echet distance, which is a tractable and natural dissimilarity measure for curves. Our clustering algorithms achieve sublinear dependency on the number of input curves via subsampling. Also, we show that the Fr\'echet distance can not be approximated within any factor of less than \sqrt{2} by probabilistically reducing the dependency on the number of vertices of the curves.

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve perfect reconstruction of the tree cut. In the non-realizable setting, we rely on known important-sampling procedures to obtain regret and query complexity bounds. Our algorithms come with theoretical guarantees on the statistical error and, more importantly, lend themselves to {\em linear-time} implementations in the relevant parameters of the problem. We discuss such implementations, prove running time guarantees for them, and present preliminary experiments on real-world datasets showing the compelling practical performance of our algorithms as compared to both passive learning and simple active learning baselines.

The fuzzy or soft k -means objective is a popular generalization of the well-known k -means problem, extending the clustering capability of the k -means to datasets that are uncertain, vague and otherwise hard to cluster. In this paper, we propose a semi-supervised active clustering framework, where the learner is allowed to interact with an oracle (domain expert), asking for the similarity between a certain set of chosen items. We study the query and computational complexities of clustering in this framework. We prove that having a few of such similarity queries enables one to get a polynomial-time approximation algorithm to an otherwise conjecturally NP-hard problem. In particular, we provide algorithms for fuzzy clustering in this setting that ask O(\mathsf{poly}(k)\log n) similarity queries and run with polynomial-time-complexity, where n is the number of items.

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable co-clustering method designed to uncover intricate patterns in high-dimensional, large-scale datasets. Specifically, we first propose a large matrix partitioning algorithm that partitions a large matrix into smaller submatrices, enabling parallel co-clustering. This method employs a probabilistic model to optimize the configuration of submatrices, balancing the computational efficiency and depth of analysis. Additionally, we propose a hierarchical co-cluster merging algorithm that efficiently identifies and merges co-clusters from these submatrices, enhancing the robustness and reliability of the process. Extensive evaluations validate the effectiveness and efficiency of our method. Experimental results demonstrate a significant reduction in computation time, with an approximate 83% decrease for dense matrices and up to 30% for sparse matrices.