Self-Supervised Learning (SSL) surmises that inputs and pairwise positive relationships are enough to learn meaningful representations. Although SSL has recently reached a milestone: outperforming supervised methods in many modalities\dots the theoretical foundations are limited, method-specific, and fail to provide principled design guidelines to practitioners. In this paper, we propose a unifying framework under the helm of spectral manifold learning. Through the course of this study, we will demonstrate that VICReg, SimCLR, BarlowTwins et al. correspond to eponymous spectral methods such as Laplacian Eigenmaps, ISOMAP et al.From this unified viewpoint, we obtain (i) the close-form optimal representation, (ii) the close-form optimal network parameters in the linear regime, (iii) the impact of the pairwise relations used during training on each of those quantities and on downstream task performances, and most importantly, (iv) the first theoretical bridge between contrastive and non-contrastive methods to global and local spectral methods respectively hinting at the benefits and limitations of each. For example, if the pairwise relation is aligned with the downstream task, all SSL methods produce optimal representations for that downstream task.

Self-Supervised Learning (SSL) surmises that inputs and pairwise positive relationships are enough to learn meaningful representations. Although SSL has recently reached a milestone: outperforming supervised methods in many modalities\dots the theoretical foundations are limited, method-specific, and fail to provide principled design guidelines to practitioners. In this paper, we propose a unifying framework under the helm of spectral manifold learning. Through the course of this study, we will demonstrate that VICReg, SimCLR, BarlowTwins et al. correspond to eponymous spectral methods such as Laplacian Eigenmaps, ISOMAP et al.From this unified viewpoint, we obtain (i) the close-form optimal representation, (ii) the close-form optimal network parameters in the linear regime, (iii) the impact of the pairwise relations used during training on each of those quantities and on downstream task performances, and most importantly, (iv) the first theoretical bridge between contrastive and non-contrastive methods to global and local spectral methods respectively hinting at the benefits and limitations of each. For example, if the pairwise relation is aligned with the downstream task, all SSL methods produce optimal representations for that downstream task.

Correlation clustering is a powerful unsupervised learning paradigm that supports positive and negative similarities. In this paper, we assume the similarities are not known in advance. Instead, we employ active learning to iteratively query similarities in a cost-efficient way. In particular, we develop three effective acquisition functions to be used in this setting. One is based on the notion of inconsistency (i.e., when similarities violate the transitive property). The remaining two are based on information-theoretic quantities, i.e., entropy and information gain.

To understand a narrative, it is essential to comprehend the temporal event flows, especially those associated with main characters; however, this can be challenging with lengthy and unstructured narrative texts. To address this, we introduce NECE, an open-access, document-level toolkit that automatically extracts and aligns narrative events in the temporal order of their occurrence. Through extensive evaluations, we show the high quality of the NECE toolkit and demonstrates its downstream application in analyzing narrative bias regarding gender. We also openly discuss the shortcomings of the current approach, and potential of leveraging generative models in future works. Lastly the NECE toolkit includes both a Python library and a user-friendly web interface, which offer equal access to professionals and layman audience alike, to visualize event chain, obtain narrative flows, or study narrative bias.

Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available in the datasets. There are two challenges that lie at the heart of this problem: 1) how to handle the huge search space of potential hyperedges, and 2) how to define meaningful criteria to measure the relationship between the signals observed on nodes and the hypergraph structure. In this paper, for the first challenge, we adopt the assumption that the ideal hypergraph structure can be derived from a learnable graph structure that captures the pairwise relations within signals. Further, we propose a hypergraph structure learning framework HGSL with a novel dual smoothness prior that reveals a mapping between the observed node signals and the hypergraph structure, whereby each hyperedge corresponds to a subgraph with both node signal smoothness and edge signal smoothness in the learnable graph structure. Finally, we conduct extensive experiments to evaluate HGSL on both synthetic and real world datasets. Experiments show that HGSL can efficiently infer meaningful hypergraph topologies from observed signals.

Deep auto-encoders (DAEs) have achieved great success in learning data representations via the powerful representability of neural networks. But most DAEs only focus on the most dominant structures which are able to reconstruct the data from a latent space and neglect rich latent structural information. In this work, we propose a new representation learning method that explicitly models and leverages sample relations, which in turn is used as supervision to guide the representation learning. Different from previous work, our framework well preserves the relations between samples. Since the prediction of pairwise relations themselves is a fundamental problem, our model adaptively learns them from data. This provides much flexibility to encode real data manifold. The important role of relation and representation learning is evaluated on the clustering task. Extensive experiments on benchmark data sets demonstrate the superiority of our approach. By seeking to embed samples into subspace, we further show that our method can address the large-scale and out-of-sample problem.

Ordinal peer grading has been proposed as a simple and scalable solution for computing reliable information about student performance in massive open online courses. The idea is to outsource the grading task to the students themselves as follows. After the end of an exam, each student is asked to rank -- in terms of quality -- a bundle of exam papers by fellow students. An aggregation rule then combines the individual rankings into a global one that contains all students. We define a broad class of simple aggregation rules, which we call type-ordering aggregation rules, and present a theoretical framework for assessing their effectiveness. When statistical information about the grading behaviour of students is available (in terms of a noise matrix that characterizes the grading behaviour of the average student from a student population), the framework can be used to compute the optimal rule from this class with respect to a series of performance objectives that compare the ranking returned by the aggregation rule to the underlying ground truth ranking. For example, a natural rule known as Borda is proved to be optimal when students grade correctly. In addition, we present extensive simulations that validate our theory and prove it to be extremely accurate in predicting the performance of aggregation rules even when only rough information about grading behaviour (i.e., an approximation of the noise matrix) is available. Both in the application of our theoretical framework and in our simulations, we exploit data about grading behaviour of students that have been extracted from two field experiments in the University of Patras.

A Classification-Based Approach to Semi-Supervised Clustering with Pairwise Constraints Marek Smieja a,, Łukasz Struski a, Mário A. T. Figueiredo b a Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland b Instituto de T elecomunicações, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, PortugalAbstract In this paper, we introduce a neural network framework for semi-supervised clustering (SSC) with pairwise (must-link or cannot-link) constraints. In contrast to existing approaches, we decompose SSC into two simpler classification tasks/stages: the first stage uses a pair of Siamese neural networks to label the unlabeled pairs of points as must-link or cannot-link; the second stage uses the fully pairwise-labeled dataset produced by the first stage in a supervised neural-network-based clustering method. The proposed approach, S 3 C 2 (Semi-Supervised Siamese C lassifiers for C lustering), is motivated by the observation that binary classification (such as assigning pairwise relations) is usually easier than multi-class clustering with partial supervision. On the other hand, being classification-based, our method solves only well-defined classification problems, rather than less well specified clustering tasks. Extensive experiments on various datasets demonstrate the high performance of the proposed method. Keywords: semi-supervised clustering, deep learning, neural networks, pairwise constraints 1. Introduction Clustering is an important unsupervised learning tool often used to analyze the structure of complex high-dimensional data. Semi-supervised clustering (SSC) methods tackle this issue by leveraging partial prior information about class labels, with the goal of obtaining partitions that are better aligned with true classes [1, 2, 3, 4, 5, 6]. One typical way of injecting class label information into clustering is in the form of pairwise constraints (typically, must-link and cannot-link constraints), or pairwise preferences (e.g., should-link and shouldn't-link), which indicate whether a given pair of points is believed to belong to the same or different classes. Most SSC approaches rely on adapting existing unsupervised clustering methods to handle partial (namely, pairwise) information [7, 8, 4, 5, 6, 9]. This requires transferring class-label knowledge into a clustering algorithm, which is often unnatural and puts a higher weight on clustering structure than on class labels.

Accurately identifying anatomical landmarks is a crucial step in deformation analysis and surgical planning for craniomaxillofacial (CMF) bones. Available methods require segmentation of the object of interest for precise landmarking. Unlike those, our purpose in this study is to perform anatomical landmarking using the inherent relation of CMF bones without explicitly segmenting them. We propose a new deep network architecture, called relational reasoning network (RRN), to accurately learn the local and the global relations of the landmarks. Specifically, we are interested in learning landmarks in CMF region: mandible, maxilla, and nasal bones. The proposed RRN works in an end-to-end manner, utilizing learned relations of the landmarks based on dense-block units and without the need for segmentation. For a given a few landmarks as input, the proposed system accurately and efficiently localizes the remaining landmarks on the aforementioned bones. For a comprehensive evaluation of RRN, we used cone-beam computed tomography (CBCT) scans of 250 patients. The proposed system identifies the landmark locations very accurately even when there are severe pathologies or deformations in the bones. The proposed RRN has also revealed unique relationships among the landmarks that help us infer several reasoning about informativeness of the landmark points. RRN is invariant to order of landmarks and it allowed us to discover the optimal configurations (number and location) for landmarks to be localized within the object of interest (mandible) or nearby objects (maxilla and nasal). To the best of our knowledge, this is the first of its kind algorithm finding anatomical relations of the objects using deep learning.