Developments in the theory of randomized shortest paths with a comparison of graph node distances

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into account the global structure of the graph. In this article, we develop the theory of one family of graph node distances, known as the randomized shortest path dissimilarity, which has its foundation in statistical physics. We show that the randomized shortest path dissimilarity can be easily computed in closed form for all pairs of nodes of a graph. Moreover, we come up with a new definition of a distance measure that we call the free energy distance. The free energy distance can be seen as an upgrade of the randomized shortest path dissimilarity as it defines a metric, in addition to which it satisfies the graph-geodetic property. The derivation and computation of the free energy distance are also straightforward. We then make a comparison between a set of generalized distances that interpolate between the shortest path distance and the commute time, or resistance distance. This comparison focuses on the applicability of the distances in graph node clustering and classification. The comparison, in general, shows that the parametrized distances perform well in the tasks. In particular, we see that the results obtained with the free energy distance are among the best in all the experiments.Comment: 30 pages, 4 figures, 3 table

Knowledge Transfer for Out-of-Knowledge-Base Entities: A Graph Neural Network Approach

Knowledge base completion (KBC) aims to predict missing information in a knowledge base.In this paper, we address the out-of-knowledge-base (OOKB) entity problem in KBC:how to answer queries concerning test entities not observed at training time. Existing embedding-based KBC models assume that all test entities are available at training time, making it unclear how to obtain embeddings for new entities without costly retraining. To solve the OOKB entity problem without retraining, we use graph neural networks (Graph-NNs) to compute the embeddings of OOKB entities, exploiting the limited auxiliary knowledge provided at test time.The experimental results show the effectiveness of our proposed model in the OOKB setting.Additionally, in the standard KBC setting in which OOKB entities are not involved, our model achieves state-of-the-art performance on the WordNet dataset. The code and dataset are available at https://github.com/takuo-h/GNN-for-OOKBComment: This paper has been accepted by IJCAI1

Ridge Regression, Hubness, and Zero-Shot Learning

This paper discusses the effect of hubness in zero-shot learning, when ridge regression is used to find a mapping between the example space to the label space. Contrary to the existing approach, which attempts to find a mapping from the example space to the label space, we show that mapping labels into the example space is desirable to suppress the emergence of hubs in the subsequent nearest neighbor search step. Assuming a simple data model, we prove that the proposed approach indeed reduces hubness. This was verified empirically on the tasks of bilingual lexicon extraction and image labeling: hubness was reduced with both of these tasks and the accuracy was improved accordingly.Comment: To be presented at ECML/PKDD 201

Learning Decorrelated Representations Efficiently Using Fast Fourier Transform

Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. Although these models are as effective as conventional representation learning models, their training can be computationally demanding if the dimension d of the projected embeddings is high. As the regularizers are defined in terms of individual elements of a cross-correlation or covariance matrix, computing the loss for n samples takes O(n d^2) time. In this paper, we propose a relaxed decorrelating regularizer that can be computed in O(n d log d) time by Fast Fourier Transform. We also propose an inexpensive technique to mitigate undesirable local minima that develop with the relaxation. The proposed regularizer exhibits accuracy comparable to that of existing regularizers in downstream tasks, whereas their training requires less memory and is faster for large d. The source code is available.Comment: Accepted for CVPR 202

Action Class Relation Detection and Classification Across Multiple Video Datasets

The Meta Video Dataset (MetaVD) provides annotated relations between action classes in major datasets for human action recognition in videos. Although these annotated relations enable dataset augmentation, it is only applicable to those covered by MetaVD. For an external dataset to enjoy the same benefit, the relations between its action classes and those in MetaVD need to be determined. To address this issue, we consider two new machine learning tasks: action class relation detection and classification. We propose a unified model to predict relations between action classes, using language and visual information associated with classes. Experimental results show that (i) pre-trained recent neural network models for texts and videos contribute to high predictive performance, (ii) the relation prediction based on action label texts is more accurate than based on videos, and (iii) a blending approach that combines predictions by both modalities can further improve the predictive performance in some cases.Comment: Accepted to Pattern Recognition Letters. 12 pages, 4 figure

Cross-Modal Perception in the Framework of Non-Riemannian Sensory Space

Though human sensations, such as the senses of hearing, sight, etc., are independent each other, the interference between two of them is sometimes observed, and is called cross-modal perception[1]. Hitherto we studied unimodal perception of visual sensation[2] and auditory sensation[3] respectively by differential geometry[4]. We interpreted the parallel alley and the distance alley as two geodesics under different conditions in a visual space, and depicted the trace of continuous vowel speech as the geodesics through phonemes on a vowel plane. In this work, cross-modal perception is similarly treated from the standpoint of non-Riemannian geometry, where each axis of a cross-modal sensory space represents unimodal sensation. The geometry allows us to treat asymmetric metric tensor and hence a non-Euclidean concept of anholonomic objects, representing unidirectional property of cross-modal perception. The McGurk effect in audiovisual perception[5] and ‘rubber hand’ illusion in visual tactile perception[6] can afford experimental evidence of torsion tensor. The origin of ‘bouncing balls’ illusion[7] is discussed from the standpoint of an audiovisual cross-modal sensory space in a qualitative manner