A Consistent Diffusion-Based Algorithm for Semi-Supervised Graph Learning

The task of semi-supervised classification aims at assigning labels to all nodes of a graph based on the labels known for a few nodes, called the seeds. One of the most popular algorithms relies on the principle of heat diffusion, where the labels of the seeds are spread by thermoconductance and the temperature of each node at equilibrium is used as a score function for each label. In this paper, we prove that this algorithm is not consistent unless the temperatures of the nodes at equilibrium are centered before scoring. This crucial step does not only make the algorithm provably consistent on a block model but brings significant performance gains on real graphs.

Integrating the Wikidata Taxonomy into YAGO

Wikidata is one of the largest public general-purpose Knowledge Bases (KBs). Yet, due to its collaborative nature, its schema and taxonomy have become convoluted. For the YAGO 4 KB, we combined Wikidata with the ontology from Schema.org, which reduced and cleaned up the taxonomy and constraints and made it possible to run automated reasoners on the data. However, it also cut away large parts of the Wikidata taxonomy. In this paper, we present our effort to merge the entire Wikidata taxonomy into the YAGO KB as much as possible. We pay particular attention to logical constraints and a careful distinction of classes and instances. Our work creates YAGO 4.5, which adds a rich layer of informative classes to YAGO, while at the same time keeping the KB logically consistent.

A Self-Encoder for Learning Nearest Neighbors

We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to distribute the data samples in the embedding space so that they are linearly separable from one another. This induces a geometry where two samples are close in the embedding space when they are not easy to differentiate. The self-encoder can then be combined with a nearest-neighbor classifier or regressor for any subsequent supervised task. Unlike regular nearest neighbors, the predictions resulting from this encoding of data are invariant to any scaling of features, making any preprocessing like min-max scaling not necessary. The experiments show the efficiency of the approach, especially on heterogeneous data mixing numerical features and categorical features.

KNNs of Semantic Encodings for Rating Prediction

This paper explores a novel application of textual semantic similarity to user-preference representation for rating prediction. The approach represents a user's preferences as a graph of textual snippets from review text, where the edges are defined by semantic similarity. This textual, memory-based approach to rating prediction enables review-based explanations for recommendations. The method is evaluated quantitatively, highlighting that leveraging text in this way outperforms both strong memory-based and model-based collaborative filtering baselines.

Pairwise Adjusted Mutual Information

A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two clusterings being similar by chance. Unfortunately, this adjustment makes the metric computationally expensive. In this paper, we propose a novel adjustment based on {pairwise} label permutations instead of full label permutations. Specifically, we consider permutations where only two samples, selected uniformly at random, exchange their labels. We show that the corresponding adjusted metric, which can be expressed explicitly, behaves similarly to the standard adjusted mutual information for assessing the quality of a clustering, while having a much lower time complexity. Both metrics are compared in terms of quality and performance on experiments based on synthetic and real data.

A Consistent Diffusion-Based Algorithm for Semi-Supervised Classification on Graphs

Semi-supervised classification on graphs aims at assigning labels to all nodes of a graph based on the labels known for a few nodes, called the seeds. The most popular algorithm relies on the principle of heat diffusion, where the labels of the seeds are spread by thermo-conductance and the temperature of each node is used as a score function for each label. Using a simple block model, we prove that this algorithm is not consistent unless the temperatures of the nodes are centered before classification. We show that this simple modification of the algorithm is enough to get significant performance gains on real data.

Time Series Source Separation with Slow Flows

In this paper, we show that slow feature analysis (SFA), a common time series decomposition method, naturally fits into the flow-based models (FBM) framework, a type of invertible neural latent variable models. Building upon recent advances on blind source separation, we show that such a fit makes the time series decomposition identifiable.

Spectral embedding of regularized block models

Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we explain on a simple block model the impact of the complete graph regularization, whereby a constant is added to all entries of the adjacency matrix. Specifically, we show that the regularization forces the spectral embedding to focus on the largest blocks, making the representation less sensitive to noise or outliers. We illustrate these results on both on both synthetic and real data, showing how regularization improves standard clustering scores.

WikiDataSets : Standardized sub-graphs from WikiData

Developing new ideas and algorithms in the fields of graph processing and relational learning requires datasets to work with and WikiData is the largest open source knowledge graph involving more than fifty millions entities. It is larger than needed in many cases and even too large to be processed easily but it is still a goldmine of relevant facts and subgraphs. Using this graph is time consuming and prone to task specific tuning which can affect reproducibility of results. Providing a unified framework to extract topic-specific subgraphs solves this problem and allows researchers to evaluate algorithms on common datasets. This paper presents various topic-specific subgraphs of WikiData along with the generic Python code used to extract them. These datasets can help develop new methods of knowledge graph processing and relational learning.

Weighted Spectral Embedding of Graphs

We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding.