Alternative similarity functions for graph kernels (original) (raw)
Related papers
2009
This paper presents a survey as well as an empirical comparison and evaluation of seven kernels on graphs and two related similarity matrices, that we globally refer to as ''kernels on graphs'' for simplicity. They are the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commute-time (or resistance-distance) kernel, the randomwalk-with-restart similarity matrix, and finally, a kernel first introduced in this paper (the regularized commute-time kernel) and two kernels defined in some of our previous work and further investigated in this paper (the Markov diffusion kernel and the relative-entropy diffusion matrix). The kernel-ongraphs approach is simple and intuitive. It is illustrated by applying the nine kernels to a collaborativerecommendation task, viewed as a link prediction problem, and to a semisupervised classification task, both on several databases. The methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commute-time and the Markov diffusion kernels perform best on the investigated tasks, closely followed by the regularized Laplacian kernel.
On the Scalability of Graph Kernels Applied to Collaborative Recommenders
2008
We study the scalability of several recent graph kernel-based collaborative recommendation algorithms. We compare the performance of several graph kernel-based recommendation algorithms, focussing on runtime and recommendation accuracy with respect to the reduced rank of the subspace. We inspect the exponential and Laplacian exponential kernels, the resistance distance kernel, the regularized Laplacian kernel, and the stochastic diffusion kernel. Furthermore, we introduce new variants of kernels based on the graph Laplacian which, in contrast to existing kernels, also allow negative edge weights and thus negative ratings. We perform an evaluation on the Netflix Prize rating corpus on prediction and recommendation tasks, showing that dimensionality reduction not only makes prediction faster, but sometimes also more accurate.
Neural Networks, 2012
This paper presents a survey as well as an empirical comparison and evaluation of seven kernels on graphs and two related similarity matrices, that we globally refer to as ''kernels on graphs'' for simplicity. They are the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commute-time (or resistance-distance) kernel, the randomwalk-with-restart similarity matrix, and finally, a kernel first introduced in this paper (the regularized commute-time kernel) and two kernels defined in some of our previous work and further investigated in this paper (the Markov diffusion kernel and the relative-entropy diffusion matrix). The kernel-ongraphs approach is simple and intuitive. It is illustrated by applying the nine kernels to a collaborativerecommendation task, viewed as a link prediction problem, and to a semisupervised classification task, both on several databases. The methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commute-time and the Markov diffusion kernels perform best on the investigated tasks, closely followed by the regularized Laplacian kernel.
Modeling collaborative similarity with the signed resistance distance kernel
Proceeding of the …, 2008
We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed resistance distance, generalizing the previously known regular resistance distance kernel which is limited to nonnegative values. We show that the signed resistance distance kernel can be computed effectively using the Moore-Penrose pseudoinverse of the Laplacian matrix of the bipartite rating graph, leading to fast computation based on the eigenvalue decomposition of the Laplacian matrix. We apply this technique to collaborative rating prediction on the Netflix Prize corpus, and show how our new kernel can replace the traditional Pearson correlation for rating prediction.
Rating Prediction via Graph Signal Processing
IEEE Transactions on Signal Processing, 2018
This paper develops new designs for recommendation systems inspired by recent advances in graph signal processing (SP). Recommendation systems aim to predict unknown ratings by exploiting the information revealed in a subset of useritem observed ratings. Leveraging the notions of graph frequency and graph filters, we demonstrate that classical collaborative filtering methods, such as k-nearest neighbors (NN), can be modeled as a specific band-stop graph filter on networks describing similarities between users or items. We also demonstrate that linear latent factor (LF) models, such as low-rank matrix completion, can be viewed as bandlimited interpolation algorithms that operate in a frequency domain given by the spectrum of a joint user and item network. These new interpretations pave the way to new methods for enhanced rating prediction. For NN-based collaborative filtering, we develop more general band stop graph filters, and present a novel predictor, called Mirror Filtering (MiFi), that filters jointly across user and item networks. For LF, we propose a low complexity method by exploiting the eigenvector of correlation matrices constructed from known ratings. The performance of our algorithms is assessed in the MovieLens 100k dataset, showing that our designs reduce the root mean squared error (up to a 6.85% for MiFi) compared to one incurred by the benchmark collaborative filtering approach.
Graph-Based Collaborative Filtering with MLP
Mathematical Problems in Engineering, 2018
The collaborative filtering (CF) methods are widely used in the recommendation systems. They learn users’ interests and preferences from their historical data and then recommend the items users may like. However, the existing methods usually measure the correlation between users by calculating the coefficient of correlation, which cannot capture any latent features between users. In this paper, we proposed an algorithm based on graph. First, we transform the users’ information into vectors and use SVD method to reduce dimensions and then learn the preferences and interests of all users based on the improved kernel function and map them to the network; finally, we predict the user’s rating for the items through the Multilayer Perceptron (MLP). Compared with existing methods, on one hand, our method can discover some latent features between users by mapping users’ information to the network. On the other hand, we improve the vectors with the ratings information to the MLP method and p...
Collaborative filtering via graph signal processing
2017 25th European Signal Processing Conference (EUSIPCO)
This paper develops new designs for recommender systems inspired by recent advances in graph signal processing. Recommender systems aim to predict unknown ratings by exploiting the information revealed in a subset of user-item observed ratings. Leveraging the notions of graph frequency and graph filters, we demonstrate that a common collaborative filtering methodk-nearest neighbors-can be modeled as a specific band-stop graph filter on networks describing similarities between users or items. These new interpretations pave the way to new methods for enhanced rating prediction. For collaborative filtering, we develop more general band stop graph filters. The performance of our algorithms is assessed in the MovieLens-100k dataset, showing that our designs reduce the root mean squared error (up to a 6.20% improvement) compared to one incurred by the benchmark collaborative filtering approach.
Users’ Rating Predictions Using Collaborating Filtering Based on Users and Items Similarity Measures
Computational Intelligence and Neuroscience
The social media has made the world a global world and we, in addition to, as part of physical society, are now part of the virtual society as well. There has been the generation of a large amount of information over the social web. By way of increasing online information, new opportunities emerged, and diverse issues have been raised, which have attracted researchers to address these research problems. In this current age, where online business and e-commerce are part of our daily lives, recommender systems (RSs) are very effective for information filtering. RSs play a significant role in our lives by assisting users in recommending items and services what they may be interesting in to purchase or avail. In this research work, our goal is to predict the users’ ratings for various items, which are an active research area in collaborative filtering (CF). In this work, we have explored various similarity measures based on user-user and item-item rating predictions on different dataset...