Complementary product recommendation is a powerful strategy to improve customer experience and retail sales. However, recommending the right product is not a simple task because of the noisy and sparse nature of user-item interactions. In this work, we propose a simple yet effective method to predict a list of complementary products given a query item, based on the structure of a directed weighted graph projected from the user-item bipartite graph. We revisit bipartite graph projections for recommender systems and propose a novel approach for inferring complementarity relationships from historical user-item interactions. We compare our model with recent methods from the literature and show, despite the simplicity of our approach, an average improvement of +43% and +38% over sequential and graph-based recommenders, respectively, over different benchmarks.

Modeling user preferences has been mainly addressed by looking at users' interaction history with the different elements available in the system. Tailoring content to individual preferences based on historical data is the main goal of sequential recommendation. The nature of the problem, as well as the good performance observed across various domains, has motivated the use of the transformer architecture, which has proven effective in leveraging increasingly larger amounts of training data when accompanied by an increase in the number of model parameters. This scaling behavior has brought a great deal of attention, as it provides valuable guidance in the design and training of even larger models. Taking inspiration from the scaling laws observed in training large language models, we explore similar principles for sequential recommendation. Addressing scalability in this context requires special considerations as some particularities of the problem depart from the language modeling case. These particularities originate in the nature of the content catalogs, which are significantly larger than the vocabularies used for language and might change over time. In our case, we start from a well-known transformer-based model from the literature and make two crucial modifications. First, we pivot from the traditional representation of catalog items as trainable embeddings to representations computed with a trainable feature extractor, making the parameter count independent of the number of items in the catalog. Second, we propose a contrastive learning formulation that provides us with a better representation of the catalog diversity. We demonstrate that, under this setting, we can train our models effectively on increasingly larger datasets under a common experimental setup. We use the full Amazon Product Data dataset, which has only been partially explored in other studies, and reveal scaling behaviors similar to those found in language models. Compute-optimal training is possible but requires a careful analysis of the compute-performance trade-offs specific to the application. We also show that performance scaling translates to downstream tasks by fine-tuning larger pre-trained models on smaller task-specific domains. Our approach and findings provide a strategic roadmap for model training and deployment in real high-dimensional preference spaces, facilitating better training and inference efficiency. We hope this paper bridges the gap between the potential of transformers and the intrinsic complexities of high-dimensional sequential recommendation in real-world recommender systems. Code and models can be found at https://github.com/mercadolibre/srt.

In this letter, we study the application of the Fisher vector (FV) to the problem of pixelwise supervised classification of polarimetric synthetic aperture radar images. This is a challenging problem since information in those images is encoded as complex-valued covariance matrices. We observe that the real parts of these matrices preserve the positive semidefiniteness property of their complex counterpart. Based on this observation, we derive an FV from a mixture of real Wishart densities and integrate it with a Potts-like energy model in order to capture spatial dependencies between neighboring regions. Experimental results on two challenging data sets show the effectiveness of the approach.

This paper addresses the problem of large-scale image search. Three constraints have to be taken into account: search accuracy, efficiency, and memory usage. We first present and evaluate different ways of aggregating local image descriptors into a vector and show that the Fisher kernel achieves better performance than the reference bag-of-visual words approach for any given vector dimension. We then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation. The evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy. Searching a 100 million image data set takes about 250 ms on one processor core.

We address image classification on a large-scale, i.e. when a large number of images and classes are involved. First, we study classification accuracy as a function of the image signature dimensionality and the training set size. We show experimentally that the larger the training set, the higher the impact of the dimensionality on the accuracy. In other words, high-dimensional signatures are important to obtain state-of-the-art results on large datasets. Second, we tackle the problem of data compression on very large signatures (on the order of 105dimensions) using two lossy compression strategies: a dimensionality reduction technique known as the hash kernel and an encoding technique based on product quantizers. We explain how the gain in storage can be traded against a loss in accuracy and/or an increase in CPU cost. We report results on two large databases - ImageNet and a dataset of lM Flickr images - showing that we can reduce the storage of our signatures by a factor 64 to 128 with little loss in accuracy. Integrating the decompression in the classifier learning yields an efficient and scalable training algorithm. On ILSVRC2010 we report a 74.3% accuracy at top-5, which corresponds to a 2.5% absolute improvement with respect to the state-of-the-art. On a subset of 10K classes of ImageNet we report a top-1 accuracy of 16.7%, a relative improvement of 160% with respect to the state-of-the-art.

The problem of large-scale image search has been traditionally addressed with the bag-of-visual-words (BOV). In this article, we propose to use as an alternative the Fisher kernel framework. We first show why the Fisher representation is well-suited to the retrieval problem: it describes an image by what makes it different from other images. One drawback of the Fisher vector is that it is high-dimensional and, as opposed to the BOV, it is dense. The resulting memory and computational costs do not make Fisher vectors directly amenable to large-scale retrieval. Therefore, we compress Fisher vectors to reduce their memory footprint and speed-up the retrieval. We compare three binarization approaches: a simple approach devised for this representation and two standard compression techniques. We show on two publicly available datasets that compressed Fisher vectors perform very well using as little as a few hundreds of bits per image, and significantly better than a very recent compressed BOV approach.

Kernel machines rely on an implicit mapping of the data such that non-linear classification in the original space corresponds to linear classification in the new space. As kernel machines are difficult to scale to large training sets, it has been proposed to perform an explicit mapping of the data and to learn directly linear classifiers in the new space. In this paper, we consider the problem of learning image categorizers on large image sets (e.g. > 100k images) using bag-of-visual-words (BOV) image representations and Support Vector Machine classifiers. We experiment with three approaches to BOV embedding: 1) kernel PCA (kPCA), 2) a modified kPCA we propose for additive kernels and 3) random projections for shift-invariant kernels. We report experiments on 3 datasets: Cal-tech101, VOC07 and ImageNet. An important conclusion is that simply square-rooting BOV vectors - which corresponds to an exact mapping for the Bhattacharyya kernel - already leads to large improvements, often quite close to the best results obtained with additive kernels. Another conclusion is that, although it is possible to go beyond additive kernels, the embedding comes at a much higher cost.