We present Open Images V4, a dataset of 9.2M images with unified annotations for image classification, object detection and visual relationship detection. The images have a Creative Commons Attribution license that allows to share and adapt the material, and they have been collected from Flickr without a predefined list of class names or tags, leading to natural class statistics and avoiding an initial design bias. Open Images V4 offers large scale across several dimensions: 30.1M image-level labels for 19.8k concepts, 15.4M bounding boxes for 600 object classes, and 375k visual relationship annotations involving 57 classes. For object detection in particular, we provide 15x more bounding boxes than the next largest datasets (15.4M boxes on 1.9M images). The images often show complex scenes with several objects (8 annotated objects per image on average). We annotated visual relationships between them, which support visual relationship detection, an emerging task that requires structured reasoning. We provide in-depth comprehensive statistics about the dataset, we validate the quality of the annotations, we study how the performance of several modern models evolves with increasing amounts of training data, and we demonstrate two applications made possible by having unified annotations of multiple types coexisting in the same images. We hope that the scale, quality, and variety of Open Images V4 will foster further research and innovation even beyond the areas of image classification, object detection, and visual relationship detection.

Web-based services often run randomized experiments to improve their products. A popular way to run these experiments is to use geographical regions as units of experimentation, since this does not require tracking of individual users or browser cookies. Since users may issue queries from multiple geographical locations, geo-regions cannot be considered independent and interference may be present in the experiment. In this paper, we study this problem, and first present GeoCUTS, a novel algorithm that forms geographical clusters to minimize interference while preserving balance in cluster size. We use a random sample of anonymized traffic from Google Search to form a graph representing user movements, then construct a geographically coherent clustering of the graph. Our main technical contribution is a statistical framework to measure the effectiveness of clusterings. Furthermore, we perform empirical evaluations showing that the performance of GeoCUTS is comparable to hand-crafted geo-regions with respect to both novel and existing metrics.

Many documents with mathematical content are published on the Web, but conventional search engines that rely on keyword search only cannot fully exploit their mathematical information. In particular, keyword search is insufficient when expressions in a document are not annotated with natural keywords or the user cannot describe her query with keywords. Retrieving documents by querying their mathematical content directly is very appealing in various domains such as education, digital libraries, engineering, patent documents, medical sciences, etc. Capturing the relevance of mathematical expressions also greatly enhances document classification in such domains.

The Web contains a large collection of documents, some with mathematical expressions. Because mathematical expressions are objects with complex structures and rather few distinct symbols, conventional text retrieval systems are not very successful in mathematics retrieval. The lack of a definition for similarity between mathematical expressions, and the inadequacy of searching for exact matches only, makes the problem of mathematics retrieval even harder. As a result, the few existing mathematics retrieval systems are not very helpful in addressing users' needs.