MapReduce is a programming model and an associated implementation for processing and generating large data sets. Users specify a map function that processes a key/value pair to generate a set of intermediate key/value pairs, and a reduce function that merges all intermediate values associated with the same intermediate key. Many real world tasks are expressible in this model, as shown in the paper.

Programs written in this functional style are automatically parallelized and executed on a large cluster of commodity machines. The run-time system takes care of the details of partitioning the input data, scheduling the program's execution across a set of machines, handling machine failures, and managing the required inter-machine communication. This allows programmers without any experience with parallel and distributed systems to easily utilize the resources of a large distributed system.

Our implementation of MapReduce runs on a large cluster of commodity machines and is highly scalable: a typical MapReduce computation processes many terabytes of data on thousands of machines. Programmers find the system easy to use: hundreds of MapReduce programs have been implemented and upwards of one thousand MapReduce jobs are executed on Google's clusters every day.

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MapReduce: simplified data processing on large clusters

MapReduce is a programming model and an associated implementation for processing and generating large datasets that is amenable to a broad variety of real-world tasks. Users specify the computation in terms of a map and a reduce function, and the underlying runtime system automatically parallelizes the computation across large-scale clusters of machines, handles machine failures, and schedules inter-machine communication to make efficient use of the network and disks. Programmers find the system easy to use: more than ten thousand distinct MapReduce programs have been implemented internally at Google over the past four years, and an average of one hundred thousand MapReduce jobs are executed on Google's clusters every day, processing a total of more than twenty petabytes of data per day.

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Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

Today, visual recognition systems are still rarely employed in robotics applications. Perhaps one of the main reasons for this is the lack of demanding benchmarks that mimic such scenarios. In this paper, we take advantage of our autonomous driving platform to develop novel challenging benchmarks for the tasks of stereo, optical flow, visual odometry/SLAM and 3D object detection. Our recording platform is equipped with four high resolution video cameras, a Velodyne laser scanner and a state-of-the-art localization system. Our benchmarks comprise 389 stereo and optical flow image pairs, stereo visual odometry sequences of 39.2 km length, and more than 200k 3D object annotations captured in cluttered scenarios (up to 15 cars and 30 pedestrians are visible per image). Results from state-of-the-art algorithms reveal that methods ranking high on established datasets such as Middlebury perform below average when being moved outside the laboratory to the real world. Our goal is to reduce this bias by providing challenging benchmarks with novel difficulties to the computer vision community. Our benchmarks are available online at: www.cvlibs.net/datasets/kitti

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Are we ready for autonomous driving? The KITTI vision benchmark suite

An imaging system configured to take panoramic pictures is disclosed. In one embodiment, the imaging system includes a camera, range finder associated with the camera and configured to provide depth information for objects within a field of view of the camera; and a processor coupled to receive information from the camera and depth information from the range finder, and configured to unwrap pictures taken by the camera according to the depth information.

Apparatus and method for sensing depth in every direction

This disclosure is directed to a hardware system for inverse graphics capture. An inverse graphics capture system (IGCS) captures data regarding a physical space that can be used to generate a photorealistic graphical model of that physical space. In certain approaches, the system includes hardware and accompanying software used to create a photorealistic six degree of freedom (6DOF) graphical model of the physical space. In certain approaches, the system includes hardware and accompanying software used for projection mapping onto the physical space. In certain approaches, the model produced by the IGCS is built using data regarding the geometry, lighting, surfaces, and environment of the physical space. In certain approaches, the model produced by the IGCS is both photorealistic and fully modifiable.

Hardware system for inverse graphics capture

A user identification system includes an image recognition network to analyze image data and generate shape data based on the image data. The system also includes a generalist network to analyze the shape data and generate general category data based on the shape data. The system further includes a specialist network to compare the general category data with a characteristic to generate narrow category data. Moreover, the system includes a classifier layer including a plurality of nodes to represent a classification decision based on the narrow category data.

Devices, methods and systems for biometric user recognition utilizing neural networks

In one embodiment, a method includes converting unsupervised data into supervised data using multiple processes and training multiple supervised classifiers with the supervised data of the processes. In such manner, supervised classifiers may be used to classify unsupervised data. Affinity measures may be determined and data clustered using the resulting trained classifiers. Other embodiments are described and claimed.

Gary Bradski

Papers

Apparatus and method for sensing depth in every direction

Hardware system for inverse graphics capture

Devices, methods and systems for biometric user recognition utilizing neural networks

Using supervised classifiers with unsupervised data

Object detection, shape recovery, and 3D modelling by depth-encoded hough voting