Implementation of distributed machine learning algorithms in MapReduce faces three challenges: low execution efficiency of iterative algorithms, poor data scalability, and high complexity in decomposing a complicated algorithm into the rigid structure of Map and Reduce operations. The last challenge makes many useful algorithms for big data analysis unavailable in current distributed systems. In this paper, we propose LogoML, a library of machine learning algorithms for distributed big data analysis. LogoML is implemented on top of the Local Operation and Global Operation (LOGO) distributed computing framework and the Random Sample Partition (RSP) data representation model. Unlike MapReduce algorithms, the algorithms in LogoML are sequential in nature. With LogoML, a data analysis task is carried out with two core operations in the LOGO distributed computing framework. The Local Operation (LO) operation executes a data analytic algorithm in multiple nodes or virtual machines in parallel to process a set of random sample data blocks and generate a set of local results. The Global Operation (GO) operation executes an ensemble algorithm to aggregate the local results into the final ensemble result. Through innovative design and implementation, the LogoML library exhibits the following merits in distributed big data analysis: It has rich algorithms because sequential algorithms are easy to implement in LogoML, is efficient in execution of iterative algorithms and scalable to big data and its open structure allows the user to add new algorithms to the library. The performance, efficiency, and data scalability of LogoML algorithms are demonstrated with the experiment results of both synthetic and real-datasets.

Distributed computing frameworks are the fundamental component of distributed computing systems. They provide an essential way to support the efficient processing of big data on clusters or cloud. The size of big data increases at a pace that is faster than the increase in the big data processing capacity of clusters. Thus, distributed computing frameworks based on the MapReduce computing model are not adequate to support big data analysis tasks which often require running complex analytical algorithms on extremely big data sets in terabytes. In performing such tasks, these frameworks face three challenges: computational inefficiency due to high I/O and communication costs, non-scalability to big data due to memory limit, and limited analytical algorithms because many serial algorithms cannot be implemented in the MapReduce programming model. New distributed computing frameworks need to be developed to conquer these challenges. In this paper, we review MapReduce-type distributed computing frameworks that are currently used in handling big data and discuss their problems when conducting big data analysis. In addition, we present a non-MapReduce distributed computing framework that has the potential to overcome big data analysis challenges.

This is a review of quantum methods for machine learning problems that consists of two parts. The first part, "quantum tools", presents the fundamentals of qubits, quantum registers, and quantum states, introduces important quantum tools based on known quantum search algorithms and SWAP-test, and discusses the basic quantum procedures used for quantum search methods. The second part, "quantum classification algorithms", introduces several classification problems that can be accelerated by using quantum subroutines and discusses the quantum methods used for classification.

This is a review of quantum methods for machine learning problems that consists of two parts. The first part, "quantum tools", presented some of the fundamentals and introduced several quantum tools based on known quantum search algorithms. This second part of the review presents several classification problems in machine learning that can be accelerated with quantum subroutines. We have chosen supervised learning tasks as typical classification problems to illustrate the use of quantum methods for classification.