Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Data Mining Practical Machine Learning Tools and Techniques

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Convex Analysisの二,三の進展について

Real and Complex Analysis

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Introduction To Electrodynamics

We present an analytical study of the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for solving time-varying Maxwell's equations and compare its accuracy with that of the Crank-Nicolson (CN) and Yee FDTD schemes. The closed form of the truncation error is obtained for two and three dimensions. The dependence of the truncation error on the square of the time step multiplied by the spatial derivatives of the fields is found to be a unique feature of the ADI-FDTD scheme. We illustrate the limitation on accuracy imposed by these truncation error terms by simulating a simple parallel-plate structure excited by a low-frequency voltage source. Excellent agreement is obtained between field data computed with the implicit CN scheme using time steps greatly exceeding the Courant limit and field data computed with the explicit Yee scheme. Such results are not obtained with ADI-FDTD.

On the accuracy of the ADI-FDTD method

Graphene-based devices constitute a pioneering field of research for their extraordinary electromagnetic properties. The incorporation of appropriate models into numerical simulators is necessary in order to take advantage of these properties. In this work, we propose a method to incorporate graphene-sheet models into the FDTD method. The use of vector-fitting techniques expands the permittivity of graphene into a rational function series of complex conjugate pole-residue pairs, which is implemented into FDTD by an auxiliary differential equation formulation. Simple waveguiding problems validate our approach.

FDTD Modeling of Graphene Devices Using Complex Conjugate Dispersion Material Model

A Tutorial on Distance Metric Learning: Mathematical Foundations, Algorithms, Experimental Analysis, Prospects and Challenges

In the above-named work [ibid., vol. 1, pp. 31–34, 2002], (22) was misaligned. The corrected version is provided.

Errata to "On the accuracy of the ADI-FDTD method"

This paper describes an extension of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method to analyze problems involving Debye media.

Salvador García

Papers

On the accuracy of the ADI-FDTD method

FDTD Modeling of Graphene Devices Using Complex Conjugate Dispersion Material Model

A Tutorial on Distance Metric Learning: Mathematical Foundations, Algorithms, Experimental Analysis, Prospects and Challenges

Errata to "On the accuracy of the ADI-FDTD method"

Extension of the ADI-FDTD method to Debye media