There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and 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

Letters: Two-stage dimensionality reduction approach based on 2DLDA and fuzzy rough sets technique

To compensate for the lack of historical incident data available for the risk assessment of unmanned ships, this study adopted failure mode and effects analysis (FMEA) to analyse potential failures, andbased on experts’ experience, ranked them in terms of the likelihood of failure occurrence, severity of consequences and difficulty of detection. First, fuzzy linguistic variables were introduced to indicate experts’ preferences when addressing the inherent uncertainty of unmanned cargo ships' failure modes. Second, in the expert survey, the indicator of hesitance was introduced to reflect experts' degree of familiarity with the evaluated failure modes. Third, to overcome the inability of FMEA to sort failure modes of the same risk value, this study adopted a technique for order of preference by similarity to ideal solution (TOPSIS) to further rank the identified failure modes. Finally, 19 failure modes for the automooring system were selected to demonstrate how the assessment was conducted. The empirical analysis results indicated that the developed model can effectively screen out failure modes with high-level risks. This study also provides risk control options (RCOs) and offers a new and practical approach to the risk assessment of unmanned cargo ships. 

A novel approach to risk analysis of automooring operations on autonomous vessels

Most of the Zero-Shot Learning (ZSL) algorithms currently use pre-trained models as their feature extractors, which are usually trained on ImageNet by using deep neural networks. The richness of the feature information embedded in the pre-trained models can help the ZSL model extract more useful features from its limited training data. However, sometimes the difference between the training data of the current ZSL task and the ImageNet is too large, which may cause the use of pre-trained models has no obvious help or even negative impact on the model performance. To solve this problem, this paper proposes a biologically inspired feature enhancement framework for ZSL. Specifically, we design a dual-channel learning framework that uses auxiliary data sets to enhance the feature extractor of the ZSL model and propose a novel method to guide the selection of the auxiliary data sets based on the knowledge of biological taxonomy. Extensive experimental results show that our proposed method can effectively improve the generalization ability of the ZSL model and achieve state-of-the-art results on three benchmark ZSL tasks. We also explained the experimental phenomena through the way of feature visualization.

A Biologically Inspired Feature Enhancement Framework for Zero-Shot Learning

This paper introduces a new type-2 intuitionistic exponential triangular fuzzy number. Basic generalized exponential triangular intuitionistic fuzzy numbers are formulated by (α,β)-cuts. Some of properties and theorems of this type of fuzzy number with graphical representations have been studied and some examples are given to show the effectiveness of the proposed method. Also, the ranking function of the generalized exponential triangular intuitionistic fuzzy number is computed. This ranking method is based on the centroid concept and Euclidean distance. Based on the ranking method, we develop an approach to solving an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Then, we solve an intuitionistic fuzzy transportation problem where transportation cost, source, and demand were generalized type-2 intuitionistic fuzzy numbers by the ranking method for Euclidean distance. Intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. We have taken the intuitionistic fuzzy failure to start of an automobile as known basic fault events such as Ignition failure, Battery internal shortage, Spark plug failure and fuel pump failure using Type-2 Intuitionistic Exponential Triangular Fuzzy Number. Our computational procedure is very simple to implement for calculations in intuitionistic fuzzy failure. The major advantage of using Intuitionistic fuzzy sets over fuzzy sets is that intuitionistic fuzzy sets separate the positive and the negative evidence for the membership of an element in a set. Furthermore, the proposed technique can be suitably utilized to solve the start of an automobile problem, because the result of system failure in this method is significant. Finally, the proposed method has been compared with other existing method through numerical examples.

A New Type-2 Intuitionistic Exponential Triangular Fuzzy Number and Its Ranking Method with Centroid Concept and Euclidean Distance

This paper develops an infinite polynomial kernel k c for support vector machines. We also propose a mapping from an original data space into the high dimensional feature space on which the inner product is defined by the infinite polynomial kernel k c . Via this mapping, any two finite sets of data in the original space will become linearly separable in the feature space. Numerical experiments indicate that the proposed infinite polynomial kernel possesses some properties and performance better than the existing finite polynomial kernels.

Xizhao Wang

Papers

Letters: Two-stage dimensionality reduction approach based on 2DLDA and fuzzy rough sets technique

A novel approach to risk analysis of automooring operations on autonomous vessels

A Biologically Inspired Feature Enhancement Framework for Zero-Shot Learning

A New Type-2 Intuitionistic Exponential Triangular Fuzzy Number and Its Ranking Method with Centroid Concept and Euclidean Distance

The infinite polynomial kernel for support vector machine