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

Dot product kernels are a class of important kernel in the theory of support vector machine. This paper develops a method to construct the mapping that map the original data set into the high dimensional feature space, on which the inner product is defined by a dot product kernel. Our method can also be applied to the Gaussian kernels. Via this mapping, the structure of features in the feature space is easy to be observed, and the linear separability of data sets in the feature space is studied. We obtain that any two finite sets of data with empty overlap in the original space will become linearly separable in an infinite dimensional feature space, and a sufficient and necessary condition is also developed for two infinite sets of data in the original data space being linearly separable in the feature space, this condition can be applied to examine the existences and uniqueness of the hyperplane which can separate all the possible inputs correctly.

A method to construct the mapping to the feature space for the dot product kernels

Instance selection also named sample selection is an important preprocessing step for pattern classification. Almost all of the existing instance selection methods are developed for specific classifiers, such as nearest neighbor (NN) classifier, support vector machine (SVM) classifier. Few of them are designed for single hidden layer feed-forward neural networks (SLFNs) classifier. Based on sample entropy, this paper presents an instance selection method for efficient data classification with extreme learning machine (ELM), which is used to train a SLFN. The proposed method is compared with four state-of-the-art approaches by a series of experiments. The experimental results show that the proposed method can provide similar generalization performance but lower computation time complexity.

Instance selection based on sample entropy for efficient data classification with ELM

In this paper, we focus on kernel learning vector quantization (KLVQ) for handling novelty detection. The two key issues are addressed: the existing KLVQ methods are reviewed and revisited, while the reformulated KLVQ is applied to tackle novelty detection problems. Although the calculation of kernelising the learning vector quantization (LVQ) may add an extra computational cost, the proposed method exhibits better performance over the LVQ. The numerical study on one synthetic data set confirms the benefit in using the proposed KLVQ.

Application of kernel learning vector quantization to novelty detection

In this paper, a method of combining fuzzy decision tree with optimal fuzzy-valued feature subset selection (OFFSS) is proposed. This algorithm can first select a feature subset from the entire feature space, and then constructs the fuzzy decision tree on the selected feature subset. This work conducts some experiments to compare the proposed algorithm with fuzzy-ID3. The experiment results show that fuzzy decision trees on feature subset are superior to that on entire feature space in terms of speed and accuracy for classification.

https://ieeexplore.ieee.org/iel5/9459/30161/01384571.pdf

Xizhao Wang

Papers

A method to construct the mapping to the feature space for the dot product kernels

Instance selection based on sample entropy for efficient data classification with ELM

Application of kernel learning vector quantization to novelty detection

A comparison between fuzzy-ID3 and OFFSS-based fuzzy-ID3

Learning to recommend journals for submission based on embedding models