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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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

Statistics for Spatial Data.

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

Clustering with multiview data is becoming a hot topic in data mining, pattern recognition, and machine learning. In order to realize an effective multiview clustering, two issues must be addressed, namely, how to combine the clustering result from each view and how to identify the importance of each view. In this paper, based on a newly proposed objective function which explicitly incorporates two penalty terms, a basic multiview fuzzy clustering algorithm, called collaborative fuzzy c-means (Co-FCM), is firstly proposed. It is then extended into its weighted view version, called weighted view collaborative fuzzy c-means (WV-Co-FCM), by identifying the importance of each view. The WV-Co-FCM algorithm indeed tackles the above two issues simultaneously. Its relationship with the latest multiview fuzzy clustering algorithm Collaborative Fuzzy K-Means (Co-FKM) is also revealed. Extensive experimental results on various multiview datasets indicate that the proposed WV-Co-FCM algorithm outperforms or is at least comparable to the existing state-of-the-art multitask and multiview clustering algorithms and the importance of different views of the datasets can be effectively identified.

Collaborative Fuzzy Clustering From Multiple Weighted Views

The fuzziness index m has important influence on the clustering result of fuzzy clustering algorithms, and it should not be forced to fix at the usual value m = 2. In view of its distinctive features in applications and its limitation in having m = 2 only, a recent advance of fuzzy clustering called fuzzy c-means clustering with improved fuzzy partitions (IFP-FCM) is extended in this paper, and a generalized algorithm called GIFP-FCM for more effective clustering is proposed. By introducing a novel membership constraint function, a new objective function is constructed, and furthermore, GIFP-FCM clustering is derived. Meanwhile, from the viewpoints of L p norm distance measure and competitive learning, the robustness and convergence of the proposed algorithm are analyzed. Furthermore, the classical fuzzy c-means algorithm (FCM) and IFP-FCM can be taken as two special cases of the proposed algorithm. Several experimental results including its application to noisy image texture segmentation are presented to demonstrate its average advantage over FCM and IFP-FCM in both clustering and robustness capabilities.

Generalized Fuzzy C-Means Clustering Algorithm With Improved Fuzzy Partitions

Enhanced soft subspace clustering integrating within-cluster and between-cluster information

Recognition of epileptic seizures from offline EEG signals is very important in clinical diagnosis of epilepsy. Compared with manual labeling of EEG signals by doctors, machine learning approaches can be faster and more consistent. However, the classification accuracy is usually not satisfactory for two main reasons: the distributions of the data used for training and testing may be different, and the amount of training data may not be enough. In addition, most machine learning approaches generate black-box models that are difficult to interpret. In this paper, we integrate transductive transfer learning, semi-supervised learning and TSK fuzzy system to tackle these three problems. More specifically, we use transfer learning to reduce the discrepancy in data distribution between the training and testing data, employ semi-supervised learning to use the unlabeled testing data to remedy the shortage of training data, and adopt TSK fuzzy system to increase model interpretability. Two learning algorithms are proposed to train the system. Our experimental results show that the proposed approaches can achieve better performance than many state-of-the-art seizure classification algorithms.

Seizure Classification From EEG Signals Using Transfer Learning, Semi-Supervised Learning and TSK Fuzzy System

Autonomous control systems are designed to perform well under significant uncertainties in the system and environment for extended periods of time, and they must be able to compensate for system failures without external intervention. Intelligent autonomous control systems use techniques from the field of artificial intelligence to achieve this autonomy. Such control systems evolve from conventional control systems by adding intelligent components, and their development requires interdisciplinary research. A hierarchical functional intelligent autonomous control architecture is introduced here and its functions are described in detail. The fundamental issues in autonomous control system modelling and analysis are discussed.

Shitong Wang

Papers

Collaborative Fuzzy Clustering From Multiple Weighted Views

Generalized Fuzzy C-Means Clustering Algorithm With Improved Fuzzy Partitions

Enhanced soft subspace clustering integrating within-cluster and between-cluster information

Seizure Classification From EEG Signals Using Transfer Learning, Semi-Supervised Learning and TSK Fuzzy System

Towards intelligent autonomous control systems: Architecture and fundamental issues