Communications of the ACM - Special issue on parallelism
A Nearest Hyperrectangle Learning Method
Machine Learning
Artificial Intelligence Review - Special issue on lazy learning
Principles of data mining
Conceptual Spaces: The Geometry of Thought
Conceptual Spaces: The Geometry of Thought
Machine Learning
Geometry and Meaning
Improved heterogeneous distance functions
Journal of Artificial Intelligence Research
Rule induction and instance-based learning a unified approach
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
The Bayes Decision Rule Induced Similarity Measures
IEEE Transactions on Pattern Analysis and Machine Intelligence
Expert Systems with Applications: An International Journal
Neighborhood rough set based heterogeneous feature subset selection
Information Sciences: an International Journal
Neighbourhood Counting Metric for Sequences
Proceedings of the 2006 conference on Advances in Intelligent IT: Active Media Technology 2006
Conceptual Neighborhoods for Retrieval in Case-Based Reasoning
ICCBR '09 Proceedings of the 8th International Conference on Case-Based Reasoning: Case-Based Reasoning Research and Development
Neighborhood counting for financial time series forecasting
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Kernel Difference-Weighted k-Nearest Neighbors Classification
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Selecting discrete and continuous features based on neighborhood decision error minimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Method of regulatory network that can explore protein regulations for disease classification
Artificial Intelligence in Medicine
Counting all common subsequences to order alternatives
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
A time weighted neighbourhood counting similarity for time series analysis
RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
Locally centralizing samples for nearest neighbors
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
Multimodal classification: case studies
Transactions on Rough Sets V
Extended rough set-based attribute reduction in inconsistent incomplete decision systems
Information Sciences: an International Journal
Neighborhood rough sets for dynamic data mining
International Journal of Intelligent Systems
Proceedings of the 2nd ACM International Conference on Multimedia Retrieval
NMGRS: Neighborhood-based multigranulation rough sets
International Journal of Approximate Reasoning
Perceptual relativity-based local hyperplane classification
Neurocomputing
Linear reconstruction measure steered nearest neighbor classification framework
Pattern Recognition
Specific-class distance measures for nominal attributes
AI Communications
Lattice Machine Classification based on Contextual Probability
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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Finding nearest neighbors is a general idea that underlies many artificial intelligence tasks, including machine learning, data mining, natural language understanding, and information retrieval. This idea is explicitly used in the k-nearest neighbors algorithm (kNN), a popular classification method. In this paper, this idea is adopted in the development of a general methodology, neighborhood counting, for devising similarity functions. We turn our focus from neighbors to neighborhoods, a region in the data space covering the data point in question. To measure the similarity between two data points, we consider all neighborhoods that cover both data points. We propose to use the number of such neighborhoods as a measure of similarity. Neighborhood can be defined for different types of data in different ways. Here, we consider one definition of neighborhood for multivariate data and derive a formula for such similarity, called neighborhood counting measure or NCM. NCM was tested experimentally in the framework of kNN. Experiments show that NCM is generally comparable to VDM and its variants, the state-of-the-art distance functions for multivariate data, and, at the same time, is consistently better for relatively large k values. Additionally, NCM consistently outperforms HEOM (a mixture of Euclidean and Hamming distances), the "standard” and most widely used distance function for multivariate data. NCM has a computational complexity in the same order as the standard Euclidean distance function and NCM is task independent and works for numerical and categorical data in a conceptually uniform way. The neighborhood counting methodology is proven sound for multivariate data experimentally. We hope it will work for other types of data.