Probabilistic Topological Map and Binary data
نویسندگان
چکیده
The Self Organizing Map (SOM) proposed by Kohonen [7] is a well known neural model which provides both quantization and clustering of the observation space. In this paper, we adapt the Bernoulli mixture approach, proposed by [6], to the model of binary topological map [2] and show that using a probabilistic formalism gives rise to better quantization process and classi cation performances.
منابع مشابه
A Probabilistic Self-Organizing Map for Binary Data Topographic Clustering
This paper introduces a probabilistic self-organizing map for topographic clustering, analysis and visualization of multivariate binary data or categorical data using binary coding. We propose a probabilistic formalism dedicated to binary data in which cells are represented by a Bernoulli distribution. Each cell is characterized by a prototype with the same binary coding as used in the data spa...
متن کاملSome properties of continuous linear operators in topological vector PN-spaces
The notion of a probabilistic metric space corresponds to thesituations when we do not know exactly the distance. Probabilistic Metric space was introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are topological vector spaces and the open mapping an...
متن کاملMenger probabilistic normed space is a category topological vector space
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...
متن کاملTopological map for binary data
We propose a new algorithm using topological map on binary data. The usual Euclidean distance is replaced by binary distance measures, which take into account possible asymmetries of binary data. The method is illustrated on an example taken from literature. Finally an application from chemistry is presented. We show the e ciency of the proposed method when applied to high-dimensinal binary data.
متن کاملMixed Topological Map
We propose a new algorithm which is based on a topological map model and dedicated to mixed data, with numerical and binary components. The algorithm computes directly the referent vectors, as mixed data vectors sharing the same interpretation with the observations. The method is validated on a real data related to the ocean colour domain.
متن کامل