A topological hyperplane is a subspace of R (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R is a finite set H such that for any nonvoid intersection Y of topological hyperplanes in H and any H ∈ H that intersects but does not contain Y , the intersection is a topological hyperplane in Y . (We also assume...

In this paper a novel method is proposed to combine decision tree classifiers using calculated classification confidence values. This confidence in the classification is based on distance calculation to the relevant decision boundary. It is shown that these values – provided by individual classification trees – can be integrated to derive a consensus decision. The proposed combination scheme – ...

Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces...

The processing performed by a feed-forward neural network is often interpreted through use of decision hyperplanes at each layer. The adaptation process, however, is normally explained using an error landscape picture. In this paper the actual dynamics of the decision hyperplanes is investigated. As a result a mechanical analogy is drawn with a system of spins acted upon by forces. The spin obj...

Business users and analysts commonly use spreadsheets and 2D plots to analyze and understand their data. On-line Analytical Processing (OLAP) provides these users with added flexibility in pivoting data around different attributes and drilling up and down the multi-dimensional cube of aggregations. Machine learning researchers, however, have concentrated on hypothesis spaces that are foreign to...

Many learning situations involve separation of labeled training instances by hyperplanes. Consistent separation is of theoretical interest, but the real goal is rather to minimize the number of errors using a bounded number of hyperplanes. Exact minimization of empirical error in a high-dimensional grid induced into the feature space by axis-parallel hyperplanes is NP-hard. We develop two appro...

Bayesian symbol-by-symbol detection using a finite sequence observation space has been the subject of renewed research interest. The Bayesian transverse equalizer (BTE) and Bayesian decision feedback equalizer (BDFE) are two common Bayesian detectors. It is often difficult to evaluate the bit-error rate (BER) performance of these Bayesian detectors since the BER cannot be analytically evaluated...