for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

Technical products are often shipped with voluminous documentations. As to complex software products, machine-readable manuals are provided in most cases in addition to the printed version of a documentation. Although electronically stored text has many advantages in contrast to the traditional medium “paper”, the question arises how to manage the text of an online documentation. If the fact is...

Linear Discriminant (LD) techniques are typically used in pattern recognition tasks when there are many (n >> 10) datapoints in low-dimensional (d < 10) space. In this paper we argue on theoretical grounds that LD is in fact more appropriate when training data is sparse, and the dimension of the space is extremely high. To support this conclusion we present experimental results on a medical tex...

Confidence-weighted online learning is a generalization of margin-based learning of linear classifiers in which the margin constraint is replaced by a probabilistic constraint based on a distribution over classifier weights that is updated online as examples are observed. The distribution captures a notion of confidence on classifier weights, and in some cases it can also be interpreted as repl...

In this paper, we show that generative classifiers are capable of learning non-linear decision boundaries and that non-linear generative models can outperform a number of linear classifiers on some text categorization tasks. We first prove that 3-layer multinomial hierarchical generative (Bayesian) classifiers, under a particular independence assumption, can only learn the same linear decision ...

This paper presents a new algorithm for linear text segmentation. It is an adaptation of Affinity Propagation, a state-of-the-art clustering algorithm in the framework of factor graphs. Affinity Propagation for Segmentation, or APS, receives a set of pairwise similarities between data points and produces segment boundaries and segment centres – data points which best describe all other data poi...

These four solutions give four trajectories which are easy to plot. Consider the first, for example. When t = 0, the point is at (1, 1). As t increases, the point moves outward along the line y = x. As t decreases through negative values, the point moves inwards along the line, toward (0, 0). Since t is always understood to be increasing on the trajectory, the whole trajectory consists of the r...

Systems for text retrieval, routing, categorization and other IR tasks rely heavily on linear classiiers. We propose that two machine learning algorithms, the Widrow-Hoo and EG algorithms, be used in training linear text classiiers. In contrast to most IR methods, theoretical analysis provides performance guarantees and guidance on parameter settings for these algorithms. Experimental data is p...