In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable convex functions.

A: Agglomerative Bregman Clustering
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Q: The belief bias effect is a phenomenon which occurs when we think that we judge an argument based on our reasoning, but are actually influenced by our beliefs and prior knowledge. Evans, Barston and Pollard carried out a psychological syllogistic reasoning task to prove this effect. Participants were asked whether they would accept or reject a given syllogism. We discuss one specific case which is commonly assumed to be believable but which is actually not logically valid. By introducing abnormalities, abduction and background knowledge, we adequately model this case under the weak completion semantics. Our formalization reveals new questions about possible extensions in abductive reasoning. For instance, observations and their explanations might include some relevant prior abductive contextual information concerning some side-effect or leading to a contestable or refutable side-effect. A weaker notion indicates the support of some relevant consequences by a prior abductive context. Yet another definition describes jointly supported relevant consequences, which captures the idea of two observations containing mutually supportive side-effects. Though motivated with and exemplified by the running psychology application, the various new general abductive context definitions are introduced here and given a declarative semantics for the first time, and have a much wider scope of application. Inspection points, a concept introduced by Pereira and Pinto, allows us to express these definitions syntactically and intertwine them into an operational semantics.

A: Contextual Abductive Reasoning with Side-Effects
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Q: A methodology for the development of a fuzzy expert system (FES) with application to earthquake prediction is presented. The idea is to reproduce the performance of a human expert in earthquake prediction. To do this, at the first step, rules provided by the human expert are used to generate a fuzzy rule base. These rules are then fed into an inference engine to produce a fuzzy inference system (FIS) and to infer the results. In this paper, we have used a Sugeno type fuzzy inference system to build the FES. At the next step, the adaptive network-based fuzzy inference system (ANFIS) is used to refine the FES parameters and improve its performance. The proposed framework is then employed to attain the performance of a human expert used to predict earthquakes in the Zagros area based on the idea of coupled earthquakes. While the prediction results are promising in parts of the testing set, the general performance indicates that prediction methodology based on coupled earthquakes needs more investigation and more complicated reasoning procedure to yield satisfactory predictions.

A:
A Fuzzy Expert System for Earthquake Prediction, Case Study: The Zagros Range
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