Temporal and Spatial Data Mining with Second-Order Hidden Models

In the frame of designing a knowledge discovery system, we have developed stochastic models based on high-order hidden Markov models. These models are capable to map sequences of data into a Markov chain in which the transitions between the states depend on the \texttt{n} previous states according to the order of the model. We study the process of achieving information extraction fromspatial and temporal data by means of an unsupervised classification. We use therefore a French national database related to the land use of a region, named Teruti, which describes the land use both in the spatial and temporal domain. Land-use categories (wheat, corn, forest, ...) are logged every year on each site regularly spaced in the region. They constitute a temporal sequence of images in which we look for spatial and temporal dependencies. The temporal segmentation of the data is done by means of a second-order Hidden Markov Model (\hmmd) that appears to have very good capabilities to locate stationary segments, as shown in our previous work in speech recognition. Thespatial classification is performed by defining a fractal scanning ofthe images with the help of a Hilbert-Peano curve that introduces atotal order on the sites, preserving the relation ofneighborhood between the sites. We show that the \hmmd performs aclassification that is meaningful for the agronomists.Spatial and temporal classification may be achieved simultaneously by means of a 2 levels \hmmd that measures the \aposteriori probability to map a temporal sequence of images onto a set of hidden classes

Derivations in the Banach ideals of τ\tau-compact operators

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\tau$ and let $S_0(\tau)$ be the algebra of all $\tau$-compact operators affiliated with $\mathcal{M}$. Let $E(\tau)\subseteq S_0(\tau)$ be a symmetric operator space (on $\mathcal{M}$) and let $\mathcal{E}$ be a symmetrically-normed Banach ideal of $\tau$-compact operators in $\mathcal{M}$. We study (i) derivations $\delta$ on $\mathcal{M}$ with the range in $E(\tau)$ and (ii) derivations on the Banach algebra $\mathcal{E}$. In the first case our main results assert that such derivations are continuous (with respect to the norm topologies) and also inner (under some mild assumptions on $E(\tau)$). In the second case we show that any such derivation is necessarily inner when $\mathcal{M}$ is a type $I$ factor. As an interesting application of our results for the case (i) we deduce that any derivation from $\mathcal{M}$ into an $L_p$-space, $L_p(\mathcal{M},\tau)$, ($1<p<\infty$) associated with $\mathcal{M}$ is inner

Automatic case acquisition from texts for process-oriented case-based reasoning

This paper introduces a method for the automatic acquisition of a rich case representation from free text for process-oriented case-based reasoning. Case engineering is among the most complicated and costly tasks in implementing a case-based reasoning system. This is especially so for process-oriented case-based reasoning, where more expressive case representations are generally used and, in our opinion, actually required for satisfactory case adaptation. In this context, the ability to acquire cases automatically from procedural texts is a major step forward in order to reason on processes. We therefore detail a methodology that makes case acquisition from processes described as free text possible, with special attention given to assembly instruction texts. This methodology extends the techniques we used to extract actions from cooking recipes. We argue that techniques taken from natural language processing are required for this task, and that they give satisfactory results. An evaluation based on our implemented prototype extracting workflows from recipe texts is provided.Comment: Sous presse, publication pr\'evue en 201

Commutator estimates in W∗W^*-factors

Let $\mathcal{M}$ be a $W^*$-factor and let $S\left( \mathcal{M} \right)$ be the space of all measurable operators affiliated with $\mathcal{M}$. It is shown that for any self-adjoint element $a\in S(\mathcal{M})$ there exists a scalar $\lambda_0\in\mathbb{R}$, such that for all $\varepsilon > 0$, there exists a unitary element $u_\varepsilon$ from $\mathcal{M}$, satisfying $|[a,u_\varepsilon]| \geq (1-\varepsilon)|a-\lambda_0\mathbf{1}|$. A corollary of this result is that for any derivation $\delta$ on $\mathcal{M}$ with the range in an ideal $I\subseteq\mathcal{M}$, the derivation $\delta$ is inner, that is $\delta(\cdot)=\delta_a(\cdot)=[a,\cdot]$, and $a\in I$. Similar results are also obtained for inner derivations on $S(\mathcal{M})$.Comment: 21 page