Oh , sure , Sir … . . We have been experimenting with this brand-new methodology for more than one year . . . Traditional data mining and data clustering ( node forming ) methods rely heavily on Clustering algorithms most commonly with unsupervised machine learning techniques , , , Additionally , multiple sliding windows, a clustering algorithm in the initialization phase, and a centroid tracking method for maintaining enough knowledge about centroid behavior , gets an estimate of the positions, velocities and accelerations of centroids for the next point in time generally BUT NOT ALWAYS thru maintaining an up-to-date centroid movement model: However , Our Teams avoid recomputations of the clustering model.

Instead , mereotopology teaches us that :

Larger latency to read data approximates on the verge elements casting proxy for as a separate cluster and merge them into successively more massive clusters : Since the centroids change, the algorithm then re-assigns the points to the closest centroid. Therefore, the inherent ambiguity of the time coordinates of the observed ‘events’ calls for some specific intelligence like in the example above, further underlining the necessity of thinking of the topological approach in terms of a contextually situated analysis. In the specific example of the Etruscan towns, we do not consider of course our analysis as a scientific contribution to Meros versus topos in data bundles .

Thence , We now introduce another quantity which is helpful in the analysis of the distribution of points in space in epidemic and quasi-epidemic processes. When considering distances on the two-dimensional plane, generally we refer to Euclidean distances as measured by a straight line connecting the two points. This notion of distance is clearly insensitive to the distance of any of the two points with respect to their distances to other points in the plane. Therefore, if the position of another point C in the space changes, the Euclidean distance between A and B remains unaffected. However, in terms of our topological approach, as the position of each point in the spatial distribution carries a strong meaning in terms of the global organization, we have to take into account how variations in the positions of certain points may influence the whole spatial structure from the perspective of any single point belonging to it, in its relations with the other points.

To this purpose, we re-define the weights for the computation of the TWC in terms of a new free parameterγ which acts as a modifier of the Euclidean distance between points, so as to suitably ‘tune’ the optimal deformation needed to capture the actual spatial organization of the points according to alogic that is similar to the one already followed for the construction of the Alpha and Beta Maps. By computing a sequence of values of the γ parameter, ranging from 1 (no modification of the Euclidean distance) to infinity, we see how, as γi(t), that is, the deformation parameter assigned to the i-th point in the distribution, increases, the influence of the i-th point in affecting the global organization of distances increases.

In other words, a high γi(t) signals that the position of that point is highly critical in determining the expected evolution of the spatial distribution. Think for instance, in quasi-epidemic terms, of how the geography of trade and social exchange determining acertain distribution of urban settlements would be modified if one of those would suddenly acquire the status of a State Capital. All at a sudden, the relative distances of all the other points with respect to the new Capital would matter much more than in the past in determining whether another given settlement is now considered as ‘far’ or ‘central’ in the now re-defined spatial organization …

Sincerely Yours

Prof. REZA SANAYE