By Francesco Masulli, Alfredo Petrosino, Stefano Rovetta
This ebook constitutes the complaints of the foreign Workshop on Clustering High-Dimensional info, CHDD 2012, held in Naples, Italy, in may possibly 2012.
The nine papers awarded during this quantity have been rigorously reviewed and chosen from 15 submissions. They take care of the final topic and problems with high-dimensional information clustering; current examples of concepts used to discover and examine clusters in excessive dimensionality; and the most typical method of take on dimensionality difficulties, specifically, dimensionality relief and its software in clustering.
Read Online or Download Clustering High--Dimensional Data: First International Workshop, CHDD 2012, Naples, Italy, May 15, 2012, Revised Selected Papers PDF
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Extra resources for Clustering High--Dimensional Data: First International Workshop, CHDD 2012, Naples, Italy, May 15, 2012, Revised Selected Papers
Or, one can set a high density threshold to avoid overwhelming numbers of subspace clusters, and miss higher dimensional subspace clusters. Thus, dimensionality bias is a fundamental threat to meaningful subspace cluster discovery, as the distinction between dense clusters and sparse noisy areas is blurred by eﬀects of the dimensionality. In , a general deﬁnition of the notion of a dimensionality unbiased density measure is given: Definition 3. Dimensionality Unbiased Density Measure. A density measure ϕS is dimensionality unbiased if its expected density is the same for any two subspaces S1 and S2 ⊆ D: ∀ S1 , S2 : E ϕS1 = E ϕS2 Using our notion above, the density measure ϕS is the count of objects within the neighborhood: ϕS (o) = |NεS (o)|.
7 (left). While this approach has been used successfully, also in density-based subspace clustering , its scalability is limited. This is due to the inherent principle used in bottom-up approaches: a high dimensional subspace cluster is reﬂected in its lower dimensional projections. Therefore, in order to generate the interesting high dimensional subspace clusters, a very large number of (redundant) lower dimensional subspace clusters has to be generated ﬁrst. Also, these methods 44 I. Assent st -fir pth e d 1,2,3 1,2,3,4 1,2 1,2,3 1,2,4 1,3,4 2,3,4 1,3 1,4 2,3 2,4 1 2 3 breadth-first ∅ 4 3,4 1,2 1,2,3,4 1,2,4 1,3,4 2,3,4 1,3 1,4 2,3 2,4 1 2 3 4 3,4 ∅ Fig.
There are, of course, no clusters. But we do not know this fact, since in reality we would not know from which distribution the data were generated. In order to ﬁnd clusters in subspaces, we only consider projections to three dimensions here. Figure 10 illustrates a projection where we can see two clusters. One cluster is above the diagonal plane of the unit cube, the other one below. What is the chance that we can ﬁnd such a projection for our uniformly distributed data from the 10,000-dimensional unit hypercube?