### Table 2: A sample data set illustrates clusters embedded in subspaces of a high dimensional space.

2003

"... In PAGE 2: ... Hence, a good subspace clustering algorithm should be able to find clusters and the maximum associated set of dimensions. Consider, for example, a data set with 5 data points of 6 dimensional(given in Table2 ). In this data set, it is obvious that C = {x1, x2, x3} is a cluster and the maximum set of dimensions should be P = {1, 2, 3, 4}.... In PAGE 3: ...here sj is a vector defined as sj = (Aj1, Aj2, ..., Ajnj)T. Since there are possibly multiple states(or values) for a vari- able, a symbol table of a data set is usually not unique. For example, for the data set in Table2 , Table 3 is one of its symbol tables. BC BS A A A A B B B B C C C C D D D D BD BT Table 3: One of the symbol tables of the data set in Table 2.... In PAGE 3: ... For a given symbol table of the data set, the frequency table of each cluster is unique according to that symbol table. For example, for the data set in Table2 , let (C, P) be a subspace cluster, where C = {x1, x2, x3} and P = {1, 2, 3, 4}, if we use the symbol table presented in Table 3, then the corre- sponding frequency table for the subspace cluster (C, P) is given in Table 4. From the definition of frequency fjr in Equation (6), we have the following equalities: nj CG r=1 fjr(C) = |C|, j = 1, 2, .... ..."

Cited by 4

### Table 19. Test error (in % ), high-dimensional data sets.

2006

"... In PAGE 95: ... Table19 Cont. NMC KNNC LDC QDC natural textures Original 54.... ..."

### Table 2: Minimal network size for high-dimensional tori, in the form of a3 Ma25 Nmina5 .

2005

Cited by 12

### Table 1. Average MAEs for both neighborhood dimensions high-dimensional low-dimensional

"... In PAGE 9: ... Figure 3 includes the Mean Absolute Errors for high (ib) and low (svd-ib) di- mensions, as observed for each of the 5 data splits of the data set. These error values are then averaged and Table1 records the flnal results for both implemen- tations. From both the preceding flgure and table, we can conclude that applying Item- based Filtering on the low-rank neighborhood, provides a clear improvement over the higher dimension neighborhood.... ..."

Cited by 1

### Table 4.5: High-dimensional stifi ODE system II: classical approach.

2005

### TABLE 6 Simulated Flit Traversal Energy (pJ) of High-dimensional Tori

### Table 3.2 High-dimensional datasets used in experimental evaluation

### Table 3.2 High-dimensional datasets used in experimental evaluation

### Table 1: Comparing di erent robot learning paradigms based on how they address the credit assignment problem. Robot learning is one of the most interesting and di cult machine learning problems. While much progress has been made by many researchers using di erent paradigms, much more remains to be done in scaling up the algorithms to work with high-dimensional sensors such as vision, to handle partially observable states, to deal with continuous actions, and to deal with learning from limited number of examples. A good way to conclude this look 11

1996

"... In PAGE 11: ... However, designing a good simulator for the general problem of mobile robots operating in unstructured environments, such as a crowded o ce or lab, using high-dimensional sensors such as vision, is an enormously di cult task. 5 Discussion We now summarize the four learning paradigms in Table1 , according to how they address the credit assignment problem. In the inductive learning paradigm, the temporal credit assignment problem is solved by the teacher.... ..."

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