Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

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50 3. Fundamental Geo-Raster Operations Figure 3.12. Computation of the Histogram for a Raster Image For the computation of this operation we make use of the histogram calculated in Query. 3.2.2. Let B be a 1-D array containing the histogram values: B = MARRAY sdom(A),g (COND +,sdom(A),i (A[i] = g)) then, C is the array containing true values for the elements of the histogram that are greater than 0: C = MARRAY sdom(B),i (B[i] > 0) Results are shown in Fig. 3.13. Figure 3.13. Computation of the Diversity for a Raster Image Majority/Minority In a classified raster, the majority operation finds the class value with the largest number of elements in the raster. Similarly, the minority operation finds the cell value with fewest number of elements. As an example, consider the following query: Query 3.2.15. Return the cell representing the majority of all cell values contained in 2D 8-bit gray raster image A shown in Fig. 3.14(a). To solve this query we use the histogram computed in Query. 3.2.2, and then select the cell value representing the majority of the different classes. Let h be a 1-D array
3.2 Geo-Raster Operations 51 containing the histogram values, h1 a 1-D array of spatial domain[0:255] containing a list of values from 0 to 255. Let h2 be an array containing the sum of h and h1: h2 = MARRAY [0:255],g (h + h1) then, majority can be computed as follows: COND +,sdom(A),i ((max cells(h) = (h2[i] − h1[i])) ∗ h1[i]) Results are shown in Fig. 3.14. (a) Classified raster (b) Majority class Figure 3.14. Computation of a Majority Operation for a Raster Image 3.2.3 Statistical Aggregate Operations We now consider operations that consist or include one or more statistical aggregate functions. The basic statistical aggregate functions include standard deviation, root square, power, mode, median, variance, and top-k. These functions can be applied to a raster, or a set of rasters retrieved by a logical search. Consider the following examples: Variance Let n be the cardinality of the spatial domain of A, n = card(sdom(A)); and avg a variable containing the average of all cell values of A, avg=avg cells(A); then the variance v of A can be solved as follows: v(A) = 1 n ∗ COND +,sdom(A),i((A[i] − avg) ∗ (A[i] − avg)) Results are shown in Fig. 3.15.
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Applying OLAP Pre-Aggregation Techn
Page 5 and 6: Acknowledgments I would like to exp
Page 7 and 8: Abstract Large multidimensional arr
Page 9 and 10: Contents 1 Introduction and Problem
Page 11 and 12: List of Figures 2.1 3D Array . . .
Page 13 and 14: List of Tables 3.1 UNO and FAO Suit
Page 15 and 16: Chapter 1 Introduction and Problem
Page 17 and 18: Relevant and complementary question
Page 19 and 20: 1.2 Publications Related to this Th
Page 21 and 22: Chapter 2 Background and Related Wo
Page 23 and 24: 2.1 Array Databases 17 Figure 2.2 s
Page 25 and 26: 2.1 Array Databases 19 toward the s
Page 27 and 28: 2.1 Array Databases 21 • Bilinear
Page 29 and 30: 2.1 Array Databases 23 given image
Page 31 and 32: 2.2 On-Line Analytical Processing (
Page 39 and 40: 2.3 Discussion 33 spatial-vector da
Page 41 and 42: 2.3 Discussion 35 • Both applicat
Page 43 and 44: Chapter 3 Fundamental Geo-Raster Op
Page 45 and 46: 3.2 Geo-Raster Operations 39 3.1.2
Page 47 and 48: 3.2 Geo-Raster Operations 41 multip
Page 49 and 50: 3.2 Geo-Raster Operations 43 Table
Page 51 and 52: 3.2 Geo-Raster Operations 45 turn i
Page 53 and 54: 3.2 Geo-Raster Operations 47 (a) Or
Page 55: 3.2 Geo-Raster Operations 49 Query
Page 59 and 60: 3.2 Geo-Raster Operations 53 is the
Page 61 and 62: 3.2 Geo-Raster Operations 55 3.2.4
Page 63 and 64: 3.2 Geo-Raster Operations 57 As in
Page 65 and 66: 3.2 Geo-Raster Operations 59 Local
Page 67 and 68: 3.3 Summary 61 Slicing The slicing
Page 69 and 70: Chapter 4 Answering Basic Aggregate
Page 71 and 72: 4.1 Framework 65 pre-aggregated res
Page 73 and 74: 4.2 Cost Model 67 By partitioning t
Page 75 and 76: 4.2 Cost Model 69 Cost of independe
Page 77 and 78: 4.3 Implementation 71 Algorithm 1 Q
Page 79 and 80: 4.4 Experimental Results 73 Query E
Page 81 and 82: 4.5 Summary 75 pre-aggregates: inde
Page 83 and 84: Chapter 5 Pre-Aggregation Support B
Page 85 and 86: 5.2 Conceptual Framework 79 Figure
Page 87 and 88: 5.2 Conceptual Framework 81 Benefit
Page 89 and 90: 5.4 Answering Scaling Operations Us
Page 91 and 92: 5.5 Experimental Results 85 Algorit
Page 93 and 94: 5.5 Experimental Results 87 (a) Que
Page 95 and 96: 5.5 Experimental Results 89 (a) Sel
Page 97 and 98: 5.5 Experimental Results 91 vectors
Page 99 and 100: 5.5 Experimental Results 93 root no
Page 101 and 102: 5.5 Experimental Results 95 Figure
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5.6 Summary 101 we considered non-u
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Chapter 6 Conclusion One of the big
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6.1 Future Work 105 more non-spatio
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Bibliography [1] Blakeley J. A., La
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BIBLIOGRAPHY 109 [22] Moon B., Vega
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BIBLIOGRAPHY 111 [47] ESRI Inc. Arc
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BIBLIOGRAPHY 113 [73] Stefanovic N.
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BIBLIOGRAPHY 115 [97] Kotidis Y. an
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Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

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