Why do some ways to take data samples (others not) fail

Links table

Abstract and 1 introduction

2 preliminary and relevant work

2.1 On samples strategies

2.2 Other distribution strategies

2.3 CoreSets for database applications

2.4 Quadtree included

3 fast stations

4 Reducing the effect of proliferation

4.1 Calculate higher raw boundaries

4.2 of the approximate solution to reduce the spread

5 fast pressure in practice

5.1 goals and scope of experimental analysis

5.2 Experimental preparation

5.3 Sampling strategies assessment

5.4 broadcast preparation and 5.5 fast food

6 Conclusion

7 thanks and appreciation

8 evidence, false symbol, accessories and 8.1 evidence of the natural result 3.2

8.2 Reducing K-Means to K-Median

8.3 Estimating the optimum cost in a tree

8.4 Al -Khwarizmia accessories 1

Reference

5.3 Sampling strategies assessment

Theoretical guaranteed methods. First, we remove the comparison between the fast network algorithm and take samples of standard sensitivity. Specifically, the last columns of Tables 4 and 5 show that the rapid network method produces pressure from the constantly low distortion and that this

It is held across data collections, M-SCALAR values ​​and broadcasting. Nevertheless, Figure 1 shows that the 3 to 400 variable causes a written slowdown in taking allergic samples, but only Logaretami of the fast network method. This analysis confirms the theory in Section 4-obtaining an equal pressure in taking allergic samples, but they do not have a written dependence at the time of operation on K. So we do not add samples of traditional allergies to the remaining experiences.

Speed ​​for accuracy. We are now referring the reader to the remaining columns of Table 4 and to Figure 2, where we show the effect of core size through data collections by collecting M-SCALAR values. Despite the optimal level theoretical guarantees of accelerating samples methods, we see that they get competitive distortions on most data groups in the real world with faster operation than quick posts in practice. However, the uniform samples breaks on taxi and stars data groups – the taxi corresponds to the start -up sites of taxi riding in Porto and have many varied size groups while stars are the pixels values ​​for the shooting of fire (most black pixels except for a small set of White pixel units). Thus, it seems that uniform samples require well -preserved data sets, with a few extremist values ​​and consistent semesters sizes.

To verify this, consider the results of these samples strategies on the groups of artificial data in Table 4 and Figure 2: With the growth of contrast in block sizes and distributions, rapid samples methods

It has difficulty picking up all the distant points in the data set. Thus, Figure 2 shows a clear reaction between the time of operation and the quality of the sample: the sooner the method, the higher its pressure.

Although uniform samples are expected to be fragile, it may be less clear that causes light Corets fracture and weight. The explanation is simple for lightweight coresets: it is a sample according to a 1-mean solution, and therefore it is biased towards the points far from the center. Thus, as a simple counter -founder, lightweight coresets may miss a small group close to the bloc center of the data group. This can be seen in Figure 3, where we show an example in which the light construction of Coret fails to the Gaussian Mixture data collection. Since the small cycle block close to the database center, it misses the samples according to the distance from the average.

We evaluate the full range of this relationship in Table 7, where we offer the interaction between the J -Welterex’s Coret (the number of centers in the approximate solution) and the Gaussian Mixture Thiber γ (leading to a high layer defect). We can consider this answer to the question, “How much is our approximate solution before it can take samples from allergies to deal with the imbalance in the layer?” To achieve this purpose, all methods have a low distortion of the small values ​​of γ, but with γ growth, only the fast CoreSets (and to a lower limit, the heavyweight timing of greater values ​​than J) is guaranteed to distort.

In order to complete, we check that these results also maintain the K-Median task in Figure 4. We show one of five runs to emphasize the random nature of the quality of pressure when using different samples.

To take out the data group analysis, we note that BICO is constantly weak on the nuclear distortion scale[9]It is clear in Table 6. We also analyze the Streamkm ++ method through artificial data collections in Table 9 with M = 40K and we see that they get bad deformities compared to taking allergic samples. This is due to the required CoreSet size of Streamkm ++ – the logarithms in N and Opensity in D – is much larger than that of taking allergic samples (sample sample depends on any teacher). We did not include Streamkm ++ in the 4 and 5 tables due to its optimal core size, distortion and operation time.

Finally, we point out that every way to take samples work well on the standard data set, which is designed to punish the adoption of allergic samples explicitly on the initial solution. Thus, we check that there is no preparation that breaks the sensitivity samples.

Finally, we show the quality of these pressure schemes that facilitate rapid assembly on large data collections in Table 8. Keep in mind that the large in the cores means that the centers obtained on Coret represent the full data set badly. However, among the methods of taking samples with small distortion, it may be that one constantly leads to “the best” solutions. To test this, we compare the quality of the solution across all highways on data groups in the real world, where core distortions are consistent. In fact, Table 8 shows that there is no way to take samples that lead to constantly slim cost solutions.

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[9] We do not include BICO or Streamkm ++ in forms 2, 4, 5, because it does not fall into the o ˜ (ND) complex category and is only designed for Mean.