As a simple illustration of a k-means algorithm, consider the following data set consisting of the scores of two variables on each of seven individuals: Subject A B 1 1.0 1.0 2 1.5 2.0 3 3.0 4.0 4 5.0 7.0 5 3.5 5.0 6 4.5 5.0 7 3.5 4.5 This data set is to be grouped into two clusters. As a first step in finding a sensible initial partition, let the A & B values of the two individuals furthest apart (using the Euclidean distance measure), define the initial cluster means, giving: Individual Mean Vector (centroid) Group 1 1 (1.0, 1.0) Group 2 4 (5.0, 7.0) The remaining individuals are now examined in sequence and allocated to the cluster to which they are closest, in terms of Euclidean distance to the cluster mean. The mean vector is recalculated …show more content…
1, 2, 3 (1.8, 2.3) 4, 5, 6 (4.3, 5.7) 6 1, 2, 3 (1.8, 2.3) 4, 5, 6, 7 (4.1, 5.4) Now the initial partition has changed, and the two clusters at this stage having the following characteristics: Individual Mean Vector (centroid) Cluster 1 1, 2, 3 (1.8, 2.3) Cluster 2 4, 5, 6, 7 (4.1, …show more content…
So, we compare each individual’s distance to its own cluster mean and to that of the opposite cluster. And we find: Individual Distance to mean (centroid) of Cluster 1 Distance to mean (centroid) of Cluster 2 1 1.5 5.4 2 0.4 4.3 3 2.1 1.8 4 5.7 1.8 5 3.2 0.7 6 3.8 0.6 7 2.8 1.1 Only individual 3 is nearer to the mean of the opposite cluster (Cluster 2) than its own (Cluster 1). In other words, each individual's distance to its own cluster mean should be smaller that the distance to the other cluster's mean (which is not the case with individual 3). Thus, individual 3 is relocated to Cluster 2 resulting in the new partition: Individual Mean Vector (centroid) Cluster 1 1, 2 (1.3, 1.5) Cluster 2 3, 4, 5, 6, 7 (3.9, 5.1) The iterative relocation would now continue from this new partition until no more relocations occur. However, in this example each individual is now nearer its own cluster mean than that of the other cluster and the iteration stops, choosing the latest partitioning as the final cluster solution. Also, it is possible that the k-means algorithm won't find a final solution. In this case it would be a good idea to consider stopping the algorithm after a pre-chosen maximum of
Level 1 :As per the Considered Data Sets: (Generated nearby values through Rough Data Sets Theory Produces)
Haswell introduced new instructions for x86 ISA, divided into four categories. The first one is AVX2 which uses integer SIMD instructions from 128-bits to 256-bits whereas the original version was a 256 –bit extension using YMM registers, mostly the floating point instructions. In addition Haswell also had Intel’s Fused Multiply Add (FMA) which includes 36 FP instructions that performs 256-bit computations and 60 instructions for 128-bit vectors.
Median: 3, 5, 11, 12, 13, 15, 19, 35, 42, 65 = 13 + 15 = 28/2 = 14
Xij allow all auctions that ended in the last hour at a time when the auction began. Per auction component I, X Xij group consisting of groups to have the values of the (1 /3,1 /2, 1 ,2 ,4 ,6 ,12 ,24, with units of hours) was built. Each group in X, we have created new jobs consist of mean and standard deviation, minimum, maximum values of the initial offer, the shipping price and the final price. As we calculate | Xij |, and a number of similar listed for auction items in the hours before the start of the auction and the number of auctions where the item does not sell. More formally, each auction in our data set, the product tankers A x B x C which is calculated: where
Based on the given sample of student test scores of 50, 60, 74, 83, 83, 90, 90, 92, and 95 after rearranging them from least to greatest. As the mean is based on the average of sum, the average of this sample is 79.67 or 80. The mode refers to numbers that appear the most in a sequence and in this case 83 and 90 both appear twice. Range calculates the difference between the largest and smallest number, which are 95 and 50 which have a difference of 45. The variance is the difference between the sum of squares divided by the sample size, which is the number in the sample minus one (Hansen & Myers, 2012), meaning it takes each number of the set and subtracts
In order to test the effectiveness of IGA and GA when solving the timetabling problem, a comparison with the PSO algorithm was performed to investigate trends of performance. All coding was written in MATLAB code and the test case focused on the three above algorithms. All tests were executed on a 3.30 Ghz Intel core i5 processor with 16 GB of ram. The convergence graphs for IGA, GA, and PSO below shows progress until a valid solution for each of the algorithms were discovered. Each of the algorithms simulated 1,000 generations. The graph in Figure 10 - 14 provides a comparison of the proposed algorithm with the conventional population operator based algorithm.
1. For the following scores, find the mean, median, and the mode. Which would be the most appropriate measure for this data set?
In real applications, the values of the controller parameters will be usually computed for one case (generally, the typical demand) and applied for different scenarios. Therefore, it is important that the controllers adjusted for one scenario, also perform properly in other circumstances. In other words, it is necessary to have a robust controller, especially against different demand profiles.
A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126.
Calculate the ROA to find out how much profit was generated from the assets (Table 5). The existence of unnecessary wasted assets can become an obstacle to the execution of strategy. Conversely, if they can utilize assets without waste, it will be possible to carry out the strategy with less cost. In the total assets, which calculated the management resources by the amount, it is possible to know the profitability and the efficiency on a companywide basis. Figure 6 shows the trend of ROA for five years at Toyota's FY 2011 to 2015. Regarding FY 2011 to 13, it can consider a substantial recovery in net income and an increase in total assets due to an increase in notes receivable. Meanwhile, after FY 2014, the profit margin growth
The quantitative subjective data is collated and organised into forms of a line graph, table values, and the calculation of mean and median data to determine if there’s any form of deviation of data. This will prove if there’s a linear or non-linear relationship between the data and test if there’s any similarities between the data values and/or the overall skew of the graphs. The outliers will be also added onto these graphs and will be compared towards each other recognising if there is a similarity or contrast in data and in relationships between both of the data. This will determine if the hypothesis of “family size has an
This observation takes into account all the selected features x and y coordinates to come up with the mean center location. From here I did a Standard distance analysis to see if there was any pattern of distribution. As you can see in figure 5. And the results presented in table 3. The results of the test varied. BC, Ontario and NWT all had the highest mean distances but as you can see visually there are many outliers beyond the Standard distance circle. Provinces such as Manitoba and Saskatchewan are more compacted closer to the circle and a province such as PEI with the lowest standard distance, given how small the province are all contained close to the mean. The results of this test could show how results can be skewed by the present of outliers compared to the rest of the distribution.
For simple Kmeans algorithm I am using 40 as number of clusters. I tried to use different numbers with 5,10,15,20,25,30,35 but the best I can come up with is 40. That gives me the closest sum of squared error. The following is the result of the simple K means test.
Clustered data can be generated in a wide variety of settings. For instance, patients’ medical records collected throughout a city might be clustered at the clinic- and the health-practitioner-level.^1 In such cases, the individual observations cannot be considered independent and should instead be analyzed as clustered.^1
The mean center is the average location of a set of points. These points can represent regional subdivisions, landslides, water wells, and such in a region. It is the geographic center of the set of observations. In the study area, the average of X-bar and Y-bar coordinate is taken of all the features/observations. The mean center of X and Y are X-bar and Y-bar respectively. For the i-th observation of object, Xi and Yi are the coordinates and n is the number of observations.