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... formulation serves this purpose, where elasticities may be adjusted via fmincon or fitting algorithms, in conjunction with the intrinsic property of the CD-HPF that ensures global maxima for concavity. Our simulations, that include animation and graphs, support this trend (see Figures 1 and 2 in Section 3). As the physical parameters change in value, so do the function values and its maximum for all the exoplanets in the catalog, and this might rearrange the CDHS pattern with possible changes in the parameters, while maintaining consistency with the database. ...
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... optimal surface CDHS are obtained at γ = 0.8 and δ = 0.1. Using these results, 3-D graphs are generated and are shown in Figure 1. The X and Y axes represent elasticities and Z-axis represents CDHS of exoplanets. ...
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... 4, 5 and 6 show results for CRS, where the sum of the elasticities = 1 (The theoretical proof is given in Appendix C). The approximation algorithm fmincon initiates the search for the optima by starting from a random initial guess, and then it applies a step increment or decrements based on the gradient of the Figures 1 and 2 show all the elasticities for which fmincon searches for the global maximum in CDHS, indicated by a black circle. Those values are read off from the code (given in Appendix E) and printed as 0.8 and 0.1, or whichever the case may be. ...
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... surface plot essentially), corresponding to 664 exoplanets under consideration. Each frame is a visual representation of the outcome of CD-HPF and CDHS applied to each exoplanet. The X and Y axes of the 3-D plots represent elasticity constants and Z-axis represents the CDHS. Simply stated, each frame, demonstrated as snapshots of the animation in Figs. 1 and 2, is endowed with a maximum CDHS and the cumulative effect of all such frames is elegantly captured in the animation. Training-testing process is integral to machine learning, where the machine is trained to recognize patterns by assimilating a lot of data and, upon applying the learned patterns, identifies new data with a reasonable ...
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... us consider the CDPF for gaining more insight to computing the elasticity for maximization of the CDHS (Saha et al., 2016). The following heuristic produces easy and quick way to compute elasticity in real time. ...
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... agree that equation 8 is not a linear combination of Y1 and Y2 from equations 5 and 6, respectively. The formulas for Y1 and Y2 are used to show simulation visualization ( Figures 1 and 2) . The difference between the function values in equations 7 and 8 is insignificant as we saw by computing the CDHS both ways. ...
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... The habitability problem has been tackled in different ways. Explicit Earth-similarity score computation (Bora et al., 2016) based on parameters mass, radius, surface temperature and escape velocity developed into Cobb-Douglas Habitability Score helped identify candidates with similar scores to Earth. However, using Earth-similarity alone to address habitability is not sufficient unless model based evaluations (Saha et al., 2018c) are interpreted and equated with feature based classification . ...
... One of the key reasons to classify exoplanets is the limitation of finding out habitability candidates by Earth similarity alone, as proposed by several metric based evaluations, namely the Earth Similarity Index, Biological Complexity Index (Irwin et al., 2014b), Planetary Habitability Index (Méndez, 2018) and Cobb-Douglas Habitability Score (CDHS) (Bora et al., 2016). In Saha et al. (2018), an advanced tree-based classifier, Gradient Boosted Decision Tree was used to classify Proxima b and other planets in the TRAPPIST-1 system. ...
... We note, the motivation of SBAF is derived from using kx α (1 − x) 1−α as discriminating function to optimize the width of the two separating hyperplanes in an SVM-like formulation. This is equivalent to the CDHS formulation when CD-HPF (Bora et al., 2016) is written as y = kx α (1 − x) β where α + β = 1, 0 ≤ α ≤ 1, 0 ≤ β ≤ 1, and k is suitably assumed to be 1 (CRS condition). The representation ensures global maxima (maximum width of the separating hyperplanes) under such constraints (Bora et al., 2016). ...
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1.Apache software foundation projects for Big Data
2.Data acquisition
2.1 Freely available data set sources
2.2 Data collection through API’s
2.3 Web scraping
2.4 Web crawling
3. Data pre-processing and cleanup
3.1 Need for Hadoop Map Reduce and other languages for big data pre processing
3.2 Comparison of Hadoop Map Reduce, Python and R
3.3 Various examples of cleansing methods and routines.
4. Data analysis
4.1 Big data analysis using Apache Foundation Projects
4.2 Various language support by Apache Hadoop
4.3 Apache spark for big data analytics
4.4 Case study: Dimensionality reduction using Apache Spark: an illustrative example from Scientometric big data
4.4.1 Why SVD? The solution may be the problem
4.4.2 Need for SVD
4.4.3 SVD using Hadoop Streaming with NUMPY
4.4.4 SVD using Apache Mahout
4.4.5 SVD using Apache Spark
4.5 Data analysis through visualization using Python
