There have been extensions to the original MKDE proposal. MKDE home range with h min = 1 ( solid line) and h min = 4000 ( dashed line). (2019) analyze the influence of fix rate and tracking duration on the home ranges obtained with MKDE and KDE, thus providing also a comparison between the performance of the two methods on a specific set of locations.įig. Optimal simultaneous selection of all the parameters of MKDE with respect to some criterion seems computationally unfeasible even for moderate sample sizes. 13 we have plotted the MKDE home ranges for two very different values of h min but equal values of the rest of parameters: clearly, the choice of this smoothing parameter can substantially alter the resulting home range. For instance, using package adehabitatHR, in Fig. A drawback of MKDE is that it depends, thus, on the choice of several parameters, such as h min, h max and the length of the subintervals. For each time interval h i is a smooth function of the time lapse from t i and to t i+1, taking its smallest value h min at the end points and the largest (at most h max) at the midpoint. Then KDE is carried out on the known and the interpolated relocations with a variable one-dimensional smoothing parameter h i( t). MKDE consists in dividing each step or time interval into several substeps, that is, adding new points at regular intervals on each step. In the context of estimating the active utilization distribution (describing space frequency use in the active moments of the animal), Benhamou and Cornelis (2010) developed the movement-based kernel density estimation (MKDE) method. This approach does not seem appropriate, since time is not a random variable whose frequency we want to analyze, as we noted at the beginning of Section 2.2. Keating and Cherry (2009) suggested a product kernel density estimator where time was incorporated as an extra variable to the two-dimensional location vector, thus yielding three-dimensional observations. This means that, to design methods to estimate the utilization distribution density, we can proceed exactly the same as for independent data. Nevertheless, there are two important issues that should be remarked: first, the definition of the kernel density estimator for dependent data is exactly the same as for independent data, and second, regarding the fundamental problem of bandwidth selection, the data can be treated as if they were independent, since the asymptotically optimal bandwidth for independent data is also optimal under quite general conditions of dependence, as shown in Hall et al. There have been various attempts to generalize the kernel home range estimator to incorporate the time dependence between the observed locations. Experiments on different benchmarking data sets demonstrate that the proposed method has comparable performance with the state-of-art method and it is effective for a wide range of kernel methods to achieve fast learning in large data sets.Amparo Baíllo, José Enrique Chacón, in Handbook of Statistics, 2021 2.2.1.2 Kernel density estimation It has a time complexity of O(m(3)) where m is the number of the data points sampled from the training set. With just a simple sampling strategy, the resulted FastKDE method can be used to scale up various kernel methods with a theoretical guarantee that their performance does not degrade a lot. In this paper, the latest advance in fast data reduction via KDE is exploited. As a result, FastKDE approximation methods can be applied to solve these QP problems. It is based on establishing a connection between KDE and the QP problems formulated for kernel methods using an entropy-based integrated-squared-error criterion. By observing that many kernel methods can be linked up with kernel density estimate (KDE) which can be efficiently implemented by some approximation techniques, a new learning method called fast KDE (FastKDE) is proposed to scale up kernel methods. It is thus computationally infeasible in applying them to large data sets, and a replacement of the naive method for finding the quadratic programming (QP) solutions is highly desirable. Kernel methods such as the standard support vector machine and support vector regression trainings take O(N(3)) time and O(N(2)) space complexities in their naïve implementations, where N is the training set size.
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