The euclidean distance degree

Draisma, Jan; Horobet, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R.

doi:10.1145/2631948.2631951

Cited by 24 publications

(10 citation statements)

References 17 publications

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“…The resolution of the MLE for semialgebraic statistical models is a leading research problem in the area of Algebraic Statistics and, more in general, Applied Algebraic Geometry. With respect to the range based localization, some results on the Euclidean Degree of Cayley-Menger varieties are contained in [26]. However, we observe that a CM variety is not the real set of noiseless range measurements, since it is defined in terms of the squared distances between the source and the receivers.…”

Section: Discussionmentioning

confidence: 97%

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The Algebro-geometric Study of Range Maps

et al. 2016

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In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKeanVlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.

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Section: Discussionmentioning

confidence: 97%

“…In our geometrical perspective, by moving the sensors on the x-plane, we change the shape of Im(T 3 ). Let us recall equation (26) defining the Kummer's surfaceS :…”

Section: The Image Of T 3 When the Receivers Are Not Collinearmentioning

confidence: 99%

The Algebro-geometric Study of Range Maps

et al. 2016

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“…High AUC and low RMSE values indicate better performing models. To evaluate the models considering both the metrics simultaneously, we calculated the Euclidean distance from the AUC and RMSE obtained in each model to the ideal values (1 and 0 respectively) of these metrics (Draisma et al., 2014).…”

Section: Methodsmentioning

confidence: 99%

“…For the biogeographical status analyses, we applied a variation of AUC calculation, the multiclass receiver operating characteristic (ROC), which allows analysing multiclass data (Wandishin & Mullen, 2009). The RMSE indicates how close the predictions are to the actual values (Chai & Draxler, 2014 to the ideal values (1 and 0 respectively) of these metrics (Draisma et al, 2014).…”

Section: Model Construction Evaluation and Validation Stepsmentioning

confidence: 99%

bRacatus: A method to estimate the accuracy and biogeographical status of georeferenced biological data

et al. 2021

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“…Cosine similarity (Vit, 2018), Euclidian distance (Draisma, et al, 2014), Pearson correlation (Pearson, 1895), and Jaccard similarity (Michael, 1971) are used to can be used to calculate the similarity of the products or the users. Among them cosine similarity and Pearson correlation is widely used (Bobadilla et al, 2013).…”

Section: Collaborative Filteringmentioning

confidence: 99%

MovieANN: Film Öneri Sistemlerine Çok Katmanlı Yapay Sinir Ağı Kullanarak Karma Bir Yaklaşım

Yücebaş

2019

Çanakkale Onsekiz Mart Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The amount of data in World Wide Web is growing exponentially. Users are often lost in this vast ocean of data. In order to filter the valuable information from vast amount of data, recommendation systems are used. These systems are based on collaborative filtering, content based filtering and hybrid approaches. We combined collaborative and contentbased filtering to build a hybrid movie recommendation system, MovieANN, based on neural network model. To make better recommendations in a collaborative approach, both user and movie clusters are formed. In addition to rating information, content information was also considered in the formation of the clusters. Clusters are formed according to K-Means and X-Means algorithms. Final clusters are chosen according to Davies-Bouldin Index and intra cluster distance. Homogeneity and density of the clusters are also considered. Movie and user clusters are mapped in the recommendation phase. The model is tested on a MoiveLens 1M dataset that consists of six thousand users, four thousand movies and one million ratings. Four clusters are formed to represent movieuser mappings and for each cluster, a recommendation model based on multi-layer neural network is constructed. The recommendation performance in terms of accuracy is 84.52%, 84.54% in terms of precision and 99.98% in terms of recall.

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The euclidean distance degree

Cited by 24 publications

References 17 publications

The Algebro-geometric Study of Range Maps

The Algebro-geometric Study of Range Maps

bRacatus: A method to estimate the accuracy and biogeographical status of georeferenced biological data

MovieANN: Film Öneri Sistemlerine Çok Katmanlı Yapay Sinir Ağı Kullanarak Karma Bir Yaklaşım

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