| Turn Nonmetric Proximities into Metric Ones (Section 5) . | ||
|---|---|---|
| A1: Eigenvalue corrections (like clipping, flipping, shifting) are applied to the eigenspectrum of the data (Muoz & De Diego, 2006; Roth, Laub, Buhmann, & Müller, 2002; Y. Chen, Garcia, Gupta, Rahimi, & Cazzanti, 2009; Filippone, 2009). This can also be effectively done for dissimilarities by a specific preprocessing (Schleif & Gisbrecht, 2013) | A2: Embedding approaches like (variants of MDS (Cox & Cox, 2000; Choo, Bohn, Nakamura, White, & Park, 2012), t-SNE (Van der Maaten & Hinton, 2012), NeRV (Venna, Peltonen, Nybo, Aidos, & Kaski, 2010) can be used to obtain Euclidean embedding in a lower-dimensional space but also the (dis-)similarity (proximity) space is a kind of embedding leading to a vectorial representation (Pekalska & Duin, 2008a, 2008b, 2002; Pekalska, Paclík, & Duin, 2001; Pekalska, Duin, & Paclík, 2006; Kar & Jain, 2011; Duin et al., 2014), as well as nonmetric locality-sensitive hashing (Mu & Yan, 2010) and local embedding or triangle correction techniques (L. Chen & Lian, 2008) | A3: Learning of a proxy function is frequently used to obtain an alternative psd proximity matrix that has maximum alignment with the original non-psd matrix. (J. Chen & Ye, 2008; Luss & d’Aspremont, 2009; Y. Chen, Gupta, & Recht, 2009; Gu & Guo, 2012; Lu, Keles, Wright, & Wahba, 2005; Brickell, Dhillon, Sra, & Tropp, 2008; Li, Yeung, & Ko, 2015) |
| Algorithms for Learning on Nonmetric data (section 6) | ||
| B1: Algorithms with a decision function that can be based on nonmetric proximities (Kar & Jain, 2012; Tipping, 2001a; Chen, Tino, & Yao, 2009, 2014; Graepel, Herbrich, Bollmann-Sdorra, & Obermayer, 1998) | B2: Algorithms that define their models in the pseudo-Euclidean space (Haasdonk & Pekalska, 2008; Pekalska & Haasdonk, 2009; Liwicki, Zafeiriou, & Pantic, 2013; Liwicki, Zafeiriou, Tzimiropoulos, & Pantic, 2012; Zafeiriou, 2012; Kowalski, Szafranski, & Ralaivola, 2009; Xue & Chen, 2014; J. Yang & Fan, 2013; Pekalska et al., 2001) | |
| Theoretical Work for Indefinite Data Analysis and Related Overviews | ||
| Focusing on SVM (Haasdonk, 2005; Mierswa & Morik, 2008; Tien Lin & Lin, 2003; Ying, Campbell, & Girolami, 2009), indefinite kernels and pseudo-euclidean spaces (Balcan, Blum, & Srebro, 2008; Wang, Sugiyama, Yang, Hatano, & Feng, 2009; Brickell et al., 2008; Schleif & Gisbrecht, 2013; Schleif, 2014; Pekalska & Duin, 2005; Pekalska et al., 2004, 2001; Ong et al., 2004; Laub, Roth, Buhmann, & Müller, 2006; D. Chen, Wang, & Tsang, 2008; Duin & Pekalska, 2010; Gnecco, 2013; Xu et al., 2011; Higham, 1988; Goldfarb, 1984; Graepel & Obermayer, 1999; Zhou & Wang, 2011; Alpay, 1991; Haasdonk & Keysers, 2002); indexing, retrieval, and metric modification techniques (Zhang et al., 2009; Skopal & Loko, 2008; Bustos & Skopal, 2011; Vojt & Eckhardt, 2009; Jensen, Mungure, Pedersen, Srensen, & Delige, 2010); overview papers and cross-discipline studies (Y. Chen et al., 2009; Muoz & De Diego, 2006; Duin, 2010; Kinsman et al., 2012; Laub, 2004; Hodgetts & Hahn, 2012; Hodgetts et al., 2009; Kanzawa, 2012) | ||
| Turn Nonmetric Proximities into Metric Ones (Section 5) . | ||
|---|---|---|
| A1: Eigenvalue corrections (like clipping, flipping, shifting) are applied to the eigenspectrum of the data (Muoz & De Diego, 2006; Roth, Laub, Buhmann, & Müller, 2002; Y. Chen, Garcia, Gupta, Rahimi, & Cazzanti, 2009; Filippone, 2009). This can also be effectively done for dissimilarities by a specific preprocessing (Schleif & Gisbrecht, 2013) | A2: Embedding approaches like (variants of MDS (Cox & Cox, 2000; Choo, Bohn, Nakamura, White, & Park, 2012), t-SNE (Van der Maaten & Hinton, 2012), NeRV (Venna, Peltonen, Nybo, Aidos, & Kaski, 2010) can be used to obtain Euclidean embedding in a lower-dimensional space but also the (dis-)similarity (proximity) space is a kind of embedding leading to a vectorial representation (Pekalska & Duin, 2008a, 2008b, 2002; Pekalska, Paclík, & Duin, 2001; Pekalska, Duin, & Paclík, 2006; Kar & Jain, 2011; Duin et al., 2014), as well as nonmetric locality-sensitive hashing (Mu & Yan, 2010) and local embedding or triangle correction techniques (L. Chen & Lian, 2008) | A3: Learning of a proxy function is frequently used to obtain an alternative psd proximity matrix that has maximum alignment with the original non-psd matrix. (J. Chen & Ye, 2008; Luss & d’Aspremont, 2009; Y. Chen, Gupta, & Recht, 2009; Gu & Guo, 2012; Lu, Keles, Wright, & Wahba, 2005; Brickell, Dhillon, Sra, & Tropp, 2008; Li, Yeung, & Ko, 2015) |
| Algorithms for Learning on Nonmetric data (section 6) | ||
| B1: Algorithms with a decision function that can be based on nonmetric proximities (Kar & Jain, 2012; Tipping, 2001a; Chen, Tino, & Yao, 2009, 2014; Graepel, Herbrich, Bollmann-Sdorra, & Obermayer, 1998) | B2: Algorithms that define their models in the pseudo-Euclidean space (Haasdonk & Pekalska, 2008; Pekalska & Haasdonk, 2009; Liwicki, Zafeiriou, & Pantic, 2013; Liwicki, Zafeiriou, Tzimiropoulos, & Pantic, 2012; Zafeiriou, 2012; Kowalski, Szafranski, & Ralaivola, 2009; Xue & Chen, 2014; J. Yang & Fan, 2013; Pekalska et al., 2001) | |
| Theoretical Work for Indefinite Data Analysis and Related Overviews | ||
| Focusing on SVM (Haasdonk, 2005; Mierswa & Morik, 2008; Tien Lin & Lin, 2003; Ying, Campbell, & Girolami, 2009), indefinite kernels and pseudo-euclidean spaces (Balcan, Blum, & Srebro, 2008; Wang, Sugiyama, Yang, Hatano, & Feng, 2009; Brickell et al., 2008; Schleif & Gisbrecht, 2013; Schleif, 2014; Pekalska & Duin, 2005; Pekalska et al., 2004, 2001; Ong et al., 2004; Laub, Roth, Buhmann, & Müller, 2006; D. Chen, Wang, & Tsang, 2008; Duin & Pekalska, 2010; Gnecco, 2013; Xu et al., 2011; Higham, 1988; Goldfarb, 1984; Graepel & Obermayer, 1999; Zhou & Wang, 2011; Alpay, 1991; Haasdonk & Keysers, 2002); indexing, retrieval, and metric modification techniques (Zhang et al., 2009; Skopal & Loko, 2008; Bustos & Skopal, 2011; Vojt & Eckhardt, 2009; Jensen, Mungure, Pedersen, Srensen, & Delige, 2010); overview papers and cross-discipline studies (Y. Chen et al., 2009; Muoz & De Diego, 2006; Duin, 2010; Kinsman et al., 2012; Laub, 2004; Hodgetts & Hahn, 2012; Hodgetts et al., 2009; Kanzawa, 2012) | ||
Note: The table provides a brief summary and the most relevant references.