### Abstract

Diffusion distance has been shown to be significantly more effective than Euclidean distance in multi-scale recognition of similar experiences in RecognitionPrimed Decision making (Fan and Su 2010). In this paper, we first examine the experience data set used in the previous study. The visualization of the data set (using the first three dominant eigenvectors of the diffusion space) suggests the applicability of the diffusion approach. Second, we investigate two approaches to the computation of diffusion distance: Spectrum based and Probability-Matching based. Specifically, by 'Spectrum based' approach we refer to the one derived in terms of the eigenvalues/eigenvectors of the normalized diffusion matrix (Coifman and Lafon 2006). We use the term 'Probability-Matching' to refer to the use of various probability distances, where the original L^{2} diffusion distance is treated as a special case. Our preliminary result indicates that the performance of using L ^{2} diffusion distance at least is tied with the use of Spectrum based distance. Furthermore, when spectrum based approach is applied, we have to use the embedding and extending techniques for labeling new experience data (Lieu and Saito 2009), while such re-computation is not necessary when the L ^{2} diffusion distance is used. We do not need to re-compute the diffusion matrix, hence the diffusion map each time when adding a new data. It is more natural and robust especially for labeling new single experience data. The numerical examples also show the improvement on the performance. We are currently working on several other Probability-Matching approaches (e.g. the Earth-Mover's Distance).

Original language | English (US) |
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Title of host publication | Manifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report |

Pages | 59-62 |

Number of pages | 4 |

State | Published - Dec 1 2010 |

Event | 2010 AAAI Fall Symposium - Arlington, VA, United States Duration: Nov 11 2010 → Nov 13 2010 |

### Publication series

Name | AAAI Fall Symposium - Technical Report |
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Volume | FS-10-06 |

### Other

Other | 2010 AAAI Fall Symposium |
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Country | United States |

City | Arlington, VA |

Period | 11/11/10 → 11/13/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Manifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report*(pp. 59-62). (AAAI Fall Symposium - Technical Report; Vol. FS-10-06).

}

*Manifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report.*AAAI Fall Symposium - Technical Report, vol. FS-10-06, pp. 59-62, 2010 AAAI Fall Symposium, Arlington, VA, United States, 11/11/10.

**Applying diffusion distance for multi-scale analysis of an experience space.** / Su, Meng; Fan, Xiaocong; Ge, Wei Li.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Applying diffusion distance for multi-scale analysis of an experience space

AU - Su, Meng

AU - Fan, Xiaocong

AU - Ge, Wei Li

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Diffusion distance has been shown to be significantly more effective than Euclidean distance in multi-scale recognition of similar experiences in RecognitionPrimed Decision making (Fan and Su 2010). In this paper, we first examine the experience data set used in the previous study. The visualization of the data set (using the first three dominant eigenvectors of the diffusion space) suggests the applicability of the diffusion approach. Second, we investigate two approaches to the computation of diffusion distance: Spectrum based and Probability-Matching based. Specifically, by 'Spectrum based' approach we refer to the one derived in terms of the eigenvalues/eigenvectors of the normalized diffusion matrix (Coifman and Lafon 2006). We use the term 'Probability-Matching' to refer to the use of various probability distances, where the original L2 diffusion distance is treated as a special case. Our preliminary result indicates that the performance of using L 2 diffusion distance at least is tied with the use of Spectrum based distance. Furthermore, when spectrum based approach is applied, we have to use the embedding and extending techniques for labeling new experience data (Lieu and Saito 2009), while such re-computation is not necessary when the L 2 diffusion distance is used. We do not need to re-compute the diffusion matrix, hence the diffusion map each time when adding a new data. It is more natural and robust especially for labeling new single experience data. The numerical examples also show the improvement on the performance. We are currently working on several other Probability-Matching approaches (e.g. the Earth-Mover's Distance).

AB - Diffusion distance has been shown to be significantly more effective than Euclidean distance in multi-scale recognition of similar experiences in RecognitionPrimed Decision making (Fan and Su 2010). In this paper, we first examine the experience data set used in the previous study. The visualization of the data set (using the first three dominant eigenvectors of the diffusion space) suggests the applicability of the diffusion approach. Second, we investigate two approaches to the computation of diffusion distance: Spectrum based and Probability-Matching based. Specifically, by 'Spectrum based' approach we refer to the one derived in terms of the eigenvalues/eigenvectors of the normalized diffusion matrix (Coifman and Lafon 2006). We use the term 'Probability-Matching' to refer to the use of various probability distances, where the original L2 diffusion distance is treated as a special case. Our preliminary result indicates that the performance of using L 2 diffusion distance at least is tied with the use of Spectrum based distance. Furthermore, when spectrum based approach is applied, we have to use the embedding and extending techniques for labeling new experience data (Lieu and Saito 2009), while such re-computation is not necessary when the L 2 diffusion distance is used. We do not need to re-compute the diffusion matrix, hence the diffusion map each time when adding a new data. It is more natural and robust especially for labeling new single experience data. The numerical examples also show the improvement on the performance. We are currently working on several other Probability-Matching approaches (e.g. the Earth-Mover's Distance).

UR - http://www.scopus.com/inward/record.url?scp=79960140746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960140746&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79960140746

SN - 9781577354888

T3 - AAAI Fall Symposium - Technical Report

SP - 59

EP - 62

BT - Manifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report

ER -