---
_id: '20888'
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
- first_name: Kathrin
full_name: Bujna, Kathrin
last_name: Bujna
citation:
ama: Blömer J, Brauer S, Bujna K. A Complexity Theoretical Study of Fuzzy K-Means.
ACM Transactions on Algorithms. 2020;16(4):1-25. doi:10.1145/3409385
apa: Blömer, J., Brauer, S., & Bujna, K. (2020). A Complexity Theoretical Study
of Fuzzy K-Means. ACM Transactions on Algorithms, 16(4), 1–25. https://doi.org/10.1145/3409385
bibtex: '@article{Blömer_Brauer_Bujna_2020, title={A Complexity Theoretical Study
of Fuzzy K-Means}, volume={16}, DOI={10.1145/3409385},
number={4}, journal={ACM Transactions on Algorithms}, author={Blömer, Johannes
and Brauer, Sascha and Bujna, Kathrin}, year={2020}, pages={1–25} }'
chicago: 'Blömer, Johannes, Sascha Brauer, and Kathrin Bujna. “A Complexity Theoretical
Study of Fuzzy K-Means.” ACM Transactions on Algorithms 16, no. 4 (2020):
1–25. https://doi.org/10.1145/3409385.'
ieee: J. Blömer, S. Brauer, and K. Bujna, “A Complexity Theoretical Study of Fuzzy
K-Means,” ACM Transactions on Algorithms, vol. 16, no. 4, pp. 1–25, 2020.
mla: Blömer, Johannes, et al. “A Complexity Theoretical Study of Fuzzy K-Means.”
ACM Transactions on Algorithms, vol. 16, no. 4, 2020, pp. 1–25, doi:10.1145/3409385.
short: J. Blömer, S. Brauer, K. Bujna, ACM Transactions on Algorithms 16 (2020)
1–25.
date_created: 2021-01-08T08:51:42Z
date_updated: 2022-01-06T06:54:41Z
department:
- _id: '64'
doi: 10.1145/3409385
intvolume: ' 16'
issue: '4'
language:
- iso: eng
page: 1-25
project:
- _id: '45'
name: Soft-Clustering - Von Heuristiken zu Approximationsalgorithmen
publication: ACM Transactions on Algorithms
publication_identifier:
issn:
- 1549-6325
- 1549-6333
publication_status: published
status: public
title: A Complexity Theoretical Study of Fuzzy K-Means
type: journal_article
user_id: '13291'
volume: 16
year: '2020'
...
---
_id: '10790'
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
- first_name: Kathrin
full_name: Bujna, Kathrin
last_name: Bujna
- first_name: Daniel
full_name: Kuntze, Daniel
last_name: Kuntze
citation:
ama: Blömer J, Brauer S, Bujna K, Kuntze D. How well do SEM algorithms imitate EM
algorithms? A non-asymptotic analysis for mixture models. Advances in Data
Analysis and Classification. 2020;14:147–173. doi:10.1007/s11634-019-00366-7
apa: Blömer, J., Brauer, S., Bujna, K., & Kuntze, D. (2020). How well do SEM
algorithms imitate EM algorithms? A non-asymptotic analysis for mixture models.
Advances in Data Analysis and Classification, 14, 147–173. https://doi.org/10.1007/s11634-019-00366-7
bibtex: '@article{Blömer_Brauer_Bujna_Kuntze_2020, title={How well do SEM algorithms
imitate EM algorithms? A non-asymptotic analysis for mixture models}, volume={14},
DOI={10.1007/s11634-019-00366-7},
journal={Advances in Data Analysis and Classification}, author={Blömer, Johannes
and Brauer, Sascha and Bujna, Kathrin and Kuntze, Daniel}, year={2020}, pages={147–173}
}'
chicago: 'Blömer, Johannes, Sascha Brauer, Kathrin Bujna, and Daniel Kuntze. “How
Well Do SEM Algorithms Imitate EM Algorithms? A Non-Asymptotic Analysis for Mixture
Models.” Advances in Data Analysis and Classification 14 (2020): 147–173.
https://doi.org/10.1007/s11634-019-00366-7.'
ieee: J. Blömer, S. Brauer, K. Bujna, and D. Kuntze, “How well do SEM algorithms
imitate EM algorithms? A non-asymptotic analysis for mixture models,” Advances
in Data Analysis and Classification, vol. 14, pp. 147–173, 2020.
mla: Blömer, Johannes, et al. “How Well Do SEM Algorithms Imitate EM Algorithms?
A Non-Asymptotic Analysis for Mixture Models.” Advances in Data Analysis and
Classification, vol. 14, 2020, pp. 147–173, doi:10.1007/s11634-019-00366-7.
short: J. Blömer, S. Brauer, K. Bujna, D. Kuntze, Advances in Data Analysis and
Classification 14 (2020) 147–173.
date_created: 2019-07-11T08:08:25Z
date_updated: 2022-01-06T06:50:50Z
department:
- _id: '64'
doi: 10.1007/s11634-019-00366-7
intvolume: ' 14'
language:
- iso: eng
page: 147–173
project:
- _id: '45'
name: Soft-Clustering - Von Heuristiken zu Approximationsalgorithmen
publication: Advances in Data Analysis and Classification
publication_identifier:
issn:
- 1862-5347
- 1862-5355
publication_status: published
status: public
title: How well do SEM algorithms imitate EM algorithms? A non-asymptotic analysis
for mixture models
type: journal_article
user_id: '13291'
volume: 14
year: '2020'
...
---
_id: '2916'
author:
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
citation:
ama: Brauer S. Complexity of single-swap heuristics for metric facility location
and related problems. Theoretical Computer Science. 2019;754:88-106. doi:10.1016/j.tcs.2018.04.048
apa: Brauer, S. (2019). Complexity of single-swap heuristics for metric facility
location and related problems. Theoretical Computer Science, 754,
88–106. https://doi.org/10.1016/j.tcs.2018.04.048
bibtex: '@article{Brauer_2019, title={Complexity of single-swap heuristics for metric
facility location and related problems}, volume={754}, DOI={10.1016/j.tcs.2018.04.048},
journal={Theoretical Computer Science}, publisher={Elsevier}, author={Brauer,
Sascha}, year={2019}, pages={88–106} }'
chicago: 'Brauer, Sascha. “Complexity of Single-Swap Heuristics for Metric Facility
Location and Related Problems.” Theoretical Computer Science 754 (2019):
88–106. https://doi.org/10.1016/j.tcs.2018.04.048.'
ieee: S. Brauer, “Complexity of single-swap heuristics for metric facility location
and related problems,” Theoretical Computer Science, vol. 754, pp. 88–106,
2019.
mla: Brauer, Sascha. “Complexity of Single-Swap Heuristics for Metric Facility Location
and Related Problems.” Theoretical Computer Science, vol. 754, Elsevier,
2019, pp. 88–106, doi:10.1016/j.tcs.2018.04.048.
short: S. Brauer, Theoretical Computer Science 754 (2019) 88–106.
date_created: 2018-05-25T11:10:36Z
date_updated: 2022-01-06T06:58:46Z
department:
- _id: '64'
doi: 10.1016/j.tcs.2018.04.048
intvolume: ' 754'
language:
- iso: eng
page: 88-106
project:
- _id: '45'
name: Soft-Clustering - Von Heuristiken zu Approximationsalgorithmen
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
status: public
title: Complexity of single-swap heuristics for metric facility location and related
problems
type: journal_article
user_id: '13291'
volume: 754
year: '2019'
...
---
_id: '13679'
author:
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
citation:
ama: Brauer S. Classification and Approximation of Geometric Location Problems.
Paderborn; 2019. doi:10.17619/UNIPB/1-816
apa: Brauer, S. (2019). Classification and Approximation of Geometric Location
Problems. Paderborn. https://doi.org/10.17619/UNIPB/1-816
bibtex: '@book{Brauer_2019, place={Paderborn}, title={Classification and Approximation
of Geometric Location Problems}, DOI={10.17619/UNIPB/1-816},
author={Brauer, Sascha}, year={2019} }'
chicago: Brauer, Sascha. Classification and Approximation of Geometric Location
Problems. Paderborn, 2019. https://doi.org/10.17619/UNIPB/1-816.
ieee: S. Brauer, Classification and Approximation of Geometric Location Problems.
Paderborn, 2019.
mla: Brauer, Sascha. Classification and Approximation of Geometric Location Problems.
2019, doi:10.17619/UNIPB/1-816.
short: S. Brauer, Classification and Approximation of Geometric Location Problems,
Paderborn, 2019.
date_created: 2019-10-09T10:00:53Z
date_updated: 2022-01-06T06:51:41Z
department:
- _id: '64'
doi: 10.17619/UNIPB/1-816
language:
- iso: eng
place: Paderborn
project:
- _id: '45'
name: Soft-Clustering - Von Heuristiken zu Approximationsalgorithmen
status: public
supervisor:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
title: Classification and Approximation of Geometric Location Problems
type: dissertation
user_id: '13291'
year: '2019'
...
---
_id: '4344'
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
- first_name: Kathrin
full_name: Bujna, Kathrin
last_name: Bujna
citation:
ama: 'Blömer J, Brauer S, Bujna K. Coresets for Fuzzy K-Means with Applications.
In: 29th International Symposium on Algorithms and Computation (ISAAC 2018).
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik; 2018:46:1--46:12. doi:10.4230/LIPIcs.ISAAC.2018.46'
apa: 'Blömer, J., Brauer, S., & Bujna, K. (2018). Coresets for Fuzzy K-Means
with Applications. In 29th International Symposium on Algorithms and Computation
(ISAAC 2018) (pp. 46:1--46:12). Jiaoxi, Yilan County, Taiwan: Schloss Dagstuhl--Leibniz-Zentrum
fuer Informatik. https://doi.org/10.4230/LIPIcs.ISAAC.2018.46'
bibtex: '@inproceedings{Blömer_Brauer_Bujna_2018, title={Coresets for Fuzzy K-Means
with Applications}, DOI={10.4230/LIPIcs.ISAAC.2018.46},
booktitle={29th International Symposium on Algorithms and Computation (ISAAC
2018)}, publisher={Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, author={Blömer,
Johannes and Brauer, Sascha and Bujna, Kathrin}, year={2018}, pages={46:1--46:12}
}'
chicago: Blömer, Johannes, Sascha Brauer, and Kathrin Bujna. “Coresets for Fuzzy
K-Means with Applications.” In 29th International Symposium on Algorithms and
Computation (ISAAC 2018), 46:1--46:12. Schloss Dagstuhl--Leibniz-Zentrum
fuer Informatik, 2018. https://doi.org/10.4230/LIPIcs.ISAAC.2018.46.
ieee: J. Blömer, S. Brauer, and K. Bujna, “Coresets for Fuzzy K-Means with Applications,”
in 29th International Symposium on Algorithms and Computation (ISAAC 2018),
Jiaoxi, Yilan County, Taiwan, 2018, pp. 46:1--46:12.
mla: Blömer, Johannes, et al. “Coresets for Fuzzy K-Means with Applications.” 29th
International Symposium on Algorithms and Computation (ISAAC 2018), Schloss
Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, pp. 46:1--46:12, doi:10.4230/LIPIcs.ISAAC.2018.46.
short: 'J. Blömer, S. Brauer, K. Bujna, in: 29th International Symposium on Algorithms
and Computation (ISAAC 2018), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik,
2018, pp. 46:1--46:12.'
conference:
end_date: 2018-12-19
location: Jiaoxi, Yilan County, Taiwan
name: 29th International Symposium on Algorithms and Computation (ISAAC)
start_date: 2018-12-17
date_created: 2018-09-03T08:04:19Z
date_updated: 2022-01-06T07:00:57Z
department:
- _id: '64'
doi: 10.4230/LIPIcs.ISAAC.2018.46
language:
- iso: eng
page: 46:1--46:12
project:
- _id: '45'
name: Soft-Clustering - Von Heuristiken zu Approximationsalgorithmen
publication: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
publication_identifier:
isbn:
- 978-3-95977-094-1
publication_status: published
publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
status: public
title: Coresets for Fuzzy K-Means with Applications
type: conference
user_id: '13291'
year: '2018'
...
---
_id: '2381'
abstract:
- lang: eng
text: Metric facility location and K-means are well-known problems of combinatorial
optimization. Both admit a fairly simple heuristic called single-swap, which adds,
drops or swaps open facilities until it reaches a local optimum. For both problems,
it is known that this algorithm produces a solution that is at most a constant
factor worse than the respective global optimum. In this paper, we show that single-swap
applied to the weighted metric uncapacitated facility location and weighted discrete
K-means problem is tightly PLS-complete and hence has exponential worst-case running
time.
author:
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
citation:
ama: 'Brauer S. Complexity of Single-Swap Heuristics for Metric Facility Location
and Related Problems. In: Fotakis D, Pagourtzis A, Paschos VT, eds. Lecture
Notes in Computer Science. Vol 10236. Cham: Springer International Publishing;
2017:116-127. doi:10.1007/978-3-319-57586-5_11'
apa: 'Brauer, S. (2017). Complexity of Single-Swap Heuristics for Metric Facility
Location and Related Problems. In D. Fotakis, A. Pagourtzis, & V. T. Paschos
(Eds.), Lecture Notes in Computer Science (Vol. 10236, pp. 116–127). Cham:
Springer International Publishing. https://doi.org/10.1007/978-3-319-57586-5_11'
bibtex: '@inbook{Brauer_2017, place={Cham}, title={Complexity of Single-Swap Heuristics
for Metric Facility Location and Related Problems}, volume={10236}, DOI={10.1007/978-3-319-57586-5_11},
booktitle={Lecture Notes in Computer Science}, publisher={Springer International
Publishing}, author={Brauer, Sascha}, editor={Fotakis, Dimitris and Pagourtzis,
Aris and Paschos, Vangelis Th.Editors}, year={2017}, pages={116–127} }'
chicago: 'Brauer, Sascha. “Complexity of Single-Swap Heuristics for Metric Facility
Location and Related Problems.” In Lecture Notes in Computer Science, edited
by Dimitris Fotakis, Aris Pagourtzis, and Vangelis Th. Paschos, 10236:116–27.
Cham: Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-57586-5_11.'
ieee: 'S. Brauer, “Complexity of Single-Swap Heuristics for Metric Facility Location
and Related Problems,” in Lecture Notes in Computer Science, vol. 10236,
D. Fotakis, A. Pagourtzis, and V. T. Paschos, Eds. Cham: Springer International
Publishing, 2017, pp. 116–127.'
mla: Brauer, Sascha. “Complexity of Single-Swap Heuristics for Metric Facility Location
and Related Problems.” Lecture Notes in Computer Science, edited by Dimitris
Fotakis et al., vol. 10236, Springer International Publishing, 2017, pp. 116–27,
doi:10.1007/978-3-319-57586-5_11.
short: 'S. Brauer, in: D. Fotakis, A. Pagourtzis, V.T. Paschos (Eds.), Lecture Notes
in Computer Science, Springer International Publishing, Cham, 2017, pp. 116–127.'
conference:
end_date: 2017-05-26
location: Athens, Greece
name: 10th International Conference on Algorithms and Complexity
start_date: 2017-05-24
date_created: 2018-04-17T12:20:53Z
date_updated: 2022-01-06T06:56:00Z
department:
- _id: '64'
doi: 10.1007/978-3-319-57586-5_11
editor:
- first_name: Dimitris
full_name: Fotakis, Dimitris
last_name: Fotakis
- first_name: Aris
full_name: Pagourtzis, Aris
last_name: Pagourtzis
- first_name: Vangelis Th.
full_name: Paschos, Vangelis Th.
last_name: Paschos
intvolume: ' 10236'
language:
- iso: eng
page: 116-127
place: Cham
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783319575858'
- '9783319575865'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer International Publishing
status: public
title: Complexity of Single-Swap Heuristics for Metric Facility Location and Related
Problems
type: book_chapter
user_id: '13291'
volume: 10236
year: '2017'
...
---
_id: '2969'
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
- first_name: Kathrin
full_name: Bujna, Kathrin
last_name: Bujna
citation:
ama: Blömer J, Brauer S, Bujna K. Hard-Clustering with Gaussian Mixture Models.
2016.
apa: Blömer, J., Brauer, S., & Bujna, K. (2016). Hard-Clustering with Gaussian
Mixture Models. Computing Research Repository.
bibtex: '@article{Blömer_Brauer_Bujna_2016, title={Hard-Clustering with Gaussian
Mixture Models}, publisher={Computing Research Repository}, author={Blömer, Johannes
and Brauer, Sascha and Bujna, Kathrin}, year={2016} }'
chicago: Blömer, Johannes, Sascha Brauer, and Kathrin Bujna. “Hard-Clustering with
Gaussian Mixture Models.” Computing Research Repository, 2016.
ieee: J. Blömer, S. Brauer, and K. Bujna, “Hard-Clustering with Gaussian Mixture
Models.” Computing Research Repository, 2016.
mla: Blömer, Johannes, et al. Hard-Clustering with Gaussian Mixture Models.
Computing Research Repository, 2016.
short: J. Blömer, S. Brauer, K. Bujna, (2016).
date_created: 2018-06-04T12:26:51Z
date_updated: 2022-01-06T06:58:49Z
department:
- _id: '64'
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1603.06478
oa: '1'
publisher: Computing Research Repository
status: public
title: Hard-Clustering with Gaussian Mixture Models
type: preprint
user_id: '25078'
year: '2016'
...
---
_id: '2367'
abstract:
- lang: eng
text: One of the most popular fuzzy clustering techniques is the fuzzy K-means algorithm
(also known as fuzzy-c-means or FCM algorithm). In contrast to the K-means and
K-median problem, the underlying fuzzy K-means problem has not been studied from
a theoretical point of view. In particular, there are no algorithms with approximation
guarantees similar to the famous K-means++ algorithm known for the fuzzy K-means
problem. This work initiates the study of the fuzzy K-means problem from an algorithmic
and complexity theoretic perspective. We show that optimal solutions for the fuzzy
K-means problem cannot, in general, be expressed by radicals over the input points.
Surprisingly, this already holds for simple inputs in one-dimensional space. Hence,
one cannot expect to compute optimal solutions exactly. We give the first (1+eps)-approximation
algorithms for the fuzzy K-means problem. First, we present a deterministic approximation
algorithm whose runtime is polynomial in N and linear in the dimension D of the
input set, given that K is constant, i.e. a polynomial time approximation scheme
(PTAS) for fixed K. We achieve this result by showing that for each soft clustering
there exists a hard clustering with similar properties. Second, by using techniques
known from coreset constructions for the K-means problem, we develop a deterministic
approximation algorithm that runs in time almost linear in N but exponential in
the dimension D. We complement these results with a randomized algorithm which
imposes some natural restrictions on the sought solution and whose runtime is
comparable to some of the most efficient approximation algorithms for K-means,
i.e. linear in the number of points and the dimension, but exponential in the
number of clusters.
author:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
- first_name: Kathrin
full_name: Bujna, Kathrin
last_name: Bujna
citation:
ama: 'Blömer J, Brauer S, Bujna K. A Theoretical Analysis of the Fuzzy K-Means Problem.
In: 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE;
2016:805-810. doi:10.1109/icdm.2016.0094'
apa: 'Blömer, J., Brauer, S., & Bujna, K. (2016). A Theoretical Analysis of
the Fuzzy K-Means Problem. In 2016 IEEE 16th International Conference on Data
Mining (ICDM) (pp. 805–810). Barcelona, Spain: IEEE. https://doi.org/10.1109/icdm.2016.0094'
bibtex: '@inproceedings{Blömer_Brauer_Bujna_2016, title={A Theoretical Analysis
of the Fuzzy K-Means Problem}, DOI={10.1109/icdm.2016.0094},
booktitle={2016 IEEE 16th International Conference on Data Mining (ICDM)}, publisher={IEEE},
author={Blömer, Johannes and Brauer, Sascha and Bujna, Kathrin}, year={2016},
pages={805–810} }'
chicago: Blömer, Johannes, Sascha Brauer, and Kathrin Bujna. “A Theoretical Analysis
of the Fuzzy K-Means Problem.” In 2016 IEEE 16th International Conference on
Data Mining (ICDM), 805–10. IEEE, 2016. https://doi.org/10.1109/icdm.2016.0094.
ieee: J. Blömer, S. Brauer, and K. Bujna, “A Theoretical Analysis of the Fuzzy K-Means
Problem,” in 2016 IEEE 16th International Conference on Data Mining (ICDM),
Barcelona, Spain, 2016, pp. 805–810.
mla: Blömer, Johannes, et al. “A Theoretical Analysis of the Fuzzy K-Means Problem.”
2016 IEEE 16th International Conference on Data Mining (ICDM), IEEE, 2016,
pp. 805–10, doi:10.1109/icdm.2016.0094.
short: 'J. Blömer, S. Brauer, K. Bujna, in: 2016 IEEE 16th International Conference
on Data Mining (ICDM), IEEE, 2016, pp. 805–810.'
conference:
end_date: 2016-12-15
location: Barcelona, Spain
name: IEEE 16th International Conference on Data Mining (ICDM)
start_date: 2016-12-12
date_created: 2018-04-17T11:46:07Z
date_updated: 2022-01-06T06:55:58Z
department:
- _id: '64'
doi: 10.1109/icdm.2016.0094
keyword:
- unsolvability by radicals
- clustering
- fuzzy k-means
- probabilistic method
- approximation algorithms
- randomized algorithms
language:
- iso: eng
page: 805-810
publication: 2016 IEEE 16th International Conference on Data Mining (ICDM)
publication_identifier:
isbn:
- '9781509054732'
publication_status: published
publisher: IEEE
status: public
title: A Theoretical Analysis of the Fuzzy K-Means Problem
type: conference
user_id: '25078'
year: '2016'
...
---
_id: '2900'
author:
- first_name: Sascha
full_name: Brauer, Sascha
id: '13291'
last_name: Brauer
citation:
ama: Brauer S. A Probabilistic Expectation Maximization Algorithm for Multivariate
Laplacian Mixtures.; 2014.
apa: Brauer, S. (2014). A Probabilistic Expectation Maximization Algorithm for
Multivariate Laplacian Mixtures.
bibtex: '@book{Brauer_2014, title={A Probabilistic Expectation Maximization Algorithm
for Multivariate Laplacian Mixtures}, author={Brauer, Sascha}, year={2014} }'
chicago: Brauer, Sascha. A Probabilistic Expectation Maximization Algorithm for
Multivariate Laplacian Mixtures, 2014.
ieee: S. Brauer, A Probabilistic Expectation Maximization Algorithm for Multivariate
Laplacian Mixtures. 2014.
mla: Brauer, Sascha. A Probabilistic Expectation Maximization Algorithm for Multivariate
Laplacian Mixtures. 2014.
short: S. Brauer, A Probabilistic Expectation Maximization Algorithm for Multivariate
Laplacian Mixtures, 2014.
date_created: 2018-05-25T09:45:38Z
date_updated: 2022-01-06T06:58:44Z
ddc:
- '000'
department:
- _id: '64'
file:
- access_level: closed
content_type: application/pdf
creator: feidens
date_created: 2018-05-25T09:45:33Z
date_updated: 2018-05-25T09:45:33Z
file_id: '2901'
file_name: 2014_Brauer_AProbabilisticExpectationMaximizationAlgorithmForMultivariateLaplacianMixtures.pdf
file_size: 971935
relation: main_file
success: 1
file_date_updated: 2018-05-25T09:45:33Z
has_accepted_license: '1'
status: public
supervisor:
- first_name: Johannes
full_name: Blömer, Johannes
id: '23'
last_name: Blömer
title: A Probabilistic Expectation Maximization Algorithm for Multivariate Laplacian
Mixtures
type: mastersthesis
user_id: '25078'
year: '2014'
...