---
_id: '14739'
abstract:
- lang: eng
text: Attempts to incorporate topological information in supervised learning tasks
have resulted in the creation of several techniques for vectorizing persistent
homology barcodes. In this paper, we study thirteen such methods. Besides describing
an organizational framework for these methods, we comprehensively benchmark them
against three well-known classification tasks. Surprisingly, we discover that
the best-performing method is a simple vectorization, which consists only of a
few elementary summary statistics. Finally, we provide a convenient web application
which has been designed to facilitate exploration and experimentation with various
vectorization methods.
acknowledgement: "The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel
Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia
e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part
by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028.
The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la
Universidad de Sevilla para la recualificacion del sistema universitario español,
2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda
was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR
under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON
developers, for their work and their support. We are also grateful to Streamlit
for providing extra resources to deploy the web app\r\nonline on Streamlit community
cloud. We thank the anonymous referees for their helpful suggestions."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Dashti
full_name: Ali, Dashti
last_name: Ali
- first_name: Aras
full_name: Asaad, Aras
last_name: Asaad
- first_name: Maria-Jose
full_name: Jimenez, Maria-Jose
last_name: Jimenez
- first_name: Vidit
full_name: Nanda, Vidit
last_name: Nanda
- first_name: Eduardo
full_name: Paluzo-Hidalgo, Eduardo
last_name: Paluzo-Hidalgo
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
citation:
ama: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M.
A survey of vectorization methods in topological data analysis. IEEE Transactions
on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391
apa: Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano
Trigueros, M. (2023). A survey of vectorization methods in topological data analysis.
IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391
chicago: Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo,
and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological
Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391.
ieee: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano
Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12.
IEEE, pp. 14069–14080, 2023.
ista: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros
M. 2023. A survey of vectorization methods in topological data analysis. IEEE
Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.
mla: Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data
Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.
short: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano
Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023)
14069–14080.
date_created: 2024-01-08T09:59:46Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2025-09-09T14:08:56Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/tpami.2023.3308391
external_id:
isi:
- '001104973300002'
file:
- access_level: open_access
checksum: 465c28ef0b151b4b1fb47977ed5581ab
content_type: application/pdf
creator: dernst
date_created: 2024-01-08T10:09:14Z
date_updated: 2024-01-08T10:09:14Z
file_id: '14740'
file_name: 2023_IEEEToP_Ali.pdf
file_size: 2370988
relation: main_file
success: 1
file_date_updated: 2024-01-08T10:09:14Z
has_accepted_license: '1'
intvolume: ' 45'
isi: 1
issue: '12'
keyword:
- Applied Mathematics
- Artificial Intelligence
- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Software
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 14069-14080
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: A survey of vectorization methods in topological data analysis
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 45
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '18228'
abstract:
- lang: eng
text: We introduce two constructions in geometric deep learning for 1) transporting
orientation-dependent convolutional filters over a manifold in a continuous way
and thereby defining a convolution operator that naturally incorporates the rotational
effect of holonomy; and 2) allowing efficient evaluation of manifold convolution
layers by sampling manifold valued random variables that center around a weighted
diffusion mean. Both methods are inspired by stochastics on manifolds and geometric
statistics, and provide examples of how stochastic methods – here horizontal frame
bundle flows and non-linear bridge sampling schemes, can be used in geometric
deep learning. We outline the theoretical foundation of the two methods, discuss
their relation to Euclidean deep networks and existing methodology in geometric
deep learning, and establish important properties of the proposed constructions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Stefan
full_name: Sommer, Stefan
last_name: Sommer
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
citation:
ama: Sommer S, Bronstein AM. Horizontal flows and manifold stochastics in geometric
deep learning. IEEE Transactions on Pattern Analysis and Machine Intelligence.
2020;44(2):811-822. doi:10.1109/tpami.2020.2994507
apa: Sommer, S., & Bronstein, A. M. (2020). Horizontal flows and manifold stochastics
in geometric deep learning. IEEE Transactions on Pattern Analysis and Machine
Intelligence. Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tpami.2020.2994507
chicago: Sommer, Stefan, and Alex M. Bronstein. “Horizontal Flows and Manifold Stochastics
in Geometric Deep Learning.” IEEE Transactions on Pattern Analysis and Machine
Intelligence. Institute of Electrical and Electronics Engineers, 2020. https://doi.org/10.1109/tpami.2020.2994507.
ieee: S. Sommer and A. M. Bronstein, “Horizontal flows and manifold stochastics
in geometric deep learning,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 44, no. 2. Institute of Electrical and Electronics Engineers,
pp. 811–822, 2020.
ista: Sommer S, Bronstein AM. 2020. Horizontal flows and manifold stochastics in
geometric deep learning. IEEE Transactions on Pattern Analysis and Machine Intelligence.
44(2), 811–822.
mla: Sommer, Stefan, and Alex M. Bronstein. “Horizontal Flows and Manifold Stochastics
in Geometric Deep Learning.” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 44, no. 2, Institute of Electrical and Electronics Engineers,
2020, pp. 811–22, doi:10.1109/tpami.2020.2994507.
short: S. Sommer, A.M. Bronstein, IEEE Transactions on Pattern Analysis and Machine
Intelligence 44 (2020) 811–822.
date_created: 2024-10-08T12:55:23Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2024-10-15T06:56:47Z
day: '01'
doi: 10.1109/tpami.2020.2994507
extern: '1'
external_id:
arxiv:
- '1909.06397'
intvolume: ' 44'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1909.06397
month: '02'
oa: 1
oa_version: Preprint
page: 811-822
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Horizontal flows and manifold stochastics in geometric deep learning
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2020'
...
---
OA_type: closed access
_id: '18245'
abstract:
- lang: eng
text: Intel® RealSense™ SR300 is a depth camera capable of providing a VGA-size
depth map at 60 fps and 0.125mm depth resolution. In addition, it outputs an infrared
VGA-resolution image and a 1080p color texture image at 30 fps. SR300 form-factor
enables it to be integrated into small consumer products and as a front facing
camera in laptops and Ultrabooks™. The SR300 depth camera is based on a coded-light
technology where triangulation between projected patterns and images captured
by a dedicated sensor is used to produce the depth map. Each projected line is
coded by a special temporal optical code, that enables a dense depth map reconstruction
from its reflection. The solid mechanical assembly of the camera allows it to
stay calibrated throughout temperature and pressure changes, drops, and hits.
In addition, active dynamic control maintains a calibrated depth output. An extended
API LibRS released with the camera allows developers to integrate the camera in
various applications. Algorithms for 3D scanning, facial analysis, hand gesture
recognition, and tracking are within reach for applications using the SR300. In
this paper, we describe the underlying technology, hardware, and algorithms of
the SR300, as well as its calibration procedure, and outline some use cases. We
believe that this paper will provide a full case study of a mass-produced depth
sensing product and technology.
article_processing_charge: No
article_type: original
author:
- first_name: Aviad
full_name: Zabatani, Aviad
last_name: Zabatani
- first_name: Vitaly
full_name: Surazhsky, Vitaly
last_name: Surazhsky
- first_name: Erez
full_name: Sperling, Erez
last_name: Sperling
- first_name: Sagi Ben
full_name: Moshe, Sagi Ben
last_name: Moshe
- first_name: Ohad
full_name: Menashe, Ohad
last_name: Menashe
- first_name: David H.
full_name: Silver, David H.
last_name: Silver
- first_name: Zachi
full_name: Karni, Zachi
last_name: Karni
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
- first_name: Michael K
full_name: Bronstein, Michael K
last_name: Bronstein
- first_name: Ron
full_name: Kimmel, Ron
last_name: Kimmel
citation:
ama: Zabatani A, Surazhsky V, Sperling E, et al. Intel® RealSenseTM SR300
coded light depth camera. IEEE Transactions on Pattern Analysis and Machine
Intelligence. 2020;42(10):2333-2345. doi:10.1109/tpami.2019.2915841
apa: Zabatani, A., Surazhsky, V., Sperling, E., Moshe, S. B., Menashe, O., Silver,
D. H., … Kimmel, R. (2020). Intel® RealSenseTM SR300 coded light depth
camera. IEEE Transactions on Pattern Analysis and Machine Intelligence.
Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tpami.2019.2915841
chicago: Zabatani, Aviad, Vitaly Surazhsky, Erez Sperling, Sagi Ben Moshe, Ohad
Menashe, David H. Silver, Zachi Karni, Alex M. Bronstein, Michael K Bronstein,
and Ron Kimmel. “Intel® RealSenseTM SR300 Coded Light Depth Camera.”
IEEE Transactions on Pattern Analysis and Machine Intelligence. Institute
of Electrical and Electronics Engineers, 2020. https://doi.org/10.1109/tpami.2019.2915841.
ieee: A. Zabatani et al., “Intel® RealSenseTM SR300 coded light
depth camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 42, no. 10. Institute of Electrical and Electronics Engineers, pp. 2333–2345,
2020.
ista: Zabatani A, Surazhsky V, Sperling E, Moshe SB, Menashe O, Silver DH, Karni
Z, Bronstein AM, Bronstein MK, Kimmel R. 2020. Intel® RealSenseTM SR300
coded light depth camera. IEEE Transactions on Pattern Analysis and Machine Intelligence.
42(10), 2333–2345.
mla: Zabatani, Aviad, et al. “Intel® RealSenseTM SR300 Coded Light Depth
Camera.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 42, no. 10, Institute of Electrical and Electronics Engineers, 2020, pp.
2333–45, doi:10.1109/tpami.2019.2915841.
short: A. Zabatani, V. Surazhsky, E. Sperling, S.B. Moshe, O. Menashe, D.H. Silver,
Z. Karni, A.M. Bronstein, M.K. Bronstein, R. Kimmel, IEEE Transactions on Pattern
Analysis and Machine Intelligence 42 (2020) 2333–2345.
date_created: 2024-10-08T13:04:18Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2024-10-15T09:40:01Z
day: '01'
doi: 10.1109/tpami.2019.2915841
extern: '1'
external_id:
pmid:
- '31094683'
intvolume: ' 42'
issue: '10'
language:
- iso: eng
month: '10'
oa_version: None
page: 2333-2345
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Intel® RealSense™ SR300 coded light depth camera
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2020'
...
---
_id: '6554'
abstract:
- lang: eng
text: Due to the importance of zero-shot learning, i.e. classifying images where
there is a lack of labeled training data, the number of proposed approaches has
recently increased steadily. We argue that it is time to take a step back and
to analyze the status quo of the area. The purpose of this paper is three-fold.
First, given the fact that there is no agreed upon zero-shot learning benchmark,
we first define a new benchmark by unifying both the evaluation protocols and
data splits of publicly available datasets used for this task. This is an important
contribution as published results are often not comparable and sometimes even
flawed due to, e.g. pre-training on zero-shot test classes. Moreover, we propose
a new zero-shot learning dataset, the Animals with Attributes 2 (AWA2) dataset
which we make publicly available both in terms of image features and the images
themselves. Second, we compare and analyze a significant number of the state-of-the-art
methods in depth, both in the classic zero-shot setting but also in the more realistic
generalized zero-shot setting. Finally, we discuss in detail the limitations of
the current status of the area which can be taken as a basis for advancing it.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yongqin
full_name: Xian, Yongqin
last_name: Xian
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0002-4561-241X
- first_name: Bernt
full_name: Schiele, Bernt
last_name: Schiele
- first_name: Zeynep
full_name: Akata, Zeynep
last_name: Akata
citation:
ama: Xian Y, Lampert C, Schiele B, Akata Z. Zero-shot learning - A comprehensive
evaluation of the good, the bad and the ugly. IEEE Transactions on Pattern
Analysis and Machine Intelligence. 2019;41(9):2251-2265. doi:10.1109/tpami.2018.2857768
apa: Xian, Y., Lampert, C., Schiele, B., & Akata, Z. (2019). Zero-shot learning
- A comprehensive evaluation of the good, the bad and the ugly. IEEE Transactions
on Pattern Analysis and Machine Intelligence. Institute of Electrical and
Electronics Engineers. https://doi.org/10.1109/tpami.2018.2857768
chicago: Xian, Yongqin, Christoph Lampert, Bernt Schiele, and Zeynep Akata. “Zero-Shot
Learning - A Comprehensive Evaluation of the Good, the Bad and the Ugly.” IEEE
Transactions on Pattern Analysis and Machine Intelligence. Institute of Electrical
and Electronics Engineers, 2019. https://doi.org/10.1109/tpami.2018.2857768.
ieee: Y. Xian, C. Lampert, B. Schiele, and Z. Akata, “Zero-shot learning - A comprehensive
evaluation of the good, the bad and the ugly,” IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 41, no. 9. Institute of Electrical
and Electronics Engineers, pp. 2251–2265, 2019.
ista: Xian Y, Lampert C, Schiele B, Akata Z. 2019. Zero-shot learning - A comprehensive
evaluation of the good, the bad and the ugly. IEEE Transactions on Pattern Analysis
and Machine Intelligence. 41(9), 2251–2265.
mla: Xian, Yongqin, et al. “Zero-Shot Learning - A Comprehensive Evaluation of the
Good, the Bad and the Ugly.” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 41, no. 9, Institute of Electrical and Electronics Engineers,
2019, pp. 2251–65, doi:10.1109/tpami.2018.2857768.
short: Y. Xian, C. Lampert, B. Schiele, Z. Akata, IEEE Transactions on Pattern Analysis
and Machine Intelligence 41 (2019) 2251–2265.
date_created: 2019-06-11T14:05:59Z
date_published: 2019-09-01T00:00:00Z
date_updated: 2024-12-11T11:49:58Z
day: '01'
department:
- _id: ChLa
doi: 10.1109/tpami.2018.2857768
external_id:
arxiv:
- '1707.00600'
isi:
- '000480343900015'
intvolume: ' 41'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1707.00600
month: '09'
oa: 1
oa_version: Preprint
page: 2251 - 2265
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Zero-shot learning - A comprehensive evaluation of the good, the bad and the
ugly
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 41
year: '2019'
...
---
_id: '703'
abstract:
- lang: eng
text: We consider the NP-hard problem of MAP-inference for undirected discrete graphical
models. We propose a polynomial time and practically efficient algorithm for finding
a part of its optimal solution. Specifically, our algorithm marks some labels
of the considered graphical model either as (i) optimal, meaning that they belong
to all optimal solutions of the inference problem; (ii) non-optimal if they provably
do not belong to any solution. With access to an exact solver of a linear programming
relaxation to the MAP-inference problem, our algorithm marks the maximal possible
(in a specified sense) number of labels. We also present a version of the algorithm,
which has access to a suboptimal dual solver only and still can ensure the (non-)optimality
for the marked labels, although the overall number of the marked labels may decrease.
We propose an efficient implementation, which runs in time comparable to a single
run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art
results on computational benchmarks from machine learning and computer vision.
article_processing_charge: No
arxiv: 1
author:
- first_name: Alexander
full_name: Shekhovtsov, Alexander
last_name: Shekhovtsov
- first_name: Paul
full_name: Swoboda, Paul
id: 446560C6-F248-11E8-B48F-1D18A9856A87
last_name: Swoboda
- first_name: Bogdan
full_name: Savchynskyy, Bogdan
last_name: Savchynskyy
citation:
ama: Shekhovtsov A, Swoboda P, Savchynskyy B. Maximum persistency via iterative
relaxed inference with graphical models. IEEE Transactions on Pattern Analysis
and Machine Intelligence. 2018;40(7):1668-1682. doi:10.1109/TPAMI.2017.2730884
apa: Shekhovtsov, A., Swoboda, P., & Savchynskyy, B. (2018). Maximum persistency
via iterative relaxed inference with graphical models. IEEE Transactions on
Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/TPAMI.2017.2730884
chicago: Shekhovtsov, Alexander, Paul Swoboda, and Bogdan Savchynskyy. “Maximum
Persistency via Iterative Relaxed Inference with Graphical Models.” IEEE Transactions
on Pattern Analysis and Machine Intelligence. IEEE, 2018. https://doi.org/10.1109/TPAMI.2017.2730884.
ieee: A. Shekhovtsov, P. Swoboda, and B. Savchynskyy, “Maximum persistency via iterative
relaxed inference with graphical models,” IEEE Transactions on Pattern Analysis
and Machine Intelligence, vol. 40, no. 7. IEEE, pp. 1668–1682, 2018.
ista: Shekhovtsov A, Swoboda P, Savchynskyy B. 2018. Maximum persistency via iterative
relaxed inference with graphical models. IEEE Transactions on Pattern Analysis
and Machine Intelligence. 40(7), 1668–1682.
mla: Shekhovtsov, Alexander, et al. “Maximum Persistency via Iterative Relaxed Inference
with Graphical Models.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 40, no. 7, IEEE, 2018, pp. 1668–82, doi:10.1109/TPAMI.2017.2730884.
short: A. Shekhovtsov, P. Swoboda, B. Savchynskyy, IEEE Transactions on Pattern
Analysis and Machine Intelligence 40 (2018) 1668–1682.
corr_author: '1'
date_created: 2018-12-11T11:48:01Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2026-04-16T09:54:52Z
day: '01'
department:
- _id: VlKo
doi: 10.1109/TPAMI.2017.2730884
external_id:
arxiv:
- '1508.07902'
isi:
- '000434294800010'
intvolume: ' 40'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07902
month: '07'
oa: 1
oa_version: Preprint
page: 1668-1682
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
issn:
- 0162-8828
publication_status: published
publisher: IEEE
publist_id: '6992'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximum persistency via iterative relaxed inference with graphical models
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 40
year: '2018'
...
---
_id: '18415'
abstract:
- lang: eng
text: Parsimony, including sparsity and low rank, has been shown to successfully
model data in numerous machine learning and signal processing tasks. Traditionally,
such modeling approaches rely on an iterative algorithm that minimizes an objective
function with parsimony-promoting terms. The inherently sequential structure and
data-dependent complexity and latency of iterative optimization constitute a major
limitation in many applications requiring real-time performance or involving large-scale
data. Another limitation encountered by these modeling techniques is the difficulty
of their inclusion in discriminative learning scenarios. In this work, we propose
to move the emphasis from the model to the pursuit algorithm, and develop a process-centric
view of parsimonious modeling, in which a learned deterministic fixed-complexity
pursuit process is used in lieu of iterative optimization. We show a principled
way to construct learnable pursuit process architectures for structured sparse
and robust low rank models, derived from the iteration of proximal descent algorithms.
These architectures learn to approximate the exact parsimonious representation
at a fraction of the complexity of the standard optimization methods. We also
show that appropriate training regimes allow to naturally extend parsimonious
models to discriminative settings. State-of-the-art results are demonstrated on
several challenging problems in image and audio processing with several orders
of magnitude speed-up compared to the exact optimization algorithms.
article_processing_charge: No
arxiv: 1
author:
- first_name: P.
full_name: Sprechmann, P.
last_name: Sprechmann
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
- first_name: G.
full_name: Sapiro, G.
last_name: Sapiro
citation:
ama: Sprechmann P, Bronstein AM, Sapiro G. Learning efficient sparse and low rank
models. IEEE Transactions on Pattern Analysis and Machine Intelligence.
2015;37(9):1821-1833. doi:10.1109/tpami.2015.2392779
apa: Sprechmann, P., Bronstein, A. M., & Sapiro, G. (2015). Learning efficient
sparse and low rank models. IEEE Transactions on Pattern Analysis and Machine
Intelligence. IEEE. https://doi.org/10.1109/tpami.2015.2392779
chicago: Sprechmann, P., Alex M. Bronstein, and G. Sapiro. “Learning Efficient Sparse
and Low Rank Models.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2015. https://doi.org/10.1109/tpami.2015.2392779.
ieee: P. Sprechmann, A. M. Bronstein, and G. Sapiro, “Learning efficient sparse
and low rank models,” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 37, no. 9. IEEE, pp. 1821–1833, 2015.
ista: Sprechmann P, Bronstein AM, Sapiro G. 2015. Learning efficient sparse and
low rank models. IEEE Transactions on Pattern Analysis and Machine Intelligence.
37(9), 1821–1833.
mla: Sprechmann, P., et al. “Learning Efficient Sparse and Low Rank Models.” IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 9,
IEEE, 2015, pp. 1821–33, doi:10.1109/tpami.2015.2392779.
short: P. Sprechmann, A.M. Bronstein, G. Sapiro, IEEE Transactions on Pattern Analysis
and Machine Intelligence 37 (2015) 1821–1833.
date_created: 2024-10-15T11:20:55Z
date_published: 2015-09-01T00:00:00Z
date_updated: 2024-12-18T11:40:35Z
day: '01'
doi: 10.1109/tpami.2015.2392779
extern: '1'
external_id:
arxiv:
- '1212.3631'
pmid:
- '26353129'
intvolume: ' 37'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1212.3631
month: '09'
oa: 1
oa_version: Preprint
page: 1821-1833
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Learning efficient sparse and low rank models
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2015'
...
---
_id: '18416'
abstract:
- lang: eng
text: We construct an extension of spectral and diffusion geometry to multiple modalities
through simultaneous diagonalization of Laplacian matrices. This naturally extends
classical data analysis tools based on spectral geometry, such as diffusion maps
and spectral clustering. We provide several synthetic and real examples of manifold
learning, object classification, and clustering, showing that the joint spectral
geometry better captures the inherent structure of multi-modal data. We also show
the relation of many previous approaches for multimodal manifold analysis to our
framework.
article_processing_charge: No
author:
- first_name: Davide
full_name: Eynard, Davide
last_name: Eynard
- first_name: Artiom
full_name: Kovnatsky, Artiom
last_name: Kovnatsky
- first_name: Michael M.
full_name: Bronstein, Michael M.
last_name: Bronstein
- first_name: Klaus
full_name: Glashoff, Klaus
last_name: Glashoff
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
citation:
ama: Eynard D, Kovnatsky A, Bronstein MM, Glashoff K, Bronstein AM. Multimodal manifold
snalysis by simultaneous diagonalization of Laplacians. IEEE Transactions on
Pattern Analysis and Machine Intelligence. 2015;37(12):2505-2517. doi:10.1109/tpami.2015.2408348
apa: Eynard, D., Kovnatsky, A., Bronstein, M. M., Glashoff, K., & Bronstein,
A. M. (2015). Multimodal manifold snalysis by simultaneous diagonalization of
Laplacians. IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE. https://doi.org/10.1109/tpami.2015.2408348
chicago: Eynard, Davide, Artiom Kovnatsky, Michael M. Bronstein, Klaus Glashoff,
and Alex M. Bronstein. “Multimodal Manifold Snalysis by Simultaneous Diagonalization
of Laplacians.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2015. https://doi.org/10.1109/tpami.2015.2408348.
ieee: D. Eynard, A. Kovnatsky, M. M. Bronstein, K. Glashoff, and A. M. Bronstein,
“Multimodal manifold snalysis by simultaneous diagonalization of Laplacians,”
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37,
no. 12. IEEE, pp. 2505–2517, 2015.
ista: Eynard D, Kovnatsky A, Bronstein MM, Glashoff K, Bronstein AM. 2015. Multimodal
manifold snalysis by simultaneous diagonalization of Laplacians. IEEE Transactions
on Pattern Analysis and Machine Intelligence. 37(12), 2505–2517.
mla: Eynard, Davide, et al. “Multimodal Manifold Snalysis by Simultaneous Diagonalization
of Laplacians.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 37, no. 12, IEEE, 2015, pp. 2505–17, doi:10.1109/tpami.2015.2408348.
short: D. Eynard, A. Kovnatsky, M.M. Bronstein, K. Glashoff, A.M. Bronstein, IEEE
Transactions on Pattern Analysis and Machine Intelligence 37 (2015) 2505–2517.
date_created: 2024-10-15T11:20:55Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2024-12-12T14:08:46Z
day: '01'
doi: 10.1109/tpami.2015.2408348
extern: '1'
external_id:
pmid:
- '26539854'
intvolume: ' 37'
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2505-2517
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multimodal manifold snalysis by simultaneous diagonalization of Laplacians
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2015'
...
---
_id: '18413'
abstract:
- lang: eng
text: Informative and discriminative feature descriptors play a fundamental role
in deformable shape analysis. For example, they have been successfully employed
in correspondence, registration, and retrieval tasks. In recent years, significant
attention has been devoted to descriptors obtained from the spectral decomposition
of the Laplace-Beltrami operator associated with the shape. Notable examples in
this family are the heat kernel signature (HKS) and the recently introduced wave
kernel signature (WKS). The Laplacian-based descriptors achieve state-of-the-art
performance in numerous shape analysis tasks; they are computationally efficient,
isometry-invariant by construction, and can gracefully cope with a variety of
transformations. In this paper, we formulate a generic family of parametric spectral
descriptors. We argue that to be optimized for a specific task, the descriptor
should take into account the statistics of the corpus of shapes to which it is
applied (the "signal") and those of the class of transformations to which it is
made insensitive (the "noise"). While such statistics are hard to model axiomatically,
they can be learned from examples. Following the spirit of the Wiener filter in
signal processing, we show a learning scheme for the construction of optimized
spectral descriptors and relate it to Mahalanobis metric learning. The superiority
of the proposed approach in generating correspondences is demonstrated on synthetic
and scanned human figures. We also show that the learned descriptors are robust
enough to be learned on synthetic data and transferred successfully to scanned
shapes.
article_processing_charge: No
author:
- first_name: R.
full_name: Litman, R.
last_name: Litman
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
citation:
ama: Litman R, Bronstein AM. Learning spectral descriptors for deformable shape
correspondence. IEEE Transactions on Pattern Analysis and Machine Intelligence.
2014;36(1):171-180. doi:10.1109/tpami.2013.148
apa: Litman, R., & Bronstein, A. M. (2014). Learning spectral descriptors for
deformable shape correspondence. IEEE Transactions on Pattern Analysis and
Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2013.148
chicago: Litman, R., and Alex M. Bronstein. “Learning Spectral Descriptors for Deformable
Shape Correspondence.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
IEEE, 2014. https://doi.org/10.1109/tpami.2013.148.
ieee: R. Litman and A. M. Bronstein, “Learning spectral descriptors for deformable
shape correspondence,” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 36, no. 1. IEEE, pp. 171–180, 2014.
ista: Litman R, Bronstein AM. 2014. Learning spectral descriptors for deformable
shape correspondence. IEEE Transactions on Pattern Analysis and Machine Intelligence.
36(1), 171–180.
mla: Litman, R., and Alex M. Bronstein. “Learning Spectral Descriptors for Deformable
Shape Correspondence.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 36, no. 1, IEEE, 2014, pp. 171–80, doi:10.1109/tpami.2013.148.
short: R. Litman, A.M. Bronstein, IEEE Transactions on Pattern Analysis and Machine
Intelligence 36 (2014) 171–180.
date_created: 2024-10-15T11:20:55Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2024-12-12T12:42:56Z
day: '01'
doi: 10.1109/tpami.2013.148
extern: '1'
external_id:
pmid:
- '24231874'
intvolume: ' 36'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 171-180
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Learning spectral descriptors for deformable shape correspondence
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2014'
...
---
_id: '18414'
abstract:
- lang: eng
text: We introduce an efficient computational framework for hashing data belonging
to multiple modalities into a single representation space where they become mutually
comparable. The proposed approach is based on a novel coupled siamese neural network
architecture and allows unified treatment of intra- and inter-modality similarity
learning. Unlike existing cross-modality similarity learning approaches, our hashing
functions are not limited to binarized linear projections and can assume arbitrarily
complex forms. We show experimentally that our method significantly outperforms
state-of-the-art hashing approaches on multimedia retrieval tasks.
article_processing_charge: No
arxiv: 1
author:
- first_name: Jonathan
full_name: Masci, Jonathan
last_name: Masci
- first_name: Michael M.
full_name: Bronstein, Michael M.
last_name: Bronstein
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
- first_name: Jurgen
full_name: Schmidhuber, Jurgen
last_name: Schmidhuber
citation:
ama: Masci J, Bronstein MM, Bronstein AM, Schmidhuber J. Multimodal similarity-preserving
hashing. IEEE Transactions on Pattern Analysis and Machine Intelligence.
2014;36(4):824-830. doi:10.1109/tpami.2013.225
apa: Masci, J., Bronstein, M. M., Bronstein, A. M., & Schmidhuber, J. (2014).
Multimodal similarity-preserving hashing. IEEE Transactions on Pattern Analysis
and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2013.225
chicago: Masci, Jonathan, Michael M. Bronstein, Alex M. Bronstein, and Jurgen Schmidhuber.
“Multimodal Similarity-Preserving Hashing.” IEEE Transactions on Pattern Analysis
and Machine Intelligence. IEEE, 2014. https://doi.org/10.1109/tpami.2013.225.
ieee: J. Masci, M. M. Bronstein, A. M. Bronstein, and J. Schmidhuber, “Multimodal
similarity-preserving hashing,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 36, no. 4. IEEE, pp. 824–830, 2014.
ista: Masci J, Bronstein MM, Bronstein AM, Schmidhuber J. 2014. Multimodal similarity-preserving
hashing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 36(4),
824–830.
mla: Masci, Jonathan, et al. “Multimodal Similarity-Preserving Hashing.” IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 4,
IEEE, 2014, pp. 824–30, doi:10.1109/tpami.2013.225.
short: J. Masci, M.M. Bronstein, A.M. Bronstein, J. Schmidhuber, IEEE Transactions
on Pattern Analysis and Machine Intelligence 36 (2014) 824–830.
date_created: 2024-10-15T11:20:55Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2024-12-12T13:04:27Z
day: '01'
doi: 10.1109/tpami.2013.225
extern: '1'
external_id:
arxiv:
- '1207.1522'
pmid:
- '26353203'
intvolume: ' 36'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1207.1522
month: '04'
oa: 1
oa_version: Preprint
page: 824-830
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 1939-3539
issn:
- 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multimodal similarity-preserving hashing
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2014'
...
---
_id: '18412'
abstract:
- lang: eng
text: SIFT-like local feature descriptors are ubiquitously employed in computer
vision applications such as content-based retrieval, video analysis, copy detection,
object recognition, photo tourism, and 3D reconstruction. Feature descriptors
can be designed to be invariant to certain classes of photometric and geometric
transformations, in particular, affine and intensity scale transformations. However,
real transformations that an image can undergo can only be approximately modeled
in this way, and thus most descriptors are only approximately invariant in practice.
Second, descriptors are usually high dimensional (e.g., SIFT is represented as
a 128--dimensional vector). In large-scale retrieval and matching problems, this
can pose challenges in storing and retrieving descriptor data. We map the descriptor
vectors into the Hamming space in which the Hamming metric is used to compare
the resulting representations. This way, we reduce the size of the descriptors
by representing them as short binary strings and learn descriptor invariance from
examples. We show extensive experimental validation, demonstrating the advantage
of the proposed approach.
article_processing_charge: No
article_type: original
author:
- first_name: C.
full_name: Strecha, C.
last_name: Strecha
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
- first_name: M. M.
full_name: Bronstein, M. M.
last_name: Bronstein
- first_name: P.
full_name: Fua, P.
last_name: Fua
citation:
ama: 'Strecha C, Bronstein AM, Bronstein MM, Fua P. LDAHash: Improved matching with
smaller descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence.
2012;34(1):66-78. doi:10.1109/tpami.2011.103'
apa: 'Strecha, C., Bronstein, A. M., Bronstein, M. M., & Fua, P. (2012). LDAHash:
Improved matching with smaller descriptors. IEEE Transactions on Pattern Analysis
and Machine Intelligence. Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/tpami.2011.103'
chicago: 'Strecha, C., Alex M. Bronstein, M. M. Bronstein, and P. Fua. “LDAHash:
Improved Matching with Smaller Descriptors.” IEEE Transactions on Pattern Analysis
and Machine Intelligence. Institute of Electrical and Electronics Engineers,
2012. https://doi.org/10.1109/tpami.2011.103.'
ieee: 'C. Strecha, A. M. Bronstein, M. M. Bronstein, and P. Fua, “LDAHash: Improved
matching with smaller descriptors,” IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 34, no. 1. Institute of Electrical and Electronics
Engineers, pp. 66–78, 2012.'
ista: 'Strecha C, Bronstein AM, Bronstein MM, Fua P. 2012. LDAHash: Improved matching
with smaller descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence.
34(1), 66–78.'
mla: 'Strecha, C., et al. “LDAHash: Improved Matching with Smaller Descriptors.”
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34,
no. 1, Institute of Electrical and Electronics Engineers, 2012, pp. 66–78, doi:10.1109/tpami.2011.103.'
short: C. Strecha, A.M. Bronstein, M.M. Bronstein, P. Fua, IEEE Transactions on
Pattern Analysis and Machine Intelligence 34 (2012) 66–78.
date_created: 2024-10-15T11:20:54Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2024-11-12T08:34:48Z
day: '01'
doi: 10.1109/tpami.2011.103
extern: '1'
external_id:
pmid:
- '21576750 '
intvolume: ' 34'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 66-78
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
eissn:
- 2160-9292
issn:
- 0162-8828
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'LDAHash: Improved matching with smaller descriptors'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2012'
...
---
OA_type: closed access
_id: '18411'
abstract:
- lang: eng
text: Recent works have shown the use of diffusion geometry for various pattern
recognition applications, including nonrigid shape analysis. In this paper, we
introduce spectral shape distance as a general framework for distribution-based
shape similarity and show that two recent methods for shape similarity due to
Rustamov and Mahmoudi and Sapiro are particular cases thereof.
article_processing_charge: No
article_type: original
author:
- first_name: Michael M
full_name: Bronstein, Michael M
last_name: Bronstein
- first_name: Alexander
full_name: Bronstein, Alexander
id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
last_name: Bronstein
orcid: 0000-0001-9699-8730
citation:
ama: Bronstein MM, Bronstein AM. Shape recognition with spectral distances. IEEE
Transactions on Pattern Analysis and Machine Intelligence. 2011;33(5):1065-1071.
doi:10.1109/tpami.2010.210
apa: Bronstein, M. M., & Bronstein, A. M. (2011). Shape recognition with spectral
distances. IEEE Transactions on Pattern Analysis and Machine Intelligence.
Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tpami.2010.210
chicago: Bronstein, Michael M, and Alex M. Bronstein. “Shape Recognition with Spectral
Distances.” IEEE Transactions on Pattern Analysis and Machine Intelligence.
Institute of Electrical and Electronics Engineers, 2011. https://doi.org/10.1109/tpami.2010.210.
ieee: M. M. Bronstein and A. M. Bronstein, “Shape recognition with spectral distances,”
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33,
no. 5. Institute of Electrical and Electronics Engineers, pp. 1065–1071, 2011.
ista: Bronstein MM, Bronstein AM. 2011. Shape recognition with spectral distances.
IEEE Transactions on Pattern Analysis and Machine Intelligence. 33(5), 1065–1071.
mla: Bronstein, Michael M., and Alex M. Bronstein. “Shape Recognition with Spectral
Distances.” IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 33, no. 5, Institute of Electrical and Electronics Engineers, 2011, pp. 1065–71,
doi:10.1109/tpami.2010.210.
short: M.M. Bronstein, A.M. Bronstein, IEEE Transactions on Pattern Analysis and
Machine Intelligence 33 (2011) 1065–1071.
date_created: 2024-10-15T11:20:54Z
date_published: 2011-05-01T00:00:00Z
date_updated: 2024-10-22T08:02:31Z
day: '01'
doi: 10.1109/tpami.2010.210
extern: '1'
external_id:
pmid:
- '21135442'
intvolume: ' 33'
issue: '5'
language:
- iso: eng
month: '05'
oa_version: None
page: 1065-1071
pmid: 1
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
issn:
- 0162-8828
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Shape recognition with spectral distances
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2011'
...