Toward Sparse Coding on Cosine Distance

Choi, Jonghyun; Cho, Hyunjong; Kwac, Jungsuk; Davis, Larry S.

doi:10.1109/icpr.2014.757

Cited by 9 publications

(8 citation statements)

References 26 publications

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“…1-6). Thus, the resulting clusters have geometric meaning because they represent groups of observations that have small within-cosine distance, a fact often used in the field of text analysis (Choi et al, 2014;Zhang et al, 2020;Hornik et al, 2012). In structural studies, cosine distance as dissimilarity metric was used for detecting fracture sets in outcrops (Zhan et al, 2017a) observations with substantial dip.…”

Section: Method's Capabilitiesmentioning

confidence: 99%

“…We propose to use a well-known fact (Choi et al, 2014;Zhang et al, 2020) that for unit normal vectors, the above squared distance is proportional to cosine distance ("°" denotes the scalar product between two vectors, and || • || is the Euclidean norm):…”

Section: Assumptions Underlying the Clustering Proceduresmentioning

confidence: 99%

“…In this paper, we propose clustering the 3D terrain observations using cosine distance as dissimilarity metric. This goal is achieved using a fact that squared Euclidean distance applied for unit vectors is proportional to the cosine distance (Zhang et al, 2020;Choi et al, 2014) (see also Methods). While (Michalak et al, 2019) used only normal vector representation for extracting orientation statistics, we illustrate the cartographic differences for two 3D representations of the studied terrains: normal and dip vectors with two versions of spatial clustering: irregular and regular (see also Methods).…”

Section: Study Introductionmentioning

confidence: 99%

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Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains

Michalak

Teper

Wellmann

et al. 2022

Preprint

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Abstract. The geological potential of sparse subsurface data is not being fully exploited since the available workflows are not specifically designed to detect and interpret 3D geometric anomalies hidden in the data. We develop a new unsupervised machine learning framework to cluster and analyze the spatial distribution of orientations sampled throughout a geological interface. Our method employs Delaunay triangulation and clustering with the squared Euclidean distance to cluster local unit orientations/attitude which results in minimizing the within-cluster cosine distance. We performed the clustering on two representations of the triangles: normal and dip vectors. The classes resulting from clustering were attached to a geometric centre of a triangle (irregular version). We developed also a regular version of spatial clustering which allows to answer whether points from a grid structure can be affected by anomalies. To illustrate the usefulness of the combination between cosine distance as dissimilarity metric and two cartographic versions, we analyzed subsurface data documenting two horizons: 1) the bottom Jurassic surface from the Central European Basin System (CEBS) and 2) an interface between Middle-Jurassic units within the Kraków-Silesian Homocline (KSH) which is a part of the CEBS. The empirical results suggest that clustering normal vectors may result in near collinear cluster centers and boundaries between clusters of similar trend, thus pointing to axis of a potential megafold. Clustering dip vectors resulted on the other hand in near co-circular cluster centers, thus pointing to a potential megacone. We also show that the linear arrangements of the anomalies, their topological relationships and internal structure can provide insights regarding the internal structure of the singularity, e.g. whether it may be due to drilling a nonvertical fault plane or due to a wider deformation zone composed of many smaller faults.

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Section: Method's Capabilitiesmentioning

confidence: 99%

Section: Assumptions Underlying the Clustering Proceduresmentioning

confidence: 99%

Section: Study Introductionmentioning

confidence: 99%

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Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains

Michalak

Teper

Wellmann

et al. 2022

Preprint

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“…Thus, in these experiments, MED and MCD , respectively, correspond to Euclidean distance and cosine distance. Furthermore, due to vector normalisation applied for the resolution of sparse coding (Section 5.3), and because squared difference between two normalised vectors is proportional to the cosine distance [39], RSCR and MCD will produce the same ranking. Therefore, RSCR is not included in these experiments.…”

Section: Methodsmentioning

confidence: 99%

Improving vehicle re‐identification using CNN latent spaces: Metrics comparison and track‐to‐track extension

Roman-Jimenez

Guyot²,

Malon

et al. 2021

IET Computer Vision

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Herein, the problem of vehicle re‐identification using distance comparison of images in CNN latent spaces is addressed. First, the impact of the distance metrics, comparing performances obtained with different metrics is studied: the minimal Euclidean distance (MED), the minimal cosine distance (MCD) and the residue of the sparse coding reconstruction (RSCR). These metrics are applied using features extracted from five different CNN architectures, namely ResNet18, AlexNet, VGG16, InceptionV3 and DenseNet201. We use the specific vehicle re‐identification dataset VeRi to fine‐tune these CNNs and evaluate results. Overall, independently of the CNN used, MCD outperforms MED, commonly used in the literature. These results are confirmed on other vehicle retrieval datasets. Second, the state‐of‐the‐art image‐to‐track process (I2TP) is extended to a track‐to‐track process (T2TP). The three distance metrics are extended to measure distance between tracks, enabling T2TP. T2TP and I2TP are compared using the same CNN models. Results show that T2TP outperforms I2TP for MCD and RSCR. T2TP combining DenseNet201 and MCD‐based metrics exhibits the best performances, outperforming the state‐of‐the‐art I2TP‐based models. Finally, experiments highlight two main results: i) the impact of metric choice in vehicle re‐identification, and ii) T2TP improves the performances compared with I2TP, especially when coupled with MCD‐based metrics.

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“…1 depicts an example low-dimensional ReLU network. We represent a binary classification task with the green and purple areas and compute the Saliency Map (black), Integrated Gradient (red) and Smooth Gradient (blue) for inputs in different neighborhoods A, B and C. All attribution maps are normalized to unit length so that the difference in the direction is proportional to the corresponding 2 distance [11]. We represent the surface of the output with the contour map.…”

Section: Definition 5 (Lipschitz Continuity) a General Functionmentioning

confidence: 99%

Smoothed Geometry for Robust Attribution

Wang,

Ramkumar

et al. 2020

Preprint

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Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is especially problematic in high-stakes applications where adversarially-manipulated explanations could impair safety and trustworthiness. Building on a geometric understanding of these attacks presented in recent work, we identify Lipschitz continuity conditions on models' gradient that lead to robust gradient-based attributions, and observe that smoothness may also be related to the ability of an attack to transfer across multiple attribution methods. To mitigate these attacks in practice, we propose an inexpensive regularization method that promotes these conditions in DNNs, as well as a stochastic smoothing technique that does not require re-training. Our experiments on a range of image models demonstrate that both of these mitigations consistently improve attribution robustness, and confirm the role that smooth geometry plays in these attacks on real, large-scale models.

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Toward Sparse Coding on Cosine Distance

Cited by 9 publications

References 26 publications

Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains

Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains

Improving vehicle re‐identification using CNN latent spaces: Metrics comparison and track‐to‐track extension

Smoothed Geometry for Robust Attribution

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