Distance Preservation Research Articles

Distance preserving machine learning for uncertainty aware accelerator capacitance predictions

Abstract Accurate uncertainty estimations are essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold standard for this task; however, they can struggle with large, high-dimensional datasets. Combining deep neural networks with Gaussian process approximation techniques has shown promising results, but dimensionality reduction through standard deep neural network layers is not guaranteed to maintain the distance information necessary for Gaussian process models. We build on previous work by comparing the use of the singular value decomposition against a spectral-normalized dense layer as a feature extractor for a deep neural Gaussian process approximation model and apply it to a capacitance prediction problem for the High Voltage Converter Modulators in the Oak Ridge Spallation Neutron Source. Our model shows improved distance preservation and predicts in-distribution capacitance values with less than 1% error.

On the security risk of pre-image attack on cancelable biometrics

Over the years, a number of biometric template protection schemes, often based on the notion of “cancelable biometrics”, have been proposed. An ideal cancelable biometric algorithm complies with four criteria: irreversibility, revocability, unlinkability, and performance preservation. Cancelable biometrics employs an irreversible but distance preserving transformation to convert the original biometric templates into protected templates. Matching in the transform domain can be accomplished due to the property of distance preservation. However, distance preservation also entails security issues, a point often overlooked in existing research. In this paper, we have conducted a comprehensive security analysis of distance preservation in cancelable biometrics for the first time. The analysis is based on a pre-image attack, which is launched to break the security of cancelable biometrics under Kerckhoffs’s assumption. Furthermore, we propose a general security analysis framework under the single and cross-transformation attacks, which also employs an information leakage estimation strategy based on mutual information as a complement. The experimental results performed on real face, iris, and fingerprint data demonstrate that the risks originating from the matching scores computed from the distance/similarity of two cancelable templates greatly compromise the security of cancelable biometric schemes, including the classic Biohashing, Index-of-max hashing, Non-linear multi-dimensional spectral hashing, Indexing-First-One hashing, Bloom Filter and Two-factor Protected Minutia Cylinder-Code. The security versus accuracy trade-off is discussed and recommendations for designing a biometric system secure against pre-image attacks are also proposed. The source code is available at github.com/biometricsecurity/CBrisks.

Optimization Tools for Distance-Preserving Flag Fault-Tolerant Error Correction

Lookup-table decoding is fast and distance preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup-table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup-table construction, the meet-in-the-middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separate X- and Z-counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in an increase of more than an order of magnitude in the pseudothreshold for the hexagonal color code of distance 9, from (1.34±0.01)×10−4 to (1.43±0.07)×10−3. Published by the American Physical Society 2024

Multi-agent flocking with obstacle avoidance and safety distance preservation: a fuzzy potential-based approach

Multi-agent flocking with obstacle avoidance and safety distance preservation: a fuzzy potential-based approach

Restorable Shortest Path Tiebreaking for Edge-Faulty Graphs

The restoration lemma by Afek et al. [ 3 ] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two original shortest paths. However, the lemma is tiebreaking-sensitive : if one selects a particular canonical shortest path for each node pair, it is no longer guaranteed that one can build replacement paths by concatenating two selected shortest paths. They left as an open problem whether a method of shortest path tiebreaking with this desirable property is generally possible. We settle this question affirmatively with the first general construction of restorable tiebreaking schemes . We then show applications to various problems in fault-tolerant network design. These include a faster algorithm for subset replacement paths, more efficient fault-tolerant (exact) distance labeling schemes, fault-tolerant subset distance preservers and + 4 additive spanners with improved sparsity, and fast distributed algorithms that construct these objects. For example, an almost immediate corollary of our restorable tiebreaking scheme is the first nontrivial distributed construction of sparse fault-tolerant distance preservers resilient to three faults.

Sphere2Vec: A general-purpose location representation learning over a spherical surface for large-scale geospatial predictions

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D or 3D Euclidean space as a high-dimensional vector, and has been successfully applied to various (geo)spatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets (e.g., species or satellite images taken all over the world), which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location encoder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the Double Fourier Sphere (DFS). We also provide theoretical proof that the Sphere2Vec encoding preserves the spherical surface distance between any two points, while existing encoding schemes such as Space2Vec and NeRF do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models including the state-of-the-art (SOTA) 2D location encoder (i.e., Space2Vec) and 3D encoder NeRF on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks - fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple 2D and 3D location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data of this work are available at https://gengchenmai.github.io/sphere2vec-website/.

Improved Evaluation and Generation Of Grid Layouts Using Distance Preservation Quality and Linear Assignment Sorting

AbstractImages sorted by similarity enables more images to be viewed simultaneously, and can be very useful for stock photo agencies or e‐commerce applications. Visually sorted grid layouts attempt to arrange images so that their proximity on the grid corresponds as closely as possible to their similarity. Various metrics exist for evaluating such arrangements, but there is low experimental evidence on correlation between human perceived quality and metric value. We propose distance preservation quality (DPQ) as a new metric to evaluate the quality of an arrangement. Extensive user testing revealed stronger correlation of DPQ with user‐perceived quality and performance in image retrieval tasks compared to other metrics. In addition, we introduce Fast linear assignment sorting (FLAS) as a new algorithm for creating visually sorted grid layouts. FLAS achieves very good sorting qualities while improving run time and computational resources.

Augmented Paths and Reodesics for Topologically-Stable Matching

We propose a fully-automatic method that computes from scratch point-to-point dense correspondences between isometric shapes under topological noise. While relying on pairwise distance preservation constraints is common and generally sufficient to handle isometric deformations, presence of topological noise needs further actions that we present as our main contributions. First, instead of comparing distances over two paths on two input surfaces, we cast fuzzy votes at the path endpoints based on topologically-robust heat diffusion from path vertices. Second, we make the matching even more stable to topological noise by introducing the so-called reodesics, which are locally shortest geodesics that go through robust matches. In addition to the five standard datasets for isometric shape correspondence with and without topological noise, we employ and release a sixth one geared specifically towards topological noise evaluation with ground-truth information. We demonstrate our qualitative and quantitative advantages over seven recent state-of-the-art methods on these six datasets.

Orthogonal multi-view analysis by successive approximations via eigenvectors

Orthogonality has been demonstrated to admit many desirable properties such as noise-tolerant, good for data visualization, and preserving distances. However, it is often incompatible with existing models and the resulting optimization problem is challenging even if compatible. To address these issues, we propose a trace ratio formulation for multi-view subspace learning to learn individual orthogonal projections for all views. The proposed formulation integrates the correlations within multiple views, supervised discriminant capacity, and distance preservation in a concise and compact way. It not only includes several existing models as special cases, but also inspires new models. Moreover, an efficient numerical method based on successive approximations via eigenvectors is presented to solve the associated optimization problem. The method is built upon an iterative Krylov subspace method which can easily scale up for high-dimensional datasets. Extensive experiments are conducted on various real-world datasets for multi-view discriminant analysis and multi-view multi-label classification. The experimental results demonstrate that the proposed models are consistently competitive to and often better than the compared methods.

Blur Face Recognition using Blur Metric and Some Variants of Supervised Distance Preserving Projection

This paper is focused on face recognition techniques in uncontrolled scenarios, specifically on the recognition of face images with blur effects. At first, the blur level of the testing image is determined using recently proposed blur metric. This blur metric value is used to blur the training set of gallery images using Gaussian filter. The blur level of training images is the same as that of the testing image. Two variants of Supervised Distance Preserving Projection (SDPP), SDPP as Semidefinite Least Square (SLS-SDPP) and Regularized Supervised Distance Preserving Projection (RSDPP), are used for extracting effective features of training and testing images. K-Nearest Neighbor classifier is used for matching. Numerical experiments were carried out on two benchmarking face data ORL and Yale. The performances of SLS-SDPP and RSDPP are compared with one of the leading methods Eigenface method. Experimental results show that the combination of blur metric and the feature extraction methods achieved outstanding performance in recognizing blur images of different levels and also outperforms the base methods and Eigenface method. Dhaka Univ. J. Sci. 69(3): 154-160, 2022 (June)

Degenerate local-dimension-invariant stabilizer codes and an alternative bound for the distance preservation condition

One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. In this paper we show that codes for these systems can be derived from already known codes, and in particular that degenerate stabilizer codes can have their distance also promised upon sufficiently large local-dimension, as well as a new bound on the local-dimension required to preserve the distance of local-dimension-invariant codes, which is a result which could prove to be useful for error-corrected qudit quantum computers.

Facial Expression Identification using Regularized Supervised Distance Preserving Projection

Facial expression recognition is one of the most reliable and a key technology of advanced human-computer interaction with the rapid development of computer vision and artificial intelligence. Nowadays, there has been a growing interest in improving expression recognition techniques. In most of the cases, automatic recognition system’s efficiency depends on the represented facial expression feature. Even the best classifier may fail to achieve a good recognition rate if inadequate features are provided. Therefore, feature extraction is a crucial step of the facial expression recognition process. In this paper, we have used Regularized Supervised Distance Preserving Projection for extracting the best features of the images. Numerical experiment shows that the use of this technique outperforms many of state of art approaches in terms of recognition rate. Dhaka Univ. J. Sci. 69(2): 70-75, 2021 (July)

Structured nonnegative matrix factorization for traffic flow estimation of large cloud networks

Network traffic matrix estimation is an ill-posed linear inverse problem: it requires to estimate the unobservable origin destination traffic flows, X, given the observable link traffic flows, Y, and a binary routing matrix, A, which are such that Y=AX. This is a challenging but vital problem as accurate estimation of OD flows is required for several network management tasks. In this paper, we propose a novel model for the network traffic matrix estimation problem which maps high-dimension OD flows to low-dimension latent flows with the following three constraints: (1) nonnegativity constraint on the estimated OD flows, (2) autoregression constraint that enables the proposed model to effectively capture temporal patterns of the OD flows, and (3) orthogonality constraint that ensures the mapping between low-dimensional latent flows and the corresponding link flows to be distance preserving. The parameters of the proposed model are estimated with a training algorithm based on Nesterov accelerated gradient and generally shows fast convergence. We validate the proposed traffic flow estimation model on two real backbone IP network datasets, namely Internet2 and GÉANT. Empirical results show that the proposed model outperforms the state-of-the-art models not only in terms of tracking the individual OD flows but also in terms of standard performance metrics. The proposed model is also found to be highly scalable compared to the existing state-of-the-art approaches.

Better Distance Preservers and Additive Spanners

We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers , which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work on distance preservers has exploited only a simple structural property of shortest paths, called consistency , stating that one can break shortest path ties such that no two paths intersect, split apart, and then intersect again later. We prove that consistency alone is not enough to understand distance preservers, by showing both a lower bound on the power of consistency and a new general upper bound that polynomially surpasses it. Specifically, our new upper bound is that any p demand pairs in an n -node undirected unweighted graph have a distance preserver on O( n 2/3 p 2/3 + np 1/3 edges. We leave a conjecture that the right bound is O ( n 2/3 p 2/3 + n ) or better. The second part of this paper leverages these distance preservers in a new construction of additive spanners , which are subgraphs that preserve all pairwise distances up to an additive error function. We give improved error bounds for spanners with relatively few edges; for example, we prove that all graphs have spanners on O(n) edges with + O ( n 3/7 + ε ) error. Our construction can be viewed as an extension of the popular path-buying framework to clusters of larger radii.

A note on distance-preserving graph sparsification

We consider problems of the following type: given a graph G, how many edges are needed in the worst case for a sparse subgraph H that approximately preserves distances between a given set of node pairs P? Examples include pairwise spanners, distance preservers, reachability preservers, etc. There has been a trend in the area of simple constructions based on the hitting set technique, followed by somewhat more complicated constructions that improve over the bounds obtained from hitting sets by roughly a log factor. In this note, we point out that the simpler constructions based on hitting sets don't actually need an extra log factor in the first place. This simplifies and unifies a few proofs in the area, and it improves the size of the +4 pairwise spanner from O˜(np2/7) (Kavitha (2017) [13]) to O(np2/7).

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

Random Projection is one of the most popular and successful dimensionality reduction algorithms for large volumes of data. However, given its stochastic nature, different initializations of the projection matrix can lead to very different levels of performance. This paper presents a guided random search algorithm to mitigate this problem. The proposed method uses a small number of training data samples to iteratively adjust a projection matrix, improving its performance on similarly distributed data. Experimental results show that projection matrices generated with the proposed method result in a better preservation of distances between data samples. Conveniently, this is achieved while preserving the database-friendliness of the projection matrix, as it remains sparse and comprised exclusively of integers after being tuned with our algorithm. Moreover, running the proposed algorithm on a consumer-grade CPU requires only a few seconds.

Guided Stable Dynamic Projections

AbstractProjections aim to convey the relationships and similarity of high‐dimensional data in a low‐dimensional representation. Most such techniques are designed for static data. When used for time‐dependent data, they usually fail to create a stable and suitable low dimensional representation. We propose two dynamic projection methods (PCD‐tSNE and LD‐tSNE) that use global guides to steer projection points. This avoids unstable movement that does not encode data dynamics while keeping t‐SNE's neighborhood preservation ability. PCD‐tSNE scores a good balance between stability, neighborhood preservation, and distance preservation, while LD‐tSNE allows creating stable and customizable projections. We compare our methods to 11 other techniques using quality metrics and datasets provided by a recent benchmark for dynamic projections.

Enabling Simultaneous Content Regulation and Privacy Protection for Cloud Storage Image

The population of cloud computing greatly facilitates the sharing of explosively generated image today. While benefiting from the convenient of cloud, the privacy protection mechanism that commonly applied in cloud service makes the spreading of illegal and harmful data very hard to be detected or controlled. Such a realistic threat should be seriously treated, yet is largely overlooked in the literature. To address this issue, we propose the first cloud service framework that can simultaneously provide privacy protection and content regulation for the cloud storage image. In specific, we design a secure multi-party computation (MPC) protocol to protect the data privacy via random projection. By leveraging the distance preserving properties residing in random projection, we propose a privacy-preserving principal component analysis (PCA)-based recognition approach over the random projection domain to achieve content matching while respecting the data privacy. To facilitate the efficiency, we implement our system under the compressive sensing (CS) framework. Due to the compression effect of CS, the proposed cloud service can achieve remarkable reduction on the computation and communication complexity of the content matching process. Theoretical analysis and experimental results both show that our system can achieve privacy assurance and acceptable recognition performance, while with high efficiency.

Probabilistic Semi-Supervised Learning via Sparse Graph Structure Learning.

We present a probabilistic semi-supervised learning (SSL) framework based on sparse graph structure learning. Different from existing SSL methods with either a predefined weighted graph heuristically constructed from the input data or a learned graph based on the locally linear embedding assumption, the proposed SSL model is capable of learning a sparse weighted graph from the unlabeled high-dimensional data and a small amount of labeled data, as well as dealing with the noise of the input data. Our representation of the weighted graph is indirectly derived from a unified model of density estimation and pairwise distance preservation in terms of various distance measurements, where latent embeddings are assumed to be random variables following an unknown density function to be learned, and pairwise distances are then calculated as the expectations over the density for the model robustness to the data noise. Moreover, the labeled data based on the same distance representations are leveraged to guide the estimated density for better class separation and sparse graph structure learning. A simple inference approach for the embeddings of unlabeled data based on point estimation and kernel representation is presented. Extensive experiments on various data sets show promising results in the setting of SSL compared with many existing methods and significant improvements on small amounts of labeled data.

New Results on Linear Size Distance Preservers

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 3 January 2019Accepted: 30 December 2020Published online: 12 April 2021Keywordsshortest paths, graph spanners, extremal graph theory, distance preserversAMS Subject Headings68, 05Publication DataISSN (print): 0097-5397ISSN (online): 1095-7111Publisher: Society for Industrial and Applied MathematicsCODEN: smjcat