Euclidean Distance Distribution Research Articles

Classification of movements of collegiate female soccer players using inertial measurement units

This study aimed to classify the movements of female soccer players during matches using raw data measured by inertial measurement units (IMUs). Twelve collegiate female soccer players were equipped with IMUs (100 Hz), and raw triaxial acceleration data from eight official matches were analyzed. The measurement data were separated every 3 s, and a Fast Fourier Transform (FFT) was performed. After FFT, the Euclidean distances between the data when the players were in the stationary state and other states were calculated to classify the movements of the players using the k-means method. The data of the clustering numbers classified as the stationary state were eliminated after analyzing the movements of players by video filming the matches. After classification, the average Euclidean distances between the stationary state and other movements were calculated. Consequently, the results showed that the upward and downward directions of the raw data affected the classification. Using the methods of this study, it was also shown that the distribution of Euclidean distances differed from player to player. Our findings indicate that the method used in this study can be used to classify and characterize the movements of female collegiate soccer players.

A Deep Learning Model for Automatically Quantifying the Anterior Segment in Ultrasound Biomicroscopy Images of Implantable Collamer Lens Candidates

ObjectiveThis study aimed to develop and evaluate a deep learning-based model that could automatically measure anterior segment (AS) parameters on preoperative ultrasound biomicroscopy (UBM) images of implantable Collamer lens (ICL) surgery candidates. MethodsA total of 1164 panoramic UBM images were preoperatively obtained from 321 patients who received ICL surgery in the Eye Center of Renmin Hospital of Wuhan University (Wuhan, China) to develop an imaging database. First, the UNet++ network was utilized to segment AS tissues automatically, such as corneal lens and iris. In addition, image processing techniques and geometric localization algorithms were developed to automatically identify the anatomical landmarks (ALs) of pupil diameter (PD), anterior chamber depth (ACD), angle-to-angle distance (ATA), and sulcus-to-sulcus distance (STS). Based on the results of the latter two processes, PD, ACD, ATA, and STS can be measured. Meanwhile, an external dataset of 294 images from Huangshi Aier Eye Hospital was employed to further assess the model's performance in other center. Lastly, a subset of 100 random images from the external test set was chosen to compare the performance of the model with senior experts. ResultsWhether in the internal test dataset or external test dataset, using manual labeling as the reference standard, the models achieved a mean Dice coefficient exceeding 0.880. Additionally, the intra-class correlation coefficients (ICCs) of ALs’ coordinates were all greater than 0.947, and the percentage of Euclidean distance distribution of ALs within 250 μm was over 95.24%.While the ICCs for PD, ACD, ATA, and STS were greater than 0.957, furthermore, the average relative error (ARE) of PD, ACD, ATA, and STS were below 2.41%. In terms of human versus machine performance, the ICCs between the measurements performed by the model and those by senior experts were all greater than 0.931. ConclusionA deep learning-based model could measure AS parameters using UBM images of ICL candidates, and exhibited a performance similar to that of a senior ophthalmologist.

Abstract PO-068: Intratumoral heterogeneity of prognostic multigene signatures for breast cancer

Abstract Background Multigene assays for breast cancer are becoming more commonly used for research, diagnostic, and treatment-selection purposes. These assays are commonly based on a single tumor sample, so this study assesses whether clinically-relevant multigene scores are subject to misclassification due to technical variation or intratumoral heterogeneity. Methods Using FFPE blocks, tumors from 37 patients were sampled at different pathologist-selected spatial locations, targeting regions with distinct histological appearance. A second pathologist assessed mitotic activity and presence of immune infiltration for each specimen. Gene expression was quantified using the PAM50 assay. Samples were classified with respect to intrinsic subtype (Luminal A, Luminal B, HER2-enriched, or Basal-like) and risk of recurrence with proliferation score (ROR-P, high vs. med/low). Euclidean distances between samples were calculated across the 50 genes, and the distribution of Euclidean distances were compared for samples that were concordant vs. discordant for each multigene classifier for PAM50 or ROR-P. Results Of the 37 tumors, 11 had samples with discordant PAM50 subtype and 7 had samples with discordant ROR-P group (75% and 83% agreement, respectively). The Euclidean distance between paired samples with discordant PAM50 intrinsic subtype or ROR-P score was significantly greater than that among concordant tumors. Samples discordant for ROR-P had more heterogeneity in histological characteristics, while discordance of PAM50 subtype call was generally not predicted by heterogeneity of these histological characteristics. Conclusion The concordance of PAM50 subtype calls and ROR-P, despite oversampling of heterogenous-appearing tumor regions, demonstrates reproducibility of the PAM50 classifier for breast cancer tumor intrinsic subtyping. However, assay sampling strategies for histologically heterogeneous tumors merit further consideration. Citation Format: Amber N. Hurson, Alina Hamilton, Linnea T. Olsson, Erin L. Kirk, Benjamin C. Calhoun, Joseph Geradts, Mark E. Sherman, Melissa A. Troester. Intratumoral heterogeneity of prognostic multigene signatures for breast cancer [abstract]. In: Proceedings of the AACR Virtual Special Conference on Tumor Heterogeneity: From Single Cells to Clinical Impact; 2020 Sep 17-18. Philadelphia (PA): AACR; Cancer Res 2020;80(21 Suppl):Abstract nr PO-068.

Network embedding for link prediction: The pitfall and improvement.

Link prediction plays a significant role in various applications of complex networks. The existing link prediction methods can be divided into two categories: structural similarity algorithms in network domain and network embedding algorithms in the field of machine learning. However, few researchers focus on comparing these two categories of algorithms and exploring the intrinsic relationship between them. In this study, we systematically compare the two categories of algorithms and study the shortcomings of network embedding algorithms. The results indicate that network embedding algorithms have poor performance in short-path networks. Then, we explain the reasons for this phenomenon by computing the Euclidean distance distribution of node pairs after a given network has been embedded into a vector space. In the vector space of a short-path network, the distance distribution of existent and nonexistent links are often less distinguishable, which can sharply reduce the algorithmic performance. In contrast, structural similarity algorithms, which are not restricted by the distance function, can represent node similarity accurately in short-path networks. To address the above pitfall of network embedding, we propose a novel method for link prediction aiming to supplement network embedding algorithms with local structural information. The experimental results suggest that our proposed algorithm has significant performance improvement in many empirical networks, especially in short-path networks. AUC and Precision can be improved by 36.7%-94.4% and 53.2%-207.2%, respectively.

Classification Based on Euclidean Distance Distribution for Blind Identification of Error Correcting Codes in Noncooperative Contexts

The use of channel code is mandatory in current digital communication systems. It allows us to access the information on the receiver side despite the presence of noise. In this paper, we are interested in the blind identification of the parameters of an error correcting code from a received noisy data stream. The literature provides a large amount of contributions for this problem in the hard-decision case but few in the soft-decision case. It is well known that soft-decision methods allow significant gain in decoding techniques. Thence, we propose an algorithm which is able to identify the length of a code through a classification process from the bits likelihood values. It highlights a difference of behavior between an independent identically distributed sequence and an encoded one. This method does not rely on any a priori knowledge about the encoder involved. Indeed, the distribution of n-length code words in an n-dimensional space depends on the encoder characteristics. Some areas of this n-dimensional space are left vacant because of the redundancy added by the encoder. Despite the presence of noise, it is still possible to detect this phenomenon. Furthermore, an adaptation of a collisions method based on the birthday paradox gives us access to an estimation of the code dimension. Finally, we investigate the performance of this estimation methods to show their efficiency.

Bound estimation for coded faster‐than‐Nyquist system

Frame error rate bound is a useful tool to predict the performance behaviour of coded faster than Nyquist system (FTN). In this Letter, the Euclidean distance distribution (EDD) of FTN signalling is assumed continuous and obeys the Gaussian distribution for its long memory length. By using the autocorrelation properties of the error sequences, the EDD of FTN is estimated and the simplified bound is further derived which indicates that the performance of coded FTN system is bounded by the performance of employed coding scheme. Simulation results show that the bound is well matched with the simulated performance in high SNR regime.

Performance of Complex Field Network Coding in Multi-Way Relay Channels

Complex field network coding (CFNC) has been shown to achieve a throughput of 1/2 symbol per user per channel use in a multi-way relay channel (MWRC). To achieve this throughput, a superimposed combination of user symbols must be distinguishable at the relay. In this paper, full data exchange in a MWRC network with fading is considered. The pairwise error probability (PEP) of a MWRC with Rayleigh fading is presented, and a closed form approximation of the minimum Euclidean distance distribution for the relay constellation is given. Tight upper bounds on the symbol error rate (SER) are obtained using a nearest neighbours approximation and the effect of a precoding vector on system performance is investigated.

Distance Distribution in Convex n-Gons: Mathematical Framework and Wireless Networking Applications

The performance of a wireless network is related to the Euclidean distance distribution between the communication nodes, which in turn depends on network geometry. In this paper, we provide an analytical framework for the description of distance statistics in convex polygons with arbitrary number and length of sides. Simulation results validate the formulation. Comparisons with models in the literature indicate that our approach is a generalization of previous works. Representative examples show the merits of the proposal and assess its applicability in wireless networking. The main contribution of this work is the consideration of polygonal-shaped networks. The obtained formulation reduces the complexity and computational cost of the modeling and simulation of wireless systems and it is more convenient than other approaches when network planning considers n-gonal coverage areas. Moreover, it provides adequate results for the calculation of distance-dependent parameters and performance metrics of wireless networks.

Change detection using a statistical model in an optimally selected color space

We present a new noise model for color channels for statistical change detection. Based on this noise modeling, we estimate the distribution of Euclidean distances between the pixel colors of the background image and those of the foreground image. The optimal threshold for change detection is automatically determined using the estimated distribution. We show that our noise modeling is appropriate for various color spaces. Because the detection results differ according to the color space, we utilize the expected number of error pixels to select the appropriate color space for our method. Even if we detect changes based on the optimal threshold in a properly selected color space, there will inevitably be some false classifications. To reject these erroneous cases, we adopt graph cuts that efficiently minimize the global energy while taking into account the effect of neighboring pixels. To validate the proposed method, we show experimental results for a large number of images including indoor and outdoor scenes with complex clutter.

Metric and non-metric randomization methods, geographic variation, and the single-species hypothesis for Asian and African Homo erectus

This paper proposes a statistical test of the single-species hypothesis using non-metric characters as a complement to statistical tests using more traditional metric characters. The sample examined is that of Asian and African Homo erectus. The paleoanthropological community is divided on the taxonomic distinction of these fossils, with workers arguing both for and against the species-level distinction between Asian and African populations. Previous arguments have focused on patterns of apparent morphological differentiation between the African and Asian cranial samples. To assess this question, three tests were performed that compared the range of variation in the fossil sample to a single-species group with a similar geographic distribution; this comparative sample was composed of 221 modern humans from Africa and Asia. For the first test, 23 metric characters were analyzed on the fossil and comparative samples. Using resampling procedures, the variation for these characters was examined, recreating 1000 samples from the human analogs and comparing the CV distributions of these samples to the CVs of the fossil group. The second test used the metric data to calculate a Euclidean distance between the African and Asian fossil samples. This distance was compared to a distribution of Euclidean distances calculated between 1000 randomly selected samples of African and Asian modern humans. For the third test, a grading scale was created for ten non-metric characters that encompassed the total morphological variation found in the fossil and modern human samples. The Manhattan distance between the Asian and African fossil samples was calculated and compared to a distribution of distances calculated between 1000 randomly selected samples of African and Asian moderns. The first two tests, using the metric data, failed to falsify the null hypothesis. However, in the third test, using non-metric data, the total Manhattan distance for the fossil sample approached the 100 th percentile of the resampled distances calculated from the moderns. The implications of the contrasting results are discussed.

On Distances in Uniformly Random Networks

The distribution of Euclidean distances in Poisson point processes is determined. The main result is the density function of the distance to the n-nearest neighbor of a homogeneous process in Ropfm, which is shown to be governed by a generalized Gamma distribution. The result has many implications for large wireless networks of randomly distributed nodes

Neuronavigation accuracy dependence on CT and MR imaging parameters: a phantom-based study

Clinical benefits from neuronavigation are well established. However, the complexity of its technical environment requires a careful evaluation of different types of errors. In this work, a detailed phantom study which investigates the accuracy in a neuronavigation procedure is presented. The dependence on many different imaging parameters, such as field of view, slice thickness and different kind of sequences (sequential and spiral for CT, T1-weighted and T2-weighted for MRI), is quantified. Moreover, data based on CT images are compared to those based on MR images, taking into account MRI distortion. Finally, the contributions to global accuracy coming from image acquisition, registration and navigation itself are discussed. Results demonstrate the importance of imaging accuracy. Procedures based on CT proved to be more accurate than procedures based on MRI. In the former, values from 2 to 2.5 mm are obtained for 95% fractiles of cumulative distribution of Euclidean distances between the intended target and the reached one while, in the latter, the measured values range from 3 to 4 mm. The absence of imaging distortion proved to be crucial for registration accuracy in MR-based procedures.

Construction and performance evaluation of a rate 8/10 MSN code for periodically time‐varying trellis diagram

A conventional 8/10 MSN code was constructed so as not to generate a quasi-catastrophic sequence in the decoder trellis diagram, and needing sliding block decoders. In this article, a new 8/10 MSN code is designed by using a periodically time-varying trellis diagram. The proposed code has an improved squared Euclidean distance distribution between PR output sequences and an improved number of paired codewords that have minimum squared free Euclidean distance decreases as compared with the conventional code. Further, this code can be decoded simply by referring codeword sequences corresponding to data sequences in a look-up table, needing no sliding block decoder. As a result, the proposed 8/10 MSN-coded PR4ML system can provide about 0.8 dB SNR gain over the conventional system at a bit error rate of 10–4 and a normalized linear density of 3. © 1999 Scripta Technica, Election Comm Jpn Pt 2, 82(3): 31–40, 1999

The random coded modulation: performance and euclidean distance spectrum evaluation

We apply the random coding argument to coded modulation. The well-known union bound on the error probability of general signaling schemes is revisited. The random coded modulation idea is introduced and a simple bound on the average performance of coded constellations is presented. A relationship between the union bound and the cut-off rate is exhibited by introducing the concept of N-dimensional partial cut-off rate. We define finite theta series for bounded finite-dimensional constellations and their related transfer functions. Bounds on the block and symbol error probability based on the transfer function are derived. The discussion is then focused on the squared Euclidean distance distribution. The evaluation of such parameters as its first two moments (average squared distance and squared distance variance) is considered by either finite theta series or transfer function of the bounded signal set. The Euclidean distance spectra of a few multidimensional coded modulation schemes based on square/cross constituent two-dimensional constellations are presented. Their respective partial cut-off rates are computed. We discuss the asymptotic behaviour and we show that almost all very long coded constellations are good (actually, they tend to become quasi-identical in a certain sense). Finally, we examine how to extend the initial union bound to Gallager-type bounds.

Community Organization in Fishes as Indicated by Morphological Features

This study uses morphological data relating to many aspects of the niche to study community organization in assemblages of stream fishes from three separate drainages. Mean values for all morphological features were compared statistically for coexisting species pairs, and those features which had significantly different means were assumed to indicate ecological differentiation that exists between the species under consideration. Average niche overlap as defined by the percentage of morphological features not differing significantly between species pairs was constant for these assemblages regardless of a nearly twofold difference in number of species present. Similarly, the average Euclidean distance between the centers of morphologically defined niches for all sympatric common species was approximately the same for all three assemblages. Moreover the distribution of Euclidean distances between species was the same in all three drainages and different than a distribution that would result from a random division of resources. Together, these results indicate that consistent patterns do exist in the organization of these stream communities, and that the species currently living together are not a random assortment of species and do not randomly divide their resources. The presence of higher numbers of species in a community seems not to be accompanied by increased packing of the niches, but rather by an occupation of more total niche space by the community as a whole.