Persistent homology analysis of multiqubit entanglement

We introduce a homology-based technique for the classification of multiqubit state vectors with genuine entanglement. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown.

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NONLINEAR STATISTICS OF HUMAN SPEECH DATA

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024086 ◽

2009 ◽

Vol 19 (07) ◽

pp. 2307-2319 ◽

Cited By ~ 10

Author(s):

KENNETH A. BROWN ◽

KEVIN P. KNUDSON

Keyword(s):

Time Delay ◽

Betti Number ◽

Persistent Homology ◽

Point Clouds ◽

Simplicial Complexes ◽

Data Sets ◽

Human Speech ◽

Speech Data ◽

Nonlinear Statistics

We study the structure of point clouds obtained as time delay embeddings of human speech signals by approximating the data sets with certain simplicial complexes and analyzing their persistent homology. Results for several different sounds are presented in embedding dimensions 3 and 4. The first Betti number allows a coarse classification of sounds into three groups: vowels, nasals and noise.

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Classification of jujube defects in small data sets based on transfer learning

Neural Computing and Applications ◽

10.1007/s00521-021-05715-2 ◽

2021 ◽

Author(s):

Jianping Ju ◽

Hong Zheng ◽

Xiaohang Xu ◽

Zhongyuan Guo ◽

Zhaohui Zheng ◽

...

Keyword(s):

Transfer Learning ◽

Loss Function ◽

Training Model ◽

Parameter Distribution ◽

Test Accuracy ◽

Small Data ◽

Data Sets ◽

Data Set ◽

Small Data Sets

AbstractAlthough convolutional neural networks have achieved success in the field of image classification, there are still challenges in the field of agricultural product quality sorting such as machine vision-based jujube defects detection. The performance of jujube defect detection mainly depends on the feature extraction and the classifier used. Due to the diversity of the jujube materials and the variability of the testing environment, the traditional method of manually extracting the features often fails to meet the requirements of practical application. In this paper, a jujube sorting model in small data sets based on convolutional neural network and transfer learning is proposed to meet the actual demand of jujube defects detection. Firstly, the original images collected from the actual jujube sorting production line were pre-processed, and the data were augmented to establish a data set of five categories of jujube defects. The original CNN model is then improved by embedding the SE module and using the triplet loss function and the center loss function to replace the softmax loss function. Finally, the depth pre-training model on the ImageNet image data set was used to conduct training on the jujube defects data set, so that the parameters of the pre-training model could fit the parameter distribution of the jujube defects image, and the parameter distribution was transferred to the jujube defects data set to complete the transfer of the model and realize the detection and classification of the jujube defects. The classification results are visualized by heatmap through the analysis of classification accuracy and confusion matrix compared with the comparison models. The experimental results show that the SE-ResNet50-CL model optimizes the fine-grained classification problem of jujube defect recognition, and the test accuracy reaches 94.15%. The model has good stability and high recognition accuracy in complex environments.

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Detection and Classification of Anomalies in Large Data Sets on the Basis of Information Granules

IEEE Transactions on Fuzzy Systems ◽

10.1109/tfuzz.2021.3076265 ◽

2021 ◽

pp. 1-1

Author(s):

Adam Kiersztyn ◽

Pawe Karczmarek ◽

Krystyna Kiersztyn ◽

Witold Pedrycz

Keyword(s):

Large Data ◽

Large Data Sets ◽

Data Sets ◽

Information Granules

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Software Benchmark—Classification Tree Algorithms for Cell Atlases Annotation Using Single-Cell RNA-Sequencing Data

Microbiology Research ◽

10.3390/microbiolres12020022 ◽

2021 ◽

Vol 12 (2) ◽

pp. 317-334

Author(s):

Omar Alaqeeli ◽

Li Xing ◽

Xuekui Zhang

Keyword(s):

Single Cell ◽

Rna Sequencing ◽

Classification Tree ◽

Area Under The Curve ◽

Data Sets ◽

Sequencing Data ◽

Single Cell Rna Sequencing ◽

Tree Algorithms ◽

R Packages

Classification tree is a widely used machine learning method. It has multiple implementations as R packages; rpart, ctree, evtree, tree and C5.0. The details of these implementations are not the same, and hence their performances differ from one application to another. We are interested in their performance in the classification of cells using the single-cell RNA-Sequencing data. In this paper, we conducted a benchmark study using 22 Single-Cell RNA-sequencing data sets. Using cross-validation, we compare packages’ prediction performances based on their Precision, Recall, F1-score, Area Under the Curve (AUC). We also compared the Complexity and Run-time of these R packages. Our study shows that rpart and evtree have the best Precision; evtree is the best in Recall, F1-score and AUC; C5.0 prefers more complex trees; tree is consistently much faster than others, although its complexity is often higher than others.

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Classification of multipartite systems featuring only $| W\rangle $ and $| {GHZ}\rangle $ genuine entangled states

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/49/8/085201 ◽

2016 ◽

Vol 49 (8) ◽

pp. 085201 ◽

Cited By ~ 5

Author(s):

Frédéric Holweck ◽

Péter Lévay

Keyword(s):

Entangled States

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A proposed procedure for the analysis of large phytosociological data sets in the classification of South African grasslands

Koedoe ◽

10.4102/koedoe.v38i1.303 ◽

1995 ◽

Vol 38 (1) ◽

Cited By ~ 6

Author(s):

G.J. Bredenkamp ◽

H. Bezuidenhout

Keyword(s):

South African ◽

Plant Communities ◽

Vegetation Type ◽

Second Step ◽

Data Sets ◽

Vegetation Types ◽

Related Plant ◽

Single Cluster ◽

Synoptic Table

A procedure for the effective classification of large phytosociological data sets, and the combination of many data sets from various parts of the South African grasslands is demonstrated. The procedure suggests a region by region or project by project treatment of the data. The analyses are performed step by step to effectively bring together all releves of similar or related plant communities. The first step involves a separate numerical classification of each subset (region), and subsequent refinement by Braun- Blanquet procedures. The resulting plant communities are summarised in a single synoptic table, by calculating a synoptic value for each species in each community. In the second step all communities in the synoptic table are classified by numerical analysis, to bring related communities from different regions or studies together in a single cluster. After refinement of these clusters by Braun-Blanquet procedures, broad vegetation types are identified. As a third step phytosociological tables are compiled for each iden- tified broad vegetation type, and a comprehensive abstract hierarchy constructed.

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The classification of imbalanced large data sets based on MapReduce and ensemble of ELM classifiers

International Journal of Machine Learning and Cybernetics ◽

10.1007/s13042-015-0478-7 ◽

2015 ◽

Vol 8 (3) ◽

pp. 1009-1017 ◽

Cited By ~ 54

Author(s):

Junhai Zhai ◽

Sufang Zhang ◽

Chenxi Wang

Keyword(s):

Large Data ◽

Large Data Sets ◽

Data Sets

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Sequential Sampling for Estimation and Classification of the Incidence of Hop Powdery Mildew II: Cone Sampling

Plant Disease ◽

10.1094/pdis-91-8-1013 ◽

2007 ◽

Vol 91 (8) ◽

pp. 1013-1020 ◽

Cited By ~ 8

Author(s):

David H. Gent ◽

William W. Turechek ◽

Walter F. Mahaffee

Keyword(s):

Powdery Mildew ◽

Binomial Distribution ◽

Disease Incidence ◽

Sequential Sampling ◽

Model Construction ◽

Data Sets ◽

Data Set ◽

Sampling Plans ◽

Simulated Sampling

Sequential sampling models for estimation and classification of the incidence of powdery mildew (caused by Podosphaera macularis) on hop (Humulus lupulus) cones were developed using parameter estimates of the binary power law derived from the analysis of 221 transect data sets (model construction data set) collected from 41 hop yards sampled in Oregon and Washington from 2000 to 2005. Stop lines, models that determine when sufficient information has been collected to estimate mean disease incidence and stop sampling, for sequential estimation were validated by bootstrap simulation using a subset of 21 model construction data sets and simulated sampling of an additional 13 model construction data sets. Achieved coefficient of variation (C) approached the prespecified C as the estimated disease incidence, [Formula: see text], increased, although achieving a C of 0.1 was not possible for data sets in which [Formula: see text] < 0.03 with the number of sampling units evaluated in this study. The 95% confidence interval of the median difference between [Formula: see text] of each yard (achieved by sequential sampling) and the true p of the original data set included 0 for all 21 data sets evaluated at levels of C of 0.1 and 0.2. For sequential classification, operating characteristic (OC) and average sample number (ASN) curves of the sequential sampling plans obtained by bootstrap analysis and simulated sampling were similar to the OC and ASN values determined by Monte Carlo simulation. Correct decisions of whether disease incidence was above or below prespecified thresholds (pt) were made for 84.6 or 100% of the data sets during simulated sampling when stop lines were determined assuming a binomial or beta-binomial distribution of disease incidence, respectively. However, the higher proportion of correct decisions obtained by assuming a beta-binomial distribution of disease incidence required, on average, sampling 3.9 more plants per sampling round to classify disease incidence compared with the binomial distribution. Use of these sequential sampling plans may aid growers in deciding the order in which to harvest hop yards to minimize the risk of a condition called “cone early maturity” caused by late-season infection of cones by P. macularis. Also, sequential sampling could aid in research efforts, such as efficacy trials, where many hop cones are assessed to determine disease incidence.

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