An Upper Bound on the Minimum Number of Monomials Required to Separate Dichotomies of {−1, 1}n

2006 ◽  
Vol 18 (12) ◽  
pp. 3119-3138 ◽  
Author(s):  
Erhan Oztop
Keyword(s):  
Upper Bound ◽  
Polynomial Function ◽  
Binary Classification ◽  
Classification Problem ◽  
Deterministic Algorithm ◽  
Higher Order ◽  
Function Solution ◽  
Order Neuron ◽  
Minimum Number ◽  
First Time

It is known that any dichotomy of {−1, 1}n can be learned (separated) with a higher-order neuron (polynomial function) with 2n inputs (monomials). In general, less than 2n monomials are sufficient to solve a given dichotomy. In spite of the efforts to develop algorithms for finding solutions with fewer monomials, there have been relatively fewer studies investigating maximum density (II(n)), the minimum number of monomials that would suffice to separate an arbitrary dichotomy of {−1, 1}n . This article derives a theoretical (upper) bound for this quantity, superseding previously known bounds. The main theorem here states that for any binary classification problem in {−1, 1}n (n > 1), one can always find a polynomial function solution with 2n −2n/4 or fewer monomials. In particular, any dichotomy of {−1, 1}n can be learned by a higher-order neuron with a fan-in of 2n −2n/4 or less. With this result, for the first time, a deterministic ratio bound independent of n is established as II (n)/2n ≤ 0 75. The main theorem is constructive, so it provides a deterministic algorithm for achieving the theoretical result. The study presented provides the basic mathematical tools and forms the basis for further analyses that may have implications for neural computation mechanisms employed in the cerebral cortex.

scholarly journals Advancing Stress Detection Methodology with Deep Learning Techniques Targeting UX Evaluation in AAL Scenarios: Applying Embeddings for Categorical Variables

Electronics ◽  
2021 ◽  
Vol 10 (13) ◽  
pp. 1550
Author(s):  
Alexandros Liapis ◽  
Evanthia Faliagka ◽  
Christos P. Antonopoulos ◽  
Georgios Keramidas ◽  
Nikolaos Voros
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
User Experience ◽  
Electrodermal Activity ◽  
Binary Classification ◽  
Research Question ◽  
Classification Problem ◽  
Categorical Variables ◽  
Stress Detection ◽  
Software Failures

Physiological measurements have been widely used by researchers and practitioners in order to address the stress detection challenge. So far, various datasets for stress detection have been recorded and are available to the research community for testing and benchmarking. The majority of the stress-related available datasets have been recorded while users were exposed to intense stressors, such as songs, movie clips, major hardware/software failures, image datasets, and gaming scenarios. However, it remains an open research question if such datasets can be used for creating models that will effectively detect stress in different contexts. This paper investigates the performance of the publicly available physiological dataset named WESAD (wearable stress and affect detection) in the context of user experience (UX) evaluation. More specifically, electrodermal activity (EDA) and skin temperature (ST) signals from WESAD were used in order to train three traditional machine learning classifiers and a simple feed forward deep learning artificial neural network combining continues variables and entity embeddings. Regarding the binary classification problem (stress vs. no stress), high accuracy (up to 97.4%), for both training approaches (deep-learning, machine learning), was achieved. Regarding the stress detection effectiveness of the created models in another context, such as user experience (UX) evaluation, the results were quite impressive. More specifically, the deep-learning model achieved a rather high agreement when a user-annotated dataset was used for validation.

scholarly journals Confidence interval for micro-averaged F1 and macro-averaged F1 scores

2021 ◽  
Author(s):  
Kanae Takahashi ◽  
Kouji Yamamoto ◽  
Aya Kuchiba ◽  
Tatsuki Koyama
Keyword(s):  
Binary Classification ◽  
Classification Problem ◽  
Classification Problems ◽  
Summary Measure ◽  
Medical Field ◽  
Predictive Values ◽  
Binary Classification Problem ◽  
Multi Class Classification ◽  
Sensitivity Specificity ◽  
Measures Of Performance

AbstractA binary classification problem is common in medical field, and we often use sensitivity, specificity, accuracy, negative and positive predictive values as measures of performance of a binary predictor. In computer science, a classifier is usually evaluated with precision (positive predictive value) and recall (sensitivity). As a single summary measure of a classifier’s performance, F1 score, defined as the harmonic mean of precision and recall, is widely used in the context of information retrieval and information extraction evaluation since it possesses favorable characteristics, especially when the prevalence is low. Some statistical methods for inference have been developed for the F1 score in binary classification problems; however, they have not been extended to the problem of multi-class classification. There are three types of F1 scores, and statistical properties of these F1 scores have hardly ever been discussed. We propose methods based on the large sample multivariate central limit theorem for estimating F1 scores with confidence intervals.

scholarly journals Understanding Smartwatch Battery Utilization in the Wild

Sensors ◽  
2020 ◽  
Vol 20 (13) ◽  
pp. 3784 ◽  
Author(s):  
Morteza Homayounfar ◽  
Amirhossein Malekijoo ◽  
Aku Visuri ◽  
Chelsea Dobbins ◽  
Ella Peltonen ◽  
...  
Keyword(s):  
Real World ◽  
Binary Classification ◽  
Classification Problem ◽  
Machine Learning Algorithms ◽  
Indexing Method ◽  
In The Wild ◽  
Art Research ◽  
Battery Discharge ◽  
Changes Over Time ◽  
Application Developers

Smartwatch battery limitations are one of the biggest hurdles to their acceptability in the consumer market. To our knowledge, despite promising studies analyzing smartwatch battery data, there has been little research that has analyzed the battery usage of a diverse set of smartwatches in a real-world setting. To address this challenge, this paper utilizes a smartwatch dataset collected from 832 real-world users, including different smartwatch brands and geographic locations. First, we employ clustering to identify common patterns of smartwatch battery utilization; second, we introduce a transparent low-parameter convolutional neural network model, which allows us to identify the latent patterns of smartwatch battery utilization. Our model converts the battery consumption rate into a binary classification problem; i.e., low and high consumption. Our model has 85.3% accuracy in predicting high battery discharge events, outperforming other machine learning algorithms that have been used in state-of-the-art research. Besides this, it can be used to extract information from filters of our deep learning model, based on learned filters of the feature extractor, which is impossible for other models. Third, we introduce an indexing method that includes a longitudinal study to quantify smartwatch battery quality changes over time. Our novel findings can assist device manufacturers, vendors and application developers, as well as end-users, to improve smartwatch battery utilization.

scholarly journals New Synthetic Methods of Novel Nanoporous Polycondensates and Excellent Oxygen Permselectivity of Their Composite Membranes

Nanomaterials ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 859
Author(s):  
Yu Zang ◽  
Toshiki Aoki ◽  
Masahiro Teraguchi ◽  
Takashi Kaneko ◽  
Hongge Jia ◽  
...  
Keyword(s):  
Contact Angle ◽  
Upper Bound ◽  
Oxygen Permeability ◽  
Membrane Surface ◽  
Composite Membranes ◽  
Synthetic Methods ◽  
Preparation Methods ◽  
First Time

Two kinds of novel nanoporous polycondensates (sc(Rf)) have been synthesized by two new preparation methods consisting of polycondensation and highly selective photocyclicaromataization of 1/3 helical cis-cis polyphenylacetylenes with polymerizable groups. By the original methods, new well-defined sheet polymers having nanopores or nanospaces have been synthesized for the first time. Their composite membranes, containing small amounts (1.0 wt%) of sc(Rf), had ultrahigh oxygen permeability (Po2 > 1000 barrer), and their plots were beyond the Robeson’s upper bound line in the graph of oxygen permselectivity (α = Po2/PN2) versus Po2. Both α and Po2 values were enhanced by adding only small amounts (1.0 wt%) of sc(Rf). One of the sc(Rf)s synthesized on the base membrane surface showed the best performance, i.e., Po2 = 5300 barrer and α = 2.5. The membrane surface was effectively covered by sc(Rf), judging from the contact angle values. It is thought that nanopores and nanospaces created in and between sc(Rf) molecules played an important role for the enhancement of both α and Po2/PN2.

scholarly journals Emotionally Informed Hate Speech Detection: A Multi-target Perspective

2021 ◽  
Author(s):  
Patricia Chiril ◽  
Endang Wahyu Pamungkas ◽  
Farah Benamara ◽  
Véronique Moriceau ◽  
Viviana Patti
Keyword(s):  
Hate Speech ◽  
Binary Classification ◽  
Online Communication ◽  
Vulnerable Groups ◽  
Speech Detection ◽  
Social Media Platforms ◽  
Sentic Computing ◽  
Specific Manifestation ◽  
The Impact ◽  
First Time

AbstractHate Speech and harassment are widespread in online communication, due to users' freedom and anonymity and the lack of regulation provided by social media platforms. Hate speech is topically focused (misogyny, sexism, racism, xenophobia, homophobia, etc.), and each specific manifestation of hate speech targets different vulnerable groups based on characteristics such as gender (misogyny, sexism), ethnicity, race, religion (xenophobia, racism, Islamophobia), sexual orientation (homophobia), and so on. Most automatic hate speech detection approaches cast the problem into a binary classification task without addressing either the topical focus or the target-oriented nature of hate speech. In this paper, we propose to tackle, for the first time, hate speech detection from a multi-target perspective. We leverage manually annotated datasets, to investigate the problem of transferring knowledge from different datasets with different topical focuses and targets. Our contribution is threefold: (1) we explore the ability of hate speech detection models to capture common properties from topic-generic datasets and transfer this knowledge to recognize specific manifestations of hate speech; (2) we experiment with the development of models to detect both topics (racism, xenophobia, sexism, misogyny) and hate speech targets, going beyond standard binary classification, to investigate how to detect hate speech at a finer level of granularity and how to transfer knowledge across different topics and targets; and (3) we study the impact of affective knowledge encoded in sentic computing resources (SenticNet, EmoSenticNet) and in semantically structured hate lexicons (HurtLex) in determining specific manifestations of hate speech. We experimented with different neural models including multitask approaches. Our study shows that: (1) training a model on a combination of several (training sets from several) topic-specific datasets is more effective than training a model on a topic-generic dataset; (2) the multi-task approach outperforms a single-task model when detecting both the hatefulness of a tweet and its topical focus in the context of a multi-label classification approach; and (3) the models incorporating EmoSenticNet emotions, the first level emotions of SenticNet, a blend of SenticNet and EmoSenticNet emotions or affective features based on Hurtlex, obtained the best results. Our results demonstrate that multi-target hate speech detection from existing datasets is feasible, which is a first step towards hate speech detection for a specific topic/target when dedicated annotated data are missing. Moreover, we prove that domain-independent affective knowledge, injected into our models, helps finer-grained hate speech detection.

scholarly journals Deep Learning for Laryngopharyngeal Reflux Diagnosis

2021 ◽  
Vol 11 (11) ◽  
pp. 4753
Author(s):  
Gen Ye ◽  
Chen Du ◽  
Tong Lin ◽  
Yan Yan ◽  
Jack Jiang
Keyword(s):  
Deep Learning ◽  
Speech Processing ◽  
Data Augmentation ◽  
Laryngopharyngeal Reflux ◽  
Ph Monitoring ◽  
Binary Classification ◽  
Classification Problem ◽  
Learning Approaches ◽  
Learning Techniques ◽  
Auc Value

(1) Background: Deep learning has become ubiquitous due to its impressive performance in various domains, such as varied as computer vision, natural language and speech processing, and game-playing. In this work, we investigated the performance of recent deep learning approaches on the laryngopharyngeal reflux (LPR) diagnosis task. (2) Methods: Our dataset is composed of 114 subjects with 37 pH-positive cases and 77 control cases. In contrast to prior work based on either reflux finding score (RFS) or pH monitoring, we directly take laryngoscope images as inputs to neural networks, as laryngoscopy is the most common and simple diagnostic method. The diagnosis task is formulated as a binary classification problem. We first tested a powerful backbone network that incorporates residual modules, attention mechanism and data augmentation. Furthermore, recent methods in transfer learning and few-shot learning were investigated. (3) Results: On our dataset, the performance is the best test classification accuracy is 73.4%, while the best AUC value is 76.2%. (4) Conclusions: This study demonstrates that deep learning techniques can be applied to classify LPR images automatically. Although the number of pH-positive images used for training is limited, deep network can still be capable of learning discriminant features with the advantage of technique.

scholarly journals Intrinsic linking and knotting in tournaments

2019 ◽  
Vol 28 (12) ◽  
pp. 1950076
Author(s):  
Thomas Fleming ◽  
Joel Foisy
Keyword(s):  
Directed Graph ◽  
Upper Bound ◽  
Directed Edge ◽  
Undirected Graphs ◽  
Oriented Cycle ◽  
Minimum Number ◽  
The Difference

A directed graph [Formula: see text] is intrinsically linked if every embedding of that graph contains a nonsplit link [Formula: see text], where each component of [Formula: see text] is a consistently oriented cycle in [Formula: see text]. A tournament is a directed graph where each pair of vertices is connected by exactly one directed edge. We consider intrinsic linking and knotting in tournaments, and study the minimum number of vertices required for a tournament to have various intrinsic linking or knotting properties. We produce the following bounds: intrinsically linked ([Formula: see text]), intrinsically knotted ([Formula: see text]), intrinsically 3-linked ([Formula: see text]), intrinsically 4-linked ([Formula: see text]), intrinsically 5-linked ([Formula: see text]), intrinsically [Formula: see text]-linked ([Formula: see text]), intrinsically linked with knotted components ([Formula: see text]), and the disjoint linking property ([Formula: see text]). We also introduce the consistency gap, which measures the difference in the order of a graph required for intrinsic [Formula: see text]-linking in tournaments versus undirected graphs. We conjecture the consistency gap to be nondecreasing in [Formula: see text], and provide an upper bound at each [Formula: see text].

scholarly journals On L h , k -Labeling Index of Inverse Graphs Associated with Finite Cyclic Groups

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
K. Mageshwaran ◽  
G. Kalaimurugan ◽  
Bussakorn Hammachukiattikul ◽  
Vediyappan Govindan ◽  
Ismail Naci Cangul
Keyword(s):  
Cyclic Group ◽  
Upper Bound ◽  
Labeling Index ◽  
Positive Difference ◽  
Cyclic Groups ◽  
Finite Cyclic Group ◽  
Minimum Number ◽  
The Difference ◽  
Radio Labeling

An L h , k -labeling of a graph G = V , E is a function f : V ⟶ 0 , ∞ such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between the vertices separated by a distance 2 is at least k . The difference between the highest and lowest assigned values is the index of an L h , k -labeling. The minimum number for which the graph admits an L h , k -labeling is called the required possible index of L h , k -labeling of G , and it is denoted by λ k h G . In this paper, we obtain an upper bound for the index of the L h , k -labeling for an inverse graph associated with a finite cyclic group, and we also establish the fact that the upper bound is sharp. Finally, we investigate a relation between L h , k -labeling with radio labeling of an inverse graph associated with a finite cyclic group.

Sign in / Sign up

Export Citation Format

Share Document