日
関

WordNet

the trace of a point whose direction of motion changes (同)curved shape
a pitch of a baseball that is thrown with spin so that its path curves as it approaches the batter (同)curve ball, breaking ball, bender
a line on a graph representing data
curved in two directions (like the letter S)
of or relating to the sigmoid flexure in the large intestine (同)sigmoidal
an inferior dog or one of mixed breed (同)mongrel, mutt
a cowardly and despicable person
having or marked by a curve or smoothly rounded bend; "the curved tusks of a walrus"; "his curved lips suggested a smile but his eyes were hard" (同)curving

PrepTutorEJDIC

『曲線』 / 『曲がり』,曲がったもの,湾曲部 / (野球で投球の)『カーブ』 / (…の方へ)『曲がる』,湾曲する《+『to』+『名』》 / …'を'曲げる;'を'湾曲させる
のら犬 / くだらない人間

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/11/27 09:36:11」(JST)

wiki en

[Wiki en表示]

The logistic curve

Plot of the error function

A sigmoid formula is a mathematical function having an "S" shape (sigmoid curve). Often, sigmoid function refers to the special case of the logistic function shown on the right and defined by the formula

Another example is the Gompertz curve. It is used in modeling systems that saturate at large values of t. Another example is the ogee curve as used in the spillway of some dams. A wide variety of sigmoid functions have been used as the activation function of artificial neurons, including the logistic and hyperbolic tangent functions. Sigmoid curves are also common in statistics as cumulative distribution functions, such as the integrals of the logistic distribution, the normal distribution, and Student's t probability density functions.

Definition[edit]

A sigmoid function is a bounded differentiable real function that is defined for all real input values and has a positive derivative at each point.^[1]

Properties[edit]

In general, a sigmoid function is real-valued and differentiable, having either a non-negative or non-positive first derivative^{[citation needed]} which is bell shaped. There are also a pair of horizontal asymptotes as . The differential equation , with the inclusion of a boundary condition providing a third degree of freedom, , provides a class of functions of this type.

Examples[edit]

Some sigmoid functions compared. In the drawing all functions are normalized in such a way that their slope at the origin is 1.

Many natural processes, including those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used^[2] .

Besides the logistic function, sigmoid functions include the ordinary arctangent, the hyperbolic tangent, the Gudermannian function, and the error function, but also the generalised logistic function and algebraic functions like .

The integral of any smooth, positive, "bump-shaped" function will be sigmoidal, thus the cumulative distribution functions for many common probability distributions are sigmoidal. The most famous such example is the error function, which is related to the Cumulative Distribution Function (CDF) of a normal distribution.

References[edit]

^ Han, Jun; Morag, Claudio (1995). "The influence of the sigmoid function parameters on the speed of backpropagation learning". In Mira, José; Sandoval, Francisco. From Natural to Artificial Neural Computation. pp. 195–201.
^ Gibbs, M.N. (Nov 2000). "Variational Gaussian process classifiers". IEEE Transactions on Neural Networks 11 (6): 1458–1464. doi:10.1109/72.883477. |accessdate= requires |url= (help)

Mitchell, Tom M. (1997). Machine Learning. WCB–McGraw–Hill. ISBN 0-07-042807-7. . In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets.
Humphrys, Mark. "Continuous output, the sigmoid function". Properties of the sigmoid, including how it can shift along axes and how its domain may be transformed.

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. Structure and function of normal hemoglobins
2. 高山病：生理学、危険因子、および一般的な予防法 high altitude illness physiology risk factors and general prevention
3. S状結腸軸捻転 sigmoid volvulus
4. 高血圧治療における目標血圧 what is goal blood pressure in the treatment of hypertension
5. 成人における抗癌剤の投与 dosing of anticancer agents in adults

English Journal

Sigmoid resection for diverticulitis is more difficult than for malignancies.

Stam M1, Draaisma WA2, Pasker P2, Consten E2, Broeders I2.
International journal of colorectal disease.Int J Colorectal Dis.2017 Jun;32(6):891-896. doi: 10.1007/s00384-017-2756-1. Epub 2017 Jan 13.
PMID 28084549

A one-step biomarker quantification methodology for DCE-MRI of adnexal masses: Capturing kinetic pattern from early to late enhancement.

Fathi Kazerooni A1,2, Nabil M3, Haghighat Khah H4, Parviz S5, Gity M5,6, Saligheh Rad H1,2.
Magnetic resonance in medicine.Magn Reson Med.2017 May 7. doi: 10.1002/mrm.26743. [Epub ahead of print]
PMID 28480550

Pharmacokinetic and pharmacodynamic integration and modeling of acetylkitasamycin in swine for Clostridium perfringens.

Nan J1,2, Hao H1,2, Xie S2,3, Pan Y2,3, Xi C2,3, Mao F2,3, Liu Z2,3, Huang L2,3, Yuan Z1,2,3.
Journal of veterinary pharmacology and therapeutics.J Vet Pharmacol Ther.2017 May 2. doi: 10.1111/jvp.12404. [Epub ahead of print]
PMID 28464333

Japanese Journal

企業リポート技術の不連続と企業成長

山本裕久
生産と技術 66(2), 75-79, 2014
NAID 40020066451

末梢リンパ球の免疫抑制薬感受性試験における IC50値とボトム値の関連

塚口真穂登,笹原浩康,杉山健太郎,磯貝和也,外山聡,佐藤博,齋藤和英,中川由紀,高橋公太,田中祥子,恩田健二,平野俊彦
Organ Biology 21(2), 260-264, 2014
… All the participantsʼ CyA bottom levels were below 0％, so we thought 2-sigmoid curve pattern(blastogenesis and killing cells). … On the other hands, Tac bottom levels were over 0％, so we thought 1-sigmoid curve pattern(blastogenesis). …
NAID 130004715815

繰り返し学習方式によるカクテルパーティ効果を伴う脳記憶系のニューロン科学的解釈 : アナログ.ディジタル的動作特性を持つニューロン.ネットワークのHebb学習モデル

清野躬行
電子情報通信学会技術研究報告. NC, ニューロコンピューティング 113(148), 1-6, 2013-07-12
私たちの脳は、何故に、一回の学習で記憶できないのでしょう? 生存上、有利な理由があるはずです。また、雑音だらけの立食パーティ会場で、何故、普通の音程で、相手と話すことが出来るのでしょう?その最大の理由は、脳の能動的な記憶機構にあります。本稿では、カクテルパーティ効果を、聴覚だけの特定感覚に限定せず、脳が有する、より一般的な、パターン認識能力の範疇で捉えます。誤字脱字にすぐ気付いたり、群衆の中から、 …
NAID 110009773316

Related Pictures

Entrepreneur is not a job description. Success is not a destination. #startup # About learning and growning cycle, Sigmoid curve | totalhuman The Sigmoid Curve….and how this relates to brokerages & sales people | John Lusink The Key to Growth: Transformational Change CareerTech Testing Center: The Sigmoid Curve, Personal Learning, and the growth | Rachel Andrea Ko Go Sigmoid-Curve-2 - Retirement Benefits InstituteRetirement Benefits Institute Insights, Advice, and Resources for Leaders: Sigmoid Curve, part 2