Linear function neurons: Structure and training

Hampson, Steven E.; Volper, Dennis J.

doi:10.1007/bf00336991

Cited by 57 publications

(36 citation statements)

References 40 publications

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“…[Hon87,Rag88]). Since there are 2 Ω(n 2 ) halfspaces over {0, 1} n a counting argument shows that there exist halfspaces over {0, 1} n that require weight 2 Ω(n) , and specific halfspaces that require weight 2 Ω(n) have been known for decades [MP68,HV86]. Håstad [Hås94] exhibited a specific halfspace that has weight n Ω(n) and his construction was subsequently refined in [AV97].…”

Section: Previous Work and Our Resultsmentioning

confidence: 99%

On the Weight of Halfspaces over Hamming Balls

Long

Servedio²

2014

SIAM J. Discrete Math.

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For S ⊆ {0, 1}n , a Boolean function f : S → {−1, 1} is a halfspace over S if there exist w ∈ R n and θ ∈ R such that f (x) = sign(w · x − θ) for all x ∈ S. We give bounds on the size of integer weights w 1 , . . . , w n ∈ Z that are required to represent halfspaces over Hamming balls S = {x ∈ {0, 1} n : x 1 + · · · + x n ≤ k}. Such weight bounds for halfspaces over Hamming balls have immediate consequences for the performance of learning algorithms in the common scenario of learning from very high-dimensional categorical examples which are such that only a small number of features are active in each example.We give upper and lower bounds on weight both for exact representation (when sign(w · x−θ) must equal f (x) for every x ∈ S) and for ε-approximate representation (when sign(w · x−θ) may disagree with f (x) for up to an ε fraction of points x ∈ S). Our results show that extremal bounds for exact representation are qualitatively rather similar whether the domain is all of {0, 1} n or the Hamming ball {0, 1} n ≤k , but extremal bounds for approximate representation are qualitatively very different between these two domains.

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Section: Previous Work and Our Resultsmentioning

confidence: 99%

On the Weight of Halfspaces over Hamming Balls

Long

Servedio²

2014

SIAM J. Discrete Math.

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“…n that require weight 2 Ω(n) , and specific halfspaces that require weight 2 Ω(n) have been known for decades [9,5]. [6] exhibited a specific halfspace that has weight n Ω(n) and his construction was subsequently refined by [1].…”

Section: Previous Work and Our Resultsmentioning

confidence: 99%

Low-weight halfspaces for sparse boolean vectors

Long¹,

Servedio

2013

Proceedings of the 4th Conference on Innovations in Theoretical Computer Science

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For S ⊆ {0, 1}n , a Boolean function f : S → {−1, 1} is a halfspace over S if there exist w ∈ R n and θ ∈ R such that f (x) = sign(w · x − θ) for all x ∈ S. We give bounds on the size of integer weights w1, . . . , wn ∈ Z that are required to represent halfspaces over Hamming balls centered at 0 n , i.e. halfspaces over S = {0, 1}n ≤k def = {x ∈ {0, 1} n : x1 + · · · + xn ≤ k}. Such weight bounds for halfspaces over Hamming balls have immediate consequences for the performance of learning algorithms in the increasingly common scenario of learning from very high-dimensional categorical examples which are such that only a small number of features are active in each example.We give upper and lower bounds on weight both for exact representation (when sign(w · x − θ) must equal f (x) for every x ∈ S) and for ε-approximate representation (when sign(w · x − θ) may disagree with f (x) for up to an ε fraction of points x ∈ S). Our results show that extremal bounds for exact representation are qualitatively rather similar whether the domain is all of {0, 1} n or the Hamming ball {0, 1} n ≤k , but extremal bounds for approximate representation are qualitatively very different between these two domains.

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“…In formulating decision trees, various impact related variables are analyzed, using previously built in models that are related with testing data to predict future events (Smith & Tansley, 2003). Decision trees are used to predict probable outcomes, such as forecasting company's future, customers' intentions and likely decisions (Potter & Potter, 1988;Fayyad & Irani, 1992;Hampson & Volper, 1986).…”

Section: Overview Of Related Studiesmentioning

confidence: 99%

“…Hampson and Volper (1986) applied decision trees in structuring and training linear function neurons in biology, Friedl and Brodley (1997) used decision trees to classify land cover from remotely sensed data while Hautaniemi et al (2005) modelled a signal response with decision tree analysis. Tso and Yau (2007) also predicted the consumption of electricity using decision trees while Goodwin, Wrights and Philips (2004) analyzed management judgments using decision tree classification.…”

Section: Overview Of Related Studiesmentioning

confidence: 99%

Investigating Web Based Marketing in the Context of Micro and Small-Scale Enterprises (MSEs): A Decision Tree Classification Technique

Agu¹,

Nabareseh²,

Osakwe³

2015

InSITE Conference

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This paper presents the findings of an exploratory study of web based marketing (WBM) usage predictor variables in the context of micro and small-scale enterprises (MSEs). By means of a cross-sectional field study, a structured questionnaire was used to elicit responses from 267 enterprises situated in the South East Region of Nigeria. The main rationale for this study is to provide a vivid description of pertinent variables that are most likely to influence an enterprise's consideration of the relevance and/or implementation of WBM. Against this backdrop, the authors used the decision tree classification technique of data mining to build a predictive model. One of the interesting findings in this study seems to show that service-oriented enterprises that have a social media presence and are equally headed by highly educated women have a higher proclivity of engaging in WBM. By and large, our findings provide an understanding of idiosyncratic factors that impact on WBM non (usage) by enterprises. Lastly, our findings have implications for practitioners and policy makers in developing countries, particularly that of Nigeria.

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Linear function neurons: Structure and training

Cited by 57 publications

References 40 publications

On the Weight of Halfspaces over Hamming Balls

On the Weight of Halfspaces over Hamming Balls

Low-weight halfspaces for sparse boolean vectors

Investigating Web Based Marketing in the Context of Micro and Small-Scale Enterprises (MSEs): A Decision Tree Classification Technique

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