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Graphical notions of a "knee" of a curve, based on curvature, are criticized due to their dependence on the coordinate scale: different choices of scale result in different points being the "knee". This criticism dates at least to the 1940s, being found in
58:) is a point where the curve visibly bends, specifically from high slope to low slope (flat or close to flat), or in the other direction. This is particularly used in
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The term "knee" as applied to curves dates at least to the 1910s, and is found more commonly by the 1940s, being common enough to draw criticism. The unabridged
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of the graph. This corresponds with the graphical intuition (it is where the curvature has a maximum), but depends on the choice of scale.
80:): the knee is where the benefit is no longer increasing rapidly, and is no longer worth the cost of further increases – a cutoff point of
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references to the significance of a so-called knee of a curve when the location of the knee was a function of the chosen coordinate scales
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Photovoltaic solar cell I-V curves where a line intersects the knee of the curves where the maximum power transfer point is located.
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is used, and depends on the particular optimization problem. A knee may also be defined purely geometrically, in terms of the
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An
Experimental Investigation of a New System for Automatically Regulating the Voltage of an Alternating Current Circuit
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Explained variance. The "elbow" is indicated by the red circle. The number of clusters chosen should therefore be 4.
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use, the term may be used informally, and a knee point identified visually, but in more formal use an explicit
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Thomas, Clayton; Sheldon, Bob (1999). "The "Knee of a Curve"— Useful Clue but
Incomplete Support".
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Kiokemeister, Fred L. (1949). "An
Analysis of Functions Describing Experimental Data".
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199:... enables one to tell how near the "knee" of the curve the iron is ...
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an abrupt change in direction in a curve (as on a graph);
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66:and a trade-off between the benefit (vertical
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193:. Rensselaer Polytechnic Institute. p.
216:National Advisory Committee for Aeronautics
111:The knee of a curve can be defined as a
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136:one approaching a right angle in shape.
124:(1971 edition) gives definition 3h of
282:Worthing, J.; Geffner, A. G. (1943).
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284:Treatment of Experimental Data
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293:Military Operations Research
170:Maximum power point tracking
148:Worthing & Geffner (1943
236:Worthing & Geffner 1943
189:Terrell, John Alan (1913).
150:, Preface), who criticize:
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336:Mathematical optimization
270:Thomas & Sheldon 1999
331:Curvature (mathematics)
253:Psychophysical Research
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121:Webster's Dictionary
27:Shape in mathematics
341:Operations research
305:10.5711/morj.4.2.17
212:NACA Wartime Report
82:diminishing returns
64:increasing function
93:objective function
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101:second derivative
16:(Redirected from
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159:Applications
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60:optimization
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107:Definitions
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325:Categories
238:, Preface.
176:References
141:Criticism
97:curvature
89:heuristic
313:43940795
99:or the
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113:vertex
309:JSTOR
214:. L.
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126:knee
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71:axis
54:(or
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301:doi
134:esp
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