Machine Learning
Summary: this tutorial demonstrates functionality relevant in the context of machine learning.
Table of contents
Dimensionality Reduction
PCA
A common approach for to reduce the dimensionality of large data sets is the use of Principal component analyis.
open Plotly.NET
open FSharp.Stats
open FSharp.Stats.ML.Unsupervised
let data =
[
[1.0; 2.0;1.0; 2.0;];
[1.1; 2.1;1.1; 2.1;];
[-1.0; -2.0;1.0; 2.0;];
[-1.1; -2.1;1.1; 2.1;];
[-1.15; -2.15;1.15; 2.15;];
]
|> FSharp.Stats.Matrix.ofJaggedList
// The PCA implementation expects column wise centered data, which can be generated by calling:
let dc = PCA.center data
// Calling compute will compute the PCA of the centered data matrix. Relevant information is stored in the result object.
let pca = PCA.compute dc
// The result of the PCA allows to visualize the analyzed data set projected onto the principal axis:
// extract components 1 and 2
let pcs = pca.PrincipalComponents |> Matrix.mapiRows (fun i v -> v.[0],v.[1])
// typical PCA "score" plot of components 1 and 2 with the explained variance indicated
let scorePlot =
Chart.Point(pcs)
|> Chart.withTemplate ChartTemplates.lightMirrored
|> Chart.withXAxisStyle (sprintf "PC1, Var explained %f" pca.VarExplainedByComponentIndividual.[0])
|> Chart.withYAxisStyle (sprintf "PC2, Var explained %f" pca.VarExplainedByComponentIndividual.[1])
|> Chart.withTitle "Score Plot"
// Additionally the variable loadings can be visualized:
// Disclaimer: there is a certain ambiguity when it comes to the use of the term loading.
// To stay consistent with other implementations the term loading is used.
/// Extract loadings of the variables onto the first and second principal component
let loadings =
pca.Loadings
|> Matrix.mapRows (fun v -> v.[0],v.[1])
// typical PCA "loading" plot
let loadingPlot =
loadings
|> Seq.map (fun l -> [0.,0.;l])
|> Seq.map Chart.Line
|> Chart.combine
|> Chart.withTemplate ChartTemplates.lightMirrored
|> Chart.withXAxisStyle "PC1"
|> Chart.withYAxisStyle "PC2"
|> Chart.withTitle "Loading Plot"
namespace Plotly
namespace Plotly.NET
module Defaults
from Plotly.NET
<summary> Contains mutable global default values. Changing these values will apply the default values to all consecutive Chart generations. </summary>
<summary> Contains mutable global default values. Changing these values will apply the default values to all consecutive Chart generations. </summary>
val mutable DefaultDisplayOptions: DisplayOptions
Multiple items
type DisplayOptions = inherit DynamicObj new: unit -> DisplayOptions static member addAdditionalHeadTags: additionalHeadTags: XmlNode list -> (DisplayOptions -> DisplayOptions) static member addDescription: description: XmlNode list -> (DisplayOptions -> DisplayOptions) static member combine: first: DisplayOptions -> second: DisplayOptions -> DisplayOptions static member getAdditionalHeadTags: displayOpts: DisplayOptions -> XmlNode list static member getDescription: displayOpts: DisplayOptions -> XmlNode list static member getPlotlyReference: displayOpts: DisplayOptions -> PlotlyJSReference static member init: ?AdditionalHeadTags: XmlNode list * ?Description: XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...
--------------------
new: unit -> DisplayOptions
type DisplayOptions = inherit DynamicObj new: unit -> DisplayOptions static member addAdditionalHeadTags: additionalHeadTags: XmlNode list -> (DisplayOptions -> DisplayOptions) static member addDescription: description: XmlNode list -> (DisplayOptions -> DisplayOptions) static member combine: first: DisplayOptions -> second: DisplayOptions -> DisplayOptions static member getAdditionalHeadTags: displayOpts: DisplayOptions -> XmlNode list static member getDescription: displayOpts: DisplayOptions -> XmlNode list static member getPlotlyReference: displayOpts: DisplayOptions -> PlotlyJSReference static member init: ?AdditionalHeadTags: XmlNode list * ?Description: XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions static member initCDNOnly: unit -> DisplayOptions ...
--------------------
new: unit -> DisplayOptions
static member DisplayOptions.init: ?AdditionalHeadTags: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?Description: Giraffe.ViewEngine.HtmlElements.XmlNode list * ?PlotlyJSReference: PlotlyJSReference -> DisplayOptions
type PlotlyJSReference =
| CDN of string
| Full
| Require of string
| NoReference
<summary> Sets how plotly is referenced in the head of html docs. </summary>
<summary> Sets how plotly is referenced in the head of html docs. </summary>
union case PlotlyJSReference.NoReference: PlotlyJSReference
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namespace FSharp
--------------------
namespace Microsoft.FSharp
namespace FSharp
--------------------
namespace Microsoft.FSharp
namespace FSharp.Stats
namespace FSharp.Stats.ML
namespace FSharp.Stats.ML.Unsupervised
val data: Matrix<float>
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module Matrix from FSharp.Stats
--------------------
type Matrix<'T> = | DenseRepr of DenseMatrix<'T> | SparseRepr of SparseMatrix<'T> interface IMatrixFormattable interface IFsiFormattable interface IEnumerable interface IEnumerable<'T> interface IStructuralEquatable interface IStructuralComparable interface IComparable override Equals: yobj: obj -> bool member Format: rowStartCount: int * rowEndCount: int * columnStartCount: int * columnEndCount: int * showInfo: bool -> string + 2 overloads member FormatStrings: rowStartCount: int * rowEndCount: int * columnStartCount: int * columnEndCount: int -> string[][] ...
module Matrix from FSharp.Stats
--------------------
type Matrix<'T> = | DenseRepr of DenseMatrix<'T> | SparseRepr of SparseMatrix<'T> interface IMatrixFormattable interface IFsiFormattable interface IEnumerable interface IEnumerable<'T> interface IStructuralEquatable interface IStructuralComparable interface IComparable override Equals: yobj: obj -> bool member Format: rowStartCount: int * rowEndCount: int * columnStartCount: int * columnEndCount: int * showInfo: bool -> string + 2 overloads member FormatStrings: rowStartCount: int * rowEndCount: int * columnStartCount: int * columnEndCount: int -> string[][] ...
val ofJaggedList: xss: float list list -> Matrix<float>
<summary> returns a dense matrix with the inner lists of the input jagged list as its rows </summary>
<summary> returns a dense matrix with the inner lists of the input jagged list as its rows </summary>
val dc: matrix
module PCA
from FSharp.Stats.ML.Unsupervised
<summary> Principle component analysis </summary>
<summary> Principle component analysis </summary>
val center: m: matrix -> matrix
<summary>Normalizes each feature by substracting the corresponing mean followed by a division by its standard deviation.<br />The centered features of the matrix are centered around 0 and possess a standard deviation of 1.<br />Expects a data matrix with rows representing observations and columns representing features.</summary>
<remarks></remarks>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
<summary>Normalizes each feature by substracting the corresponing mean followed by a division by its standard deviation.<br />The centered features of the matrix are centered around 0 and possess a standard deviation of 1.<br />Expects a data matrix with rows representing observations and columns representing features.</summary>
<remarks></remarks>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
val pca: PCA.PCA
val compute: m: matrix -> PCA.PCA
<summary>Computes the PCA of a column centered data matrix m.<br />Expects a column centered data matrix m, with rows representing observations (a.k.a. samples) and columns representing features.</summary>
<remarks></remarks>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
<summary>Computes the PCA of a column centered data matrix m.<br />Expects a column centered data matrix m, with rows representing observations (a.k.a. samples) and columns representing features.</summary>
<remarks></remarks>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
val pcs: Vector<float * float>
PCA.PCA.PrincipalComponents: Matrix<float>
<summary> Matrix with columns representing individual principal components ("raw" principal components, projections on principal directions) and rows representing samples. Also reffered to as "scores". Corresponds to the attribute "x" of the result object of Rs prcomp() function. </summary>
<summary> Matrix with columns representing individual principal components ("raw" principal components, projections on principal directions) and rows representing samples. Also reffered to as "scores". Corresponds to the attribute "x" of the result object of Rs prcomp() function. </summary>
val mapiRows: f: (int -> rowvec -> 'b) -> m: matrix -> Vector<'b>
<summary>Maps every matrix row using the position dependant function</summary>
<remarks></remarks>
<param name="f"></param>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
<summary>Maps every matrix row using the position dependant function</summary>
<remarks></remarks>
<param name="f"></param>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
val i: int
val v: rowvec
val scorePlot: GenericChart.GenericChart
type Chart =
static member AnnotatedHeatmap: zData: seq<#seq<'a1>> * annotationText: seq<#seq<string>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a3> * ?MultiX: seq<seq<'a3>> * ?XGap: int * ?Y: seq<'a4> * ?MultiY: seq<seq<'a4>> * ?YGap: int * ?Text: 'a5 * ?MultiText: seq<'a5> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload
static member Area: x: seq<#IConvertible> * y: seq<#IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?FillColor: Color * ?FillPatternShape: PatternShape * ?FillPattern: Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload
static member Bar: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload
static member BoxPlot: ?X: seq<'a0> * ?MultiX: seq<seq<'a0>> * ?Y: seq<'a1> * ?MultiY: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Text: 'a2 * ?MultiText: seq<'a2> * ?FillColor: Color * ?MarkerColor: Color * ?Marker: Marker * ?Opacity: float * ?WhiskerWidth: float * ?BoxPoints: BoxPoints * ?BoxMean: BoxMean * ?Jitter: float * ?PointPos: float * ?Orientation: Orientation * ?OutlineColor: Color * ?OutlineWidth: float * ?Outline: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?Notched: bool * ?NotchWidth: float * ?QuartileMethod: QuartileMethod * ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads
static member Bubble: x: seq<#IConvertible> * y: seq<#IConvertible> * sizes: seq<int> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: MarkerSymbol * ?MultiMarkerSymbol: seq<MarkerSymbol> * ?Marker: Marker * ?LineColor: Color * ?LineColorScale: Colorscale * ?LineWidth: float * ?LineDash: DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: Orientation * ?GroupNorm: GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload
static member Candlestick: ``open`` : seq<#IConvertible> * high: seq<#IConvertible> * low: seq<#IConvertible> * close: seq<#IConvertible> * ?X: seq<'a4> * ?MultiX: seq<seq<'a4>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Text: 'a5 * ?MultiText: seq<'a5> * ?Line: Line * ?IncreasingColor: Color * ?Increasing: FinanceMarker * ?DecreasingColor: Color * ?Decreasing: FinanceMarker * ?WhiskerWidth: float * ?ShowXAxisRangeSlider: bool * ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads
static member Column: values: seq<#IConvertible> * ?Keys: seq<'a1> * ?MultiKeys: seq<seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?MarkerColor: Color * ?MarkerColorScale: Colorscale * ?MarkerOutline: Line * ?MarkerPatternShape: PatternShape * ?MultiMarkerPatternShape: seq<PatternShape> * ?MarkerPattern: Pattern * ?Marker: Marker * ?Base: #IConvertible * ?Width: 'a4 * ?MultiWidth: seq<'a4> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload
static member Contour: zData: seq<#seq<'a1>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?Transpose: bool * ?ContourLineColor: Color * ?ContourLineDash: DrawingStyle * ?ContourLineSmoothing: float * ?ContourLine: Line * ?ContoursColoring: ContourColoring * ?ContoursOperation: ConstraintOperation * ?ContoursType: ContourType * ?ShowContourLabels: bool * ?ContourLabelFont: Font * ?Contours: Contours * ?FillColor: Color * ?NContours: int * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible)
static member Funnel: x: seq<#IConvertible> * y: seq<#IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?Width: float * ?Offset: float * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: TextPosition * ?MultiTextPosition: seq<TextPosition> * ?Orientation: Orientation * ?AlignmentGroup: string * ?OffsetGroup: string * ?MarkerColor: Color * ?MarkerOutline: Line * ?Marker: Marker * ?TextInfo: TextInfo * ?ConnectorLineColor: Color * ?ConnectorLineStyle: DrawingStyle * ?ConnectorFillColor: Color * ?ConnectorLine: Line * ?Connector: FunnelConnector * ?InsideTextFont: Font * ?OutsideTextFont: Font * ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible)
static member Heatmap: zData: seq<#seq<'a1>> * ?X: seq<'a2> * ?MultiX: seq<seq<'a2>> * ?Y: seq<'a3> * ?MultiY: seq<seq<'a3>> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?XGap: int * ?YGap: int * ?Text: 'a4 * ?MultiText: seq<'a4> * ?ColorBar: ColorBar * ?ColorScale: Colorscale * ?ShowScale: bool * ?ReverseScale: bool * ?ZSmooth: SmoothAlg * ?Transpose: bool * ?UseWebGL: bool * ?ReverseYAxis: bool * ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) + 1 overload
...
static member Chart.Point: xy: seq<#System.IConvertible * #System.IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'c * ?MultiText: seq<'c> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Point: x: seq<#System.IConvertible> * y: seq<#System.IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.Point: x: seq<#System.IConvertible> * y: seq<#System.IConvertible> * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.withTemplate: template: Template -> (GenericChart.GenericChart -> GenericChart.GenericChart)
module ChartTemplates
from Plotly.NET
val lightMirrored: Template
static member Chart.withXAxisStyle: ?TitleText: string * ?TitleFont: Font * ?TitleStandoff: int * ?Title: Title * ?Color: Color * ?AxisType: StyleParam.AxisType * ?MinMax: (#System.IConvertible * #System.IConvertible) * ?Mirror: StyleParam.Mirror * ?ShowSpikes: bool * ?SpikeColor: Color * ?SpikeThickness: int * ?ShowLine: bool * ?LineColor: Color * ?ShowGrid: bool * ?GridColor: Color * ?GridDash: StyleParam.DrawingStyle * ?ZeroLine: bool * ?ZeroLineColor: Color * ?Anchor: StyleParam.LinearAxisId * ?Side: StyleParam.Side * ?Overlaying: StyleParam.LinearAxisId * ?Domain: (float * float) * ?Position: float * ?CategoryOrder: StyleParam.CategoryOrder * ?CategoryArray: seq<#System.IConvertible> * ?RangeSlider: LayoutObjects.RangeSlider * ?RangeSelector: LayoutObjects.RangeSelector * ?BackgroundColor: Color * ?ShowBackground: bool * ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)
val sprintf: format: Printf.StringFormat<'T> -> 'T
<summary>Print to a string using the given format.</summary>
<param name="format">The formatter.</param>
<returns>The formatted result.</returns>
<example>See <c>Printf.sprintf</c> (link: <see cref="M:Microsoft.FSharp.Core.PrintfModule.PrintFormatToStringThen``1" />) for examples.</example>
<summary>Print to a string using the given format.</summary>
<param name="format">The formatter.</param>
<returns>The formatted result.</returns>
<example>See <c>Printf.sprintf</c> (link: <see cref="M:Microsoft.FSharp.Core.PrintfModule.PrintFormatToStringThen``1" />) for examples.</example>
PCA.PCA.VarExplainedByComponentIndividual: vector
<summary> Variance explained by principal components </summary>
<summary> Variance explained by principal components </summary>
static member Chart.withYAxisStyle: ?TitleText: string * ?TitleFont: Font * ?TitleStandoff: int * ?Title: Title * ?Color: Color * ?AxisType: StyleParam.AxisType * ?MinMax: (#System.IConvertible * #System.IConvertible) * ?Mirror: StyleParam.Mirror * ?ShowSpikes: bool * ?SpikeColor: Color * ?SpikeThickness: int * ?ShowLine: bool * ?LineColor: Color * ?ShowGrid: bool * ?GridColor: Color * ?GridDash: StyleParam.DrawingStyle * ?ZeroLine: bool * ?ZeroLineColor: Color * ?Anchor: StyleParam.LinearAxisId * ?Side: StyleParam.Side * ?Overlaying: StyleParam.LinearAxisId * ?AutoShift: bool * ?Shift: int * ?Domain: (float * float) * ?Position: float * ?CategoryOrder: StyleParam.CategoryOrder * ?CategoryArray: seq<#System.IConvertible> * ?RangeSlider: LayoutObjects.RangeSlider * ?RangeSelector: LayoutObjects.RangeSelector * ?BackgroundColor: Color * ?ShowBackground: bool * ?Id: StyleParam.SubPlotId -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: string * ?TitleFont: Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: string * ?TitleFont: Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)
module GenericChart
from Plotly.NET
<summary> Module to represent a GenericChart </summary>
<summary> Module to represent a GenericChart </summary>
val toChartHTML: gChart: GenericChart.GenericChart -> string
val loadings: Vector<float * float>
Extract loadings of the variables onto the first and second principal component
Extract loadings of the variables onto the first and second principal component
PCA.PCA.Loadings: Matrix<float>
<summary> Matrix with columns representing component loadings and rows individual features. Corresponds to the attribute "rotation" of the result object of Rs prcomp() function. </summary>
<summary> Matrix with columns representing component loadings and rows individual features. Corresponds to the attribute "rotation" of the result object of Rs prcomp() function. </summary>
val mapRows: f: (RowVector<float> -> 'a) -> m: matrix -> Vector<'a>
<summary>Applies function f along row axis</summary>
<remarks></remarks>
<param name="f"></param>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
<summary>Applies function f along row axis</summary>
<remarks></remarks>
<param name="f"></param>
<param name="m"></param>
<returns></returns>
<example><code></code></example>
val v: RowVector<float>
val loadingPlot: GenericChart.GenericChart
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module Seq from FSharp.Stats
<summary> Module to compute common statistical measure </summary>
--------------------
module Seq from Microsoft.FSharp.Collections
<summary>Contains operations for working with values of type <see cref="T:Microsoft.FSharp.Collections.seq`1" />.</summary>
--------------------
type Seq = new: unit -> Seq static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> seq<float> static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> seq<float>
--------------------
new: unit -> Seq
module Seq from FSharp.Stats
<summary> Module to compute common statistical measure </summary>
--------------------
module Seq from Microsoft.FSharp.Collections
<summary>Contains operations for working with values of type <see cref="T:Microsoft.FSharp.Collections.seq`1" />.</summary>
--------------------
type Seq = new: unit -> Seq static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> seq<float> static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> seq<float>
--------------------
new: unit -> Seq
val map: mapping: ('T -> 'U) -> source: seq<'T> -> seq<'U>
<summary>Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection. The given function will be applied as elements are demanded using the <c>MoveNext</c> method on enumerators retrieved from the object.</summary>
<remarks>The returned sequence may be passed between threads safely. However, individual IEnumerator values generated from the returned sequence should not be accessed concurrently.</remarks>
<param name="mapping">A function to transform items from the input sequence.</param>
<param name="source">The input sequence.</param>
<returns>The result sequence.</returns>
<exception cref="T:System.ArgumentNullException">Thrown when the input sequence is null.</exception>
<example id="item-1"><code lang="fsharp"> let inputs = ["a"; "bbb"; "cc"] inputs |> Seq.map (fun x -> x.Length) </code> Evaluates to a sequence yielding the same results as <c>seq { 1; 3; 2 }</c></example>
<summary>Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection. The given function will be applied as elements are demanded using the <c>MoveNext</c> method on enumerators retrieved from the object.</summary>
<remarks>The returned sequence may be passed between threads safely. However, individual IEnumerator values generated from the returned sequence should not be accessed concurrently.</remarks>
<param name="mapping">A function to transform items from the input sequence.</param>
<param name="source">The input sequence.</param>
<returns>The result sequence.</returns>
<exception cref="T:System.ArgumentNullException">Thrown when the input sequence is null.</exception>
<example id="item-1"><code lang="fsharp"> let inputs = ["a"; "bbb"; "cc"] inputs |> Seq.map (fun x -> x.Length) </code> Evaluates to a sequence yielding the same results as <c>seq { 1; 3; 2 }</c></example>
val l: float * float
static member Chart.Line: xy: seq<#System.IConvertible * #System.IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'c * ?MultiText: seq<'c> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?Fill: StyleParam.Fill * ?FillColor: Color * ?FillPattern: TraceObjects.Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Line: x: seq<#System.IConvertible> * y: seq<#System.IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?Fill: StyleParam.Fill * ?FillColor: Color * ?FillPattern: TraceObjects.Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.Line: x: seq<#System.IConvertible> * y: seq<#System.IConvertible> * ?ShowMarkers: bool * ?Name: string * ?ShowLegend: bool * ?Opacity: float * ?MultiOpacity: seq<float> * ?Text: 'a2 * ?MultiText: seq<'a2> * ?TextPosition: StyleParam.TextPosition * ?MultiTextPosition: seq<StyleParam.TextPosition> * ?MarkerColor: Color * ?MarkerColorScale: StyleParam.Colorscale * ?MarkerOutline: Line * ?MarkerSymbol: StyleParam.MarkerSymbol * ?MultiMarkerSymbol: seq<StyleParam.MarkerSymbol> * ?Marker: TraceObjects.Marker * ?LineColor: Color * ?LineColorScale: StyleParam.Colorscale * ?LineWidth: float * ?LineDash: StyleParam.DrawingStyle * ?Line: Line * ?AlignmentGroup: string * ?OffsetGroup: string * ?StackGroup: string * ?Orientation: StyleParam.Orientation * ?GroupNorm: StyleParam.GroupNorm * ?Fill: StyleParam.Fill * ?FillColor: Color * ?FillPattern: TraceObjects.Pattern * ?UseWebGL: bool * ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)
static member Chart.combine: gCharts: seq<GenericChart.GenericChart> -> GenericChart.GenericChart