func (lr *LinearRegression) Fit(inst *base.Instances) error {
if inst.Rows < inst.GetAttributeCount() {
return NotEnoughDataError
}
// Split into two matrices, observed results (dependent variable y)
// and the explanatory variables (X) - see http://en.wikipedia.org/wiki/Linear_regression
observed := mat64.NewDense(inst.Rows, 1, nil)
explVariables := mat64.NewDense(inst.Rows, inst.GetAttributeCount(), nil)
for i := 0; i < inst.Rows; i++ {
observed.Set(i, 0, inst.Get(i, inst.ClassIndex)) // Set observed data
for j := 0; j < inst.GetAttributeCount(); j++ {
if j == 0 {
// Set intercepts to 1.0
// Could / should be done better: http://www.theanalysisfactor.com/interpret-the-intercept/
explVariables.Set(i, 0, 1.0)
} else {
explVariables.Set(i, j, inst.Get(i, j-1))
}
}
}
n := inst.GetAttributeCount()
qr := mat64.QR(explVariables)
q := qr.Q()
reg := qr.R()
var transposed, qty mat64.Dense
transposed.TCopy(q)
qty.Mul(&transposed, observed)
regressionCoefficients := make([]float64, n)
for i := n - 1; i >= 0; i-- {
regressionCoefficients[i] = qty.At(i, 0)
for j := i + 1; j < n; j++ {
regressionCoefficients[i] -= regressionCoefficients[j] * reg.At(i, j)
}
regressionCoefficients[i] /= reg.At(i, i)
}
lr.disturbance = regressionCoefficients[0]
lr.regressionCoefficients = regressionCoefficients[1:]
lr.fitted = true
return nil
}
func TestChebyshev(t *testing.T) {
var vectorX, vectorY *mat64.Dense
chebyshev := NewChebyshev()
Convey("Given two vectors", t, func() {
vectorX = mat64.NewDense(4, 1, []float64{1, 2, 3, 4})
vectorY = mat64.NewDense(4, 1, []float64{-5, -6, 7, 8})
Convey("When calculating distance with two vectors", func() {
result := chebyshev.Distance(vectorX, vectorY)
Convey("The result should be 8", func() {
So(result, ShouldEqual, 8)
})
})
Convey("When calculating distance with row vectors", func() {
vectorX.TCopy(vectorX)
vectorY.TCopy(vectorY)
result := chebyshev.Distance(vectorX, vectorY)
Convey("The result should be 8", func() {
So(result, ShouldEqual, 8)
})
})
Convey("When calculating distance with different dimention matrices", func() {
vectorX.TCopy(vectorX)
So(func() { chebyshev.Distance(vectorX, vectorY) }, ShouldPanicWith, mat64.ErrShape)
})
})
}
func TestCranberrra(t *testing.T) {
var vectorX, vectorY *mat64.Dense
cranberra := NewCranberra()
Convey("Given two vectors that are same", t, func() {
vec := mat64.NewDense(7, 1, []float64{0, 1, -2, 3.4, 5, -6.7, 89})
distance := cranberra.Distance(vec, vec)
Convey("The result should be 0", func() {
So(distance, ShouldEqual, 0)
})
})
Convey("Given two vectors", t, func() {
vectorX = mat64.NewDense(5, 1, []float64{1, 2, 3, 4, 9})
vectorY = mat64.NewDense(5, 1, []float64{-5, -6, 7, 4, 3})
Convey("When calculating distance with two vectors", func() {
result := cranberra.Distance(vectorX, vectorY)
Convey("The result should be 2.9", func() {
So(result, ShouldEqual, 2.9)
})
})
Convey("When calculating distance with row vectors", func() {
vectorX.TCopy(vectorX)
vectorY.TCopy(vectorY)
result := cranberra.Distance(vectorX, vectorY)
Convey("The result should be 2.9", func() {
So(result, ShouldEqual, 2.9)
})
})
Convey("When calculating distance with different dimention matrices", func() {
vectorX.TCopy(vectorX)
So(func() { cranberra.Distance(vectorX, vectorY) }, ShouldPanic)
})
})
}
func TestManhattan(t *testing.T) {
var vectorX, vectorY *mat64.Dense
manhattan := NewManhattan()
Convey("Given two vectors that are same", t, func() {
vec := mat64.NewDense(7, 1, []float64{0, 1, -2, 3.4, 5, -6.7, 89})
distance := manhattan.Distance(vec, vec)
Convey("The result should be 0", func() {
So(distance, ShouldEqual, 0)
})
})
Convey("Given two vectors", t, func() {
vectorX = mat64.NewDense(3, 1, []float64{2, 2, 3})
vectorY = mat64.NewDense(3, 1, []float64{1, 4, 5})
Convey("When calculating distance with column vectors", func() {
result := manhattan.Distance(vectorX, vectorY)
Convey("The result should be 5", func() {
So(result, ShouldEqual, 5)
})
})
Convey("When calculating distance with row vectors", func() {
vectorX.TCopy(vectorX)
vectorY.TCopy(vectorY)
result := manhattan.Distance(vectorX, vectorY)
Convey("The result should be 5", func() {
So(result, ShouldEqual, 5)
})
})
Convey("When calculating distance with different dimention matrices", func() {
vectorX.TCopy(vectorX)
So(func() { manhattan.Distance(vectorX, vectorY) }, ShouldPanicWith, mat64.ErrShape)
})
})
}
// CovarianceMatrix calculates a covariance matrix (also known as a
// variance-covariance matrix) from a matrix of data, using a two-pass
// algorithm. The matrix returned will be symmetric and square.
//
// The weights wts should have the length equal to the number of rows in
// input data matrix x. If c is nil, then a new matrix with appropriate size will
// be constructed. If c is not nil, it should be a square matrix with the same
// number of columns as the input data matrix x, and it will be used as the receiver
// for the covariance data. Weights cannot be negative.
func CovarianceMatrix(cov *mat64.Dense, x mat64.Matrix, wts []float64) *mat64.Dense {
// This is the matrix version of the two-pass algorithm. It doesn't use the
// additional floating point error correction that the Covariance function uses
// to reduce the impact of rounding during centering.
// TODO(jonlawlor): indicate that the resulting matrix is symmetric, and change
// the returned type from a *mat.Dense to a *mat.Symmetric.
r, c := x.Dims()
if cov == nil {
cov = mat64.NewDense(c, c, nil)
} else if covr, covc := cov.Dims(); covr != covc || covc != c {
panic(mat64.ErrShape)
}
var xt mat64.Dense
xt.TCopy(x)
// Subtract the mean of each of the columns.
for i := 0; i < c; i++ {
v := xt.RawRowView(i)
// This will panic with ErrShape if len(wts) != len(v), so
// we don't have to check the size later.
mean := Mean(v, wts)
floats.AddConst(-mean, v)
}
var n float64
if wts == nil {
n = float64(r)
cov.MulTrans(&xt, false, &xt, true)
// Scale by the sample size.
cov.Scale(1/(n-1), cov)
return cov
}
// Multiply by the sqrt of the weights, so that multiplication is symmetric.
sqrtwts := make([]float64, r)
for i, w := range wts {
if w < 0 {
panic("stat: negative covariance matrix weights")
}
sqrtwts[i] = math.Sqrt(w)
}
// Weight the rows.
for i := 0; i < c; i++ {
v := xt.RawRowView(i)
floats.Mul(v, sqrtwts)
}
// Calculate the normalization factor.
n = floats.Sum(wts)
cov.MulTrans(&xt, false, &xt, true)
// Scale by the sample size.
cov.Scale(1/(n-1), cov)
return cov
}
func (lr *LinearRegression) Fit(inst base.FixedDataGrid) error {
// Retrieve row size
_, rows := inst.Size()
// Validate class Attribute count
classAttrs := inst.AllClassAttributes()
if len(classAttrs) != 1 {
return fmt.Errorf("Only 1 class variable is permitted")
}
classAttrSpecs := base.ResolveAttributes(inst, classAttrs)
// Retrieve relevant Attributes
allAttrs := base.NonClassAttributes(inst)
attrs := make([]base.Attribute, 0)
for _, a := range allAttrs {
if _, ok := a.(*base.FloatAttribute); ok {
attrs = append(attrs, a)
}
}
cols := len(attrs) + 1
if rows < cols {
return NotEnoughDataError
}
// Retrieve relevant Attribute specifications
attrSpecs := base.ResolveAttributes(inst, attrs)
// Split into two matrices, observed results (dependent variable y)
// and the explanatory variables (X) - see http://en.wikipedia.org/wiki/Linear_regression
observed := mat64.NewDense(rows, 1, nil)
explVariables := mat64.NewDense(rows, cols, nil)
// Build the observed matrix
inst.MapOverRows(classAttrSpecs, func(row [][]byte, i int) (bool, error) {
val := base.UnpackBytesToFloat(row[0])
observed.Set(i, 0, val)
return true, nil
})
// Build the explainatory variables
inst.MapOverRows(attrSpecs, func(row [][]byte, i int) (bool, error) {
// Set intercepts to 1.0
explVariables.Set(i, 0, 1.0)
for j, r := range row {
explVariables.Set(i, j+1, base.UnpackBytesToFloat(r))
}
return true, nil
})
n := cols
qr := mat64.QR(explVariables)
q := qr.Q()
reg := qr.R()
var transposed, qty mat64.Dense
transposed.TCopy(q)
qty.Mul(&transposed, observed)
regressionCoefficients := make([]float64, n)
for i := n - 1; i >= 0; i-- {
regressionCoefficients[i] = qty.At(i, 0)
for j := i + 1; j < n; j++ {
regressionCoefficients[i] -= regressionCoefficients[j] * reg.At(i, j)
}
regressionCoefficients[i] /= reg.At(i, i)
}
lr.disturbance = regressionCoefficients[0]
lr.regressionCoefficients = regressionCoefficients[1:]
lr.fitted = true
lr.attrs = attrs
lr.cls = classAttrs[0]
return nil
}
