public virtual double[][] Revert(double[][] data)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
int rows = data.Rows();
int cols = data.Columns();
int components = NumberOfOutputs;
double[][] reversion = Jagged.Zeros(rows, components);
// Revert the data (reversion = data * eigenVectors.Transpose())
for (int i = 0; i < components; i++)
{
for (int j = 0; j < rows; j++)
{
for (int k = 0; k < cols; k++)
{
reversion[j][i] += data[j][k] * ComponentVectors[k][i];
}
}
}
if (this.Method == PrincipalComponentMethod.Standardize || this.Method == PrincipalComponentMethod.CorrelationMatrix)
{
reversion.Multiply(StandardDeviations, dimension: (VectorType)0, result: reversion);
}
reversion.Add(Means, dimension: (VectorType)0, result: reversion);
return(reversion);
}
/// <summary>
/// Loads a jagged array from a stream.
/// </summary>
///
/// <param name="stream">The stream containing the matrix to be loaded.</param>
/// <param name="trim">Pass true to remove null or empty elements from the loaded array.</param>
///
/// <returns>A jagged array containing the values available in the given stream.</returns>
///
public static Array LoadJagged(Stream stream, bool trim = true)
{
using (var reader = new BinaryReader(stream, System.Text.Encoding.ASCII
#if !NET35 && !NET40
, leaveOpen: true
#endif
))
{
int bytes;
Type type;
int[] shape;
if (!parseReader(reader, out bytes, out type, out shape))
{
throw new FormatException();
}
Array matrix = Jagged.Zeros(type, shape);
if (type == typeof(String))
{
Array result = readStringMatrix(reader, matrix, bytes, type, shape);
if (trim)
{
return(result.Trim());
}
return(result);
}
return(readValueJagged(reader, matrix, bytes, type, shape));
}
}
private void ComputeInformation(double[][] data, int[] labels)
{
// Compute distortion and other metrics regarding the clustering
if (ComputeCovariances)
{
// Compute cluster information (optional)
Parallel.For(0, clusters.Count, ParallelOptions, i =>
{
double[][] centroids = clusters.Centroids;
// Extract the data for the current cluster
double[][] sub = data.Get(labels.Find(x => x == i));
if (sub.Length > 0)
{
// Compute the current cluster variance
clusters.Covariances[i] = sub.Covariance(centroids[i]);
}
else
{
// The cluster doesn't have any samples
clusters.Covariances[i] = Jagged.Zeros(Dimension, Dimension);
}
});
}
if (ComputeError)
{
Error = clusters.Distortion(data);
}
}
/// <summary>
/// 学習ボタンクリック
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void btnLearn_Click(object sender, EventArgs e)
{
int cntRows = dgvHistory.Rows.Count;
double[][] input = Jagged.Zeros(cntRows, 32 * 32);
int[] output = new int[cntRows];
string tmpCharDigit;
// グリッドのデータを1行ずつ学習データとして格納
for (int i = 0; i < cntRows; i++)
{
input.SetRow(i, (double[])dgvHistory.Rows[i].Cells["features"].Value);
tmpCharDigit = dgvHistory.Rows[i].Cells["answer"].Value.ToString();
output[i] = int.Parse(tmpCharDigit);
}
IKernel kernel;
kernel = new Polynomial(2, 0.0000);
kda = new KernelDiscriminantAnalysis(kernel)
{
Threshold = 0.0005,
Regularization = 0.0001
};
Application.DoEvents();
kda.Learn(input, output);
btnQuestion.Enabled = true;
}
public void computeGaussianPerplexity_1()
{
double[][] points =
{
new double[] { 2, 3, 2 },
new double[] { 5, 4, 5 },
new double[] { 9, 6, 4 },
new double[] { 4, 7, 5 },
new double[] { 8, 1, 1 },
new double[] { 1, 2, 4 },
};
double perplexity = 0.5;
int N = points.Length;
int D = 3;
var X = points.ToMatrix();
double[,] expected = new double[N, N];
TSNEWrapper.computeGaussianPerplexity(X, N, D, expected, perplexity);
double[][] actual = Jagged.Zeros(N, N);
TSNE.computeGaussianPerplexity(points, N, D, ref actual, perplexity);
Assert.IsTrue(actual.IsEqual(expected, rtol: 1e-5));
}
/// <summary>
/// Converts an image from one representation to another. When
/// converting to byte, the <see cref="Max"/> and <see cref="Min"/>
/// are ignored.
/// </summary>
///
/// <param name="input">The input image to be converted.</param>
/// <param name="output">The converted image.</param>
///
public void Convert(UnmanagedImage input, out byte[][][] output)
{
int width = input.Width;
int height = input.Height;
int pixelSize = input.PixelSize;
int offset = input.Offset;
output = Jagged.Zeros <byte>(height, width, pixelSize);
if (Channel != 0)
{
throw new InvalidOperationException("The Channel property will be ignored when converting to a rank-3 tensor.");
}
unsafe
{
byte *src = (byte *)input.ImageData.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
for (int d = 0; d < pixelSize; d++, src++)
{
output[y][x][d] = (byte)Vector.Scale(*src, (byte)0, (byte)255, Min, Max);
}
}
src += offset;
}
}
}
/// <summary>
/// Learns a model that can map the given inputs to the given outputs.
/// </summary>
/// <param name="x">The model inputs.</param>
/// <param name="y">The desired outputs associated with each <paramref name="x">inputs</paramref>.</param>
/// <param name="weights">The weight of importance for each input-output pair.</param>
/// <returns>A model that has learned how to produce <paramref name="y" /> given <paramref name="x" />.</returns>
public MinimumMeanDistanceClassifier Learn(double[][] x, int[] y, double[] weights = null)
{
NumberOfInputs = x.Columns();
NumberOfOutputs = y.Max() + 1;
means = Jagged.Zeros(NumberOfOutputs, NumberOfInputs);
int[] counts = new int[NumberOfOutputs];
// Compute the average of the input vectors for each of
// the output classes. Afterwards, a decision can be cast
// by checking to which average a new sample is closer.
for (int i = 0; i < x.Length; i++)
{
int k = y[i];
double[] mean = means[k];
for (int j = 0; j < mean.Length; j++)
{
mean[j] += x[i][j];
}
counts[k]++;
if (Token.IsCancellationRequested)
{
break;
}
}
means.Divide(counts, dimension: 1, result: means);
return(this);
}
/// <summary>
/// Converts an image from one representation to another. When
/// converting to byte, the <see cref="Max"/> and <see cref="Min"/>
/// are ignored.
/// </summary>
///
/// <param name="input">The input image to be converted.</param>
/// <param name="output">The converted image.</param>
///
public void Convert(UnmanagedImage input, out Color[][] output)
{
int width = input.Width;
int height = input.Height;
int pixelSize = input.PixelSize;
int offset = input.Offset;
output = Jagged.Zeros <Color>(input.Height, input.Width);
unsafe
{
if (input.PixelFormat == PixelFormat.Format8bppIndexed)
{
byte *src = (byte *)input.ImageData.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, src += pixelSize)
{
output[y][x] = Color.FromArgb(*src, *src, *src);
}
src += offset;
}
}
else if (input.PixelFormat == PixelFormat.Format24bppRgb ||
input.PixelFormat == PixelFormat.Format32bppRgb)
{
byte *src = (byte *)input.ImageData.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, src += pixelSize)
{
output[y][x] = Color.FromArgb(src[RGB.R], src[RGB.G], src[RGB.B]);
}
src += offset;
}
}
else if (input.PixelFormat == PixelFormat.Format32bppArgb)
{
byte *src = (byte *)input.ImageData.ToPointer();
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, src += pixelSize)
{
output[y][x] = Color.FromArgb(src[RGB.A], src[RGB.R], src[RGB.G], src[RGB.B]);
}
src += offset;
}
}
else
{
throw new UnsupportedImageFormatException("Pixel format is not supported.");
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="ResponseLayer"/> class.
/// </summary>
///
public ResponseLayer(int width, int height, int step, int filter)
{
this.Width = width;
this.Height = height;
this.Step = step;
this.Size = filter;
this.Responses = Jagged.Zeros <float>(height, width);
this.Laplacian = Jagged.Zeros <int>(height, width);
}
public void GetLengthTest()
{
var a = Jagged.Zeros(1, 1);
var b = Matrix.Zeros(1, 1);
int[] actual = a.GetLength();
int[] expected = b.GetLength();
Assert.IsTrue(actual.IsEqual(expected));
}
/// <summary>
/// Initializes a new instance of the <see cref="BasePrincipalComponentAnalysis"/> class.
/// </summary>
///
public BasePrincipalComponentAnalysis()
{
columnMeans = new double[0];
columnStdDev = new double[0];
eigenvectors = Jagged.Zeros(0, 0);
eigenvalues = new double[0];
singularValues = new double[0];
componentCumulative = new double[0];
componentProportions = new double[0];
}
/// <summary>
/// Gets the standard error for each coefficient.
/// </summary>
///
/// <param name="mse">The overall regression standard error (can be computed from <see cref="GetStandardError(double[][], double[][])"/>.</param>
/// <param name="informationMatrix">The information matrix obtained when training the model (see <see cref="OrdinaryLeastSquares.GetInformationMatrix()"/>).</param>
///
public double[][] GetStandardErrors(double[] mse, double[][] informationMatrix)
{
double[][] se = Jagged.Zeros(NumberOfOutputs, informationMatrix.Length);
for (int j = 0; j < se.Length; j++)
{
for (int i = 0; i < informationMatrix.Length; i++)
{
se[j][i] = mse[j] * Math.Sqrt(informationMatrix[i][i]);
}
}
return(se);
}
/// <summary>
/// This method should be implemented by child classes to initialize
/// their fields once the <see cref="BaseLeastSquaresMethod.NumberOfParameters" /> is known.
/// </summary>
protected override void Initialize()
{
weights = new double[NumberOfParameters];
diagonal = new double[NumberOfParameters];
gradient = new double[NumberOfParameters];
jacobian = new double[NumberOfParameters][];
Hessian = Jagged.Zeros(NumberOfParameters, NumberOfParameters);
for (var i = 0; i < Hessian.Length; i++)
{
Hessian[i] = new double[NumberOfParameters];
}
}
/// <summary>
/// Updates the response layer definitions
/// without recreating objects.
/// </summary>
///
public void Update(int width, int height, int step, int filter)
{
if (height > Height || width > Width)
{
this.Responses = Jagged.Zeros <float>(height, width);
this.Laplacian = Jagged.Zeros <int>(height, width);
}
this.Width = width;
this.Height = height;
this.Step = step;
this.Size = filter;
}
/// <summary>
/// This method should be implemented by child classes to initialize
/// their fields once the <see cref="BaseLeastSquaresMethod.NumberOfParameters" /> is known.
/// </summary>
///
protected override void Initialize()
{
this.weights = new double[NumberOfParameters];
this.diagonal = new double[NumberOfParameters];
this.gradient = new double[NumberOfParameters];
this.jacobian = new double[NumberOfParameters][];
this.hessian = Jagged.Zeros(NumberOfParameters, NumberOfParameters);
for (int i = 0; i < hessian.Length; i++)
{
hessian[i] = new double[NumberOfParameters];
}
}
// Compute gradient of the t-SNE cost function (exact)
internal static void computeExactGradient(double[][] P, double[][] Y, int N, int D, double[][] dC)
{
// Make sure the current gradient contains zeros
for (int i = 0; i < dC.Length; i++)
{
for (int j = 0; j < dC[i].Length; j++)
{
dC[i][j] = 0.0;
}
}
// Compute the squared Euclidean distance matrix
double[][] DD = Jagged.Create <double>(N, N);
computeSquaredEuclideanDistance(Y, N, D, DD);
// Compute Q-matrix and normalization sum
double[][] Q = Jagged.Zeros(N, N);
double sum_Q = 0.0;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
if (n != m)
{
Q[n][m] = 1.0 / (1.0 + DD[n][m]);
sum_Q += Q[n][m];
}
}
}
// Perform the computation of the gradient
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
if (n != m)
{
double mult = (P[n][m] - (Q[n][m] / sum_Q)) * Q[n][m];
for (int d = 0; d < D; d++)
{
dC[n][d] += (Y[n][d] - Y[m][d]) * mult;
}
}
}
}
}
public void compute_squared_distance_larger()
{
var points = yinyang.Submatrix(null, 0, 1).ToJagged();
var X = points.ToMatrix();
int N = X.Rows();
int D = X.Columns();
double[,] expected = new double[N, N];
TSNEWrapper.computeSquaredEuclideanDistance(X, expected);
double[][] actual = Jagged.Zeros(N, N);
TSNE.computeSquaredEuclideanDistance(points, N, D, actual);
Assert.IsTrue(actual.IsEqual(expected));
}
public void computeGradient_1()
{
Accord.Math.Random.Generator.Seed = 0;
double perplexity = 0.5;
double theta = 0.5;
int N = 100;
int K = (int)(3 * perplexity);
int D = 3;
uint[] row_P = Vector.Create(N + 1, new uint[] { 0, 1, 2, 3, 4, 5, 6 });
uint[] col_P = Vector.Create(N * K, new uint[] { 5, 3, 1, 1, 2, 1 });
double[] val_P = Vector.Create(N * K, new double[]
{
0.83901046609114708,
0.39701047304189827,
0.19501046869768451,
0.59401047304189827,
0.49301046869768484,
0.59901046869768451,
});
double[,] P = Matrix.Random(N, N, new NormalDistribution());
double[][] p = P.ToJagged();
double[,] Y = Matrix.Random(N, D, new NormalDistribution());
double[][] y = Y.ToJagged();
uint[] expected_row = Vector.Create(row_P);
uint[] expected_col = Vector.Create(col_P);
double[] expected_val = Vector.Create(val_P);
double[,] expected = Matrix.Zeros(N, D);
TSNEWrapper.computeGradient(P, expected_row, expected_col, expected_val, Y, N, D, expected, theta);
int[] actual_row = row_P.To <int[]>();
int[] actual_col = col_P.To <int[]>();
double[] actual_val = (double[])val_P.Clone();
double[][] actual = Jagged.Zeros(N, D);
TSNE.computeGradient(p, actual_row, actual_col, actual_val, y, N, D, actual, theta);
Assert.IsTrue(actual.IsEqual(expected));
Assert.IsTrue(actual_row.IsEqual(expected_row));
Assert.IsTrue(actual_col.IsEqual(expected_col));
Assert.IsTrue(actual_val.IsEqual(expected_val, 1e-4));
}
/// <summary>
/// Learns a model that can map the given inputs to the given outputs.
/// </summary>
/// <param name="x">The model inputs.</param>
/// <param name="y">The desired outputs associated with each <paramref name="x">inputs</paramref>.</param>
/// <param name="weights">The weight of importance for each input-output pair.</param>
/// <returns>
/// A model that has learned how to produce <paramref name="y" /> given <paramref name="x" />.
/// </returns>
public PolynomialRegression Learn(double[] x, double[] y, double[] weights = null)
{
double[][] z = Jagged.Zeros(x.Length, Degree);
for (int i = 0; i < x.Length; i++)
{
for (int j = 0; j < z[i].Length; j++)
{
z[i][j] = Math.Pow(x[i], Degree - j - 1);
}
}
var lls = new OrdinaryLeastSquares();
var linear = lls.Learn(z, y, weights);
return(new PolynomialRegression(linear));
}
public void computeGaussianPerplexity_larger()
{
var points = yinyang.Submatrix(null, 0, 1).ToJagged();
double perplexity = 0.5;
int N = points.Rows();
int D = points.Columns();
var X = points.ToMatrix();
double[,] expected = new double[N, N];
TSNEWrapper.computeGaussianPerplexity(X, N, D, expected, perplexity);
double[][] actual = Jagged.Zeros(N, N);
TSNE.computeGaussianPerplexity(points, N, D, ref actual, perplexity);
Assert.IsTrue(actual.IsEqual(expected, rtol: 1e-5));
}
public void CreateJaggedTest()
{
Array jagged = Jagged.Zeros(typeof(int), 2, 3, 1);
foreach (var idx in jagged.GetIndices(deep: true))
{
Assert.AreEqual(0, jagged.GetValue(deep: true, indices: idx));
jagged.SetValue(idx.Sum(), deep: true, indices: idx);
}
int[][][] expected =
{
new int[][] { new[] { 0 }, new[] { 1 }, new[] { 2 } },
new int[][] { new[] { 1 }, new[] { 2 }, new[] { 3 } }
};
Assert.IsTrue(expected.IsEqual(jagged));
}
private void innerComputeCovariance(double[][] data, int[] labels, int i)
{
double[][] centroids = clusters.Centroids;
// Extract the data for the current cluster
double[][] sub = data.Get(labels.Find(x => x == i));
if (sub.Length > 0)
{
// Compute the current cluster variance
clusters.Covariances[i] = sub.Covariance(centroids[i]);
}
else
{
// The cluster doesn't have any samples
clusters.Covariances[i] = Jagged.Zeros(Dimension, Dimension);
}
}
public double Distance(
double[] meanX, double[][] covX, double lnDetCovX,
double[] meanY, double[][] covY, double lnDetCovY)
{
int n = meanX.Length;
// P = (covX + covY) / 2
var P = Jagged.Zeros(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
P[i][j] = (covX[i][j] + covY[i][j]) / 2.0;
}
}
var svd = new JaggedSingularValueDecomposition(P);
double detP = svd.LogPseudoDeterminant;
double[] d = new double[meanX.Length];
for (int i = 0; i < meanX.Length; i++)
{
d[i] = meanX[i] - meanY[i];
}
double[] z = svd.Solve(d);
double r = 0.0;
for (int i = 0; i < d.Length; i++)
{
r += d[i] * z[i];
}
double mahalanobis = Math.Abs(r);
double a = (1.0 / 8.0) * mahalanobis;
double b = (0.5) * (detP - 0.5 * (lnDetCovX + lnDetCovY));
return(a + b);
}
public void pinv_precision()
{
// Inaccuracy in Accord.Math Pseudoinverse
// https://github.com/accord-net/framework/issues/313
int nPoly = 5;
double[] t = { 1352, 1354, 1356, 1358, 1360, 1362, 1364, 1366, 1368, 1370, 1372, 1374, 1376, 1378, 1380, 1382, 1384, 1386, 1388, 1390, 1392, 1394, 1396, 1398, 1400, 1402, 1404, 1406, 1408, 1410, 1412, 1414, 1416, 1418, 1420, 1422, 1424, 1426, 1428, 1430, 1432, 1434, 1436, 1438, 1440, 1442, 1444, 1446, 1448, 1450, 1452, 1454, 1456, 1458, 1460, 1462, 1464, 1466, 1468, 1470, 1472, 1474, 1476, 1478, 1480, 1482, 1484, 1486, 1488, 1490, 1492, 1494, 1496, 1498, 1500, 1502, 1504, 1506, 1508, 1510, 1512, 1514, 1516, 1518, 1520, 1522, 1524, 1526, 1528, 1530, 1532, 1534, 1536, 1538, 1540, 1542, 1544, 1546, 1548, 1550, 1552, 1554, 1556, 1558, 1560, 1562, 1564, 1566, 1568, 1570, 1572, 1574, 1576, 1578, 1580, 1582, 1584, 1586, 1588, 1590, 1592, 1594, 1596, 1598, 1600, 1602, 1604, 1606, 1608, 1610, 1612, 1614, 1616, 1618, 1620, 1622, 1624, 1626, 1628, 1630, 1632, 1634, 1636, 1638, 1640, 1642, 1644, 1646, 1648, 1650, 1652, 1654, 1656, 1658, 1660, 1662, 1664, 1666, 1668, 1670, 1672, 1674, 1676, 1678, 1680, 1682, 1684, 1686, 1688, 1690, 1692, 1694, 1696, 1698, 1700, 1702 };
//Generating the Matrix
var sPoly = Jagged.Zeros(t.Length, nPoly + 1);
for (int ii = 0; ii < t.Length; ii++)
{
for (int jj = 0; jj < nPoly + 1; jj++)
{
sPoly[ii][jj] = Math.Pow(t[ii], jj);
}
}
// B = (repmat(A, [6 1])' .^ repmat([0 1 2 3 4 5], [176 1])')';
var jagged = sPoly.PseudoInverse();
var multi = sPoly.ToMatrix().PseudoInverse();
Assert.IsTrue(jagged.IsEqual(multi, rtol: 1e-15));
var R = sPoly.Dot(sPoly.PseudoInverse()).Dot(sPoly);
Assert.IsTrue(R.IsEqual(sPoly, rtol: 1e-2));
var expected = Jagged.Parse(
@"1,20125654080206e-10 1,13236875425253e-10 1,06499525384608e-10 9,99130864205866e-11 9,34770208386440e-11 8,71907706948343e-11 8,10537577032779e-11 7,50653831433932e-11 6,92250277671434e-11 6,35320517062416e-11 5,79857943794106e-11 5,25855743996096e-11 4,73306894812560e-11 4,22204163474767e-11 3,72540106373263e-11 3,24307068130343e-11 2,77497180672282e-11 2,32102362301744e-11 1,88114316770077e-11 1,45524532349703e-11 1,04324280906333e-11 6,45046169714632e-12 2,60563768146295e-12 -1,10298224842723e-12 -4,67635839626088e-12 -8,11547317026788e-12 -1,14213311759389e-11 -1,45949593087919e-11 -1,76374068471365e-11 -2,05497455448409e-11 -2,33330697240993e-11 -2,59884963681969e-11 -2,85171652142769e-11 -3,09202388461059e-11 -3,31989027868412e-11 -3,53543655917962e-11 -3,73878589412074e-11 -3,93006377329998e-11 -4,10939801755535e-11 -4,27691878804715e-11 -4,43275859553419e-11 -4,57705230965095e-11 -4,70993716818365e-11 -4,83155278634700e-11 -4,94204116606227e-11 -5,04154670523102e-11 -5,13021620701284e-11 -5,20819888910602e-11 -5,27564639301726e-11 -5,33271279334232e-11 -5,37955460704241e-11 -5,41633080272011e-11 -5,44320280989654e-11 -5,46033452828767e-11 -5,46789233708086e-11 -5,46604510421157e-11 -5,45496419564068e-11 -5,43482348462939e-11 -5,40579936101794e-11 -5,36807074050045e-11 -5,32181907390288e-11 -5,26722835645903e-11 -5,20448513708693e-11 -5,13377852766609e-11 -5,05530021231306e-11 -4,96924445665998e-11 -4,87580811712940e-11 -4,77519065021133e-11 -4,66759412174044e-11 -4,55322321617232e-11 -4,43228524585961e-11 -4,30499016032976e-11 -4,17155055556059e-11 -4,03218168325726e-11 -3,88710146012934e-11 -3,73653047716700e-11 -3,58069200891727e-11 -3,41981202276171e-11 -3,25411918819205e-11 -3,08384488608699e-11 -2,90922321798968e-11 -2,73049101538303e-11 -2,54788784896716e-11 -2,36165603793564e-11 -2,17204065925394e-11 -1,97928955693198e-11 -1,78365335130464e-11 -1,58538544830699e-11 -1,38474204875072e-11 -1,18198215760058e-11 -9,77367593251373e-12 -7,71162996805381e-12 -5,63635841347974e-12 -3,55056441223311e-12 -1,45697961313079e-12 6,41635736882014e-13 2,74249269994829e-12 4,84277355457573e-12 6,93963170281285e-12 9,03019157752643e-12 1,11115485496153e-11 1,31807688352538e-11 1,52348894031179e-11 1,72709178816158e-11 1,92858324661383e-11 2,12765818262735e-11 2,32400850130568e-11 2,51732313661905e-11 2,70728804212796e-11 2,89358618170864e-11 3,07589752027302e-11 3,25389901449449e-11 3,42726460353122e-11 3,59566519974801e-11 3,75876867944076e-11 3,91623987356027e-11 4,06774055843480e-11 4,21292944649313e-11 4,35146217698901e-11 4,48299130672410e-11 4,60716630077087e-11 4,72363352319677e-11 4,83203622778644e-11 4,93201454876667e-11 5,02320549152725e-11 5,10524292335010e-11 5,17775756412421e-11 5,24037697707461e-11 5,29272555948617e-11 5,33442453342341e-11 5,36509193645639e-11 5,38434261238361e-11 5,39178820195501e-11 5,38703713359588e-11 5,36969461412982e-11 5,33936261950206e-11 5,29563988550328e-11 5,23812189849263e-11 5,16640088612107e-11 5,08006580805500e-11 4,97870234669942e-11 4,86189289792142e-11 4,72921656177351e-11 4,58024913321697e-11 4,41456309284536e-11 4,23172759760761e-11 4,03130847153169e-11 3,81286819644788e-11 3,57596590271200e-11 3,32015735992926e-11 3,04499496767691e-11 2,75002774622815e-11 2,43480132727534e-11 2,09885794465332e-11 1,74173642506307e-11 1,36297217879454e-11 9,62097190452815e-12 5,38640009672351e-12 9,21257418547607e-13 -3,77923961121101e-12 -8,71990910167333e-12 -1,39056038826638e-11 -1,93412115974937e-11 -2,50316547957003e-11 -3,09818910258252e-11 -3,71969129281858e-11 -4,36817483276290e-11 -5,04414603263060e-11 -5,74811473964377e-11 -6,48059434730755e-11 -7,24210180468779e-11 -8,03315762568666e-11 -8,85428589831914e-11 -9,70601429399206e-11 -1,05888740767766e-10 -1,15034001126881e-10
7,31883974043541e-08 6,89913033650384e-08 6,48864695308964e-08 6,08735805841603e-08 5,69523089261863e-08 5,31223146210725e-08 4,93832453392821e-08 4,57347363011228e-08 4,21764102202352e-08 3,87078772470566e-08 3,53287349123175e-08 3,20385680705176e-08 2,88369488433999e-08 2,57234365634416e-08 2,26975777173256e-08 1,97589058894296e-08 1,69069417052999e-08 1,41411927751371e-08 1,14611536372736e-08 8,86630570165802e-09 6,35611719332825e-09 3,93004309590195e-09 1,58752509505224e-09 -6,72008478012731e-10 -2,84914270306646e-09 -4,94447612738389e-09 -6,95862082226140e-09 -8,89220243953631e-09 -1,07458602681048e-08 -1,25202472904420e-08 -1,42160302391212e-08 -1,58338896533335e-08 -1,73745199354062e-08 -1,88386294073226e-08 -2,02269403672413e-08 -2,15401891460153e-08 -2,27791261637114e-08 -2,39445159861293e-08 -2,50371373813206e-08 -2,60577833761095e-08 -2,70072613126093e-08 -2,78863929047450e-08 -2,86960142947691e-08 -2,94369761097819e-08 -3,01101435182590e-08 -3,07163962865535e-08 -3,12566288354220e-08 -3,17317502965679e-08 -3,21426845691194e-08 -3,24903703761726e-08 -3,27757613213095e-08 -3,29998259451134e-08 -3,31635477816908e-08 -3,32679254151891e-08 -3,33139725363154e-08 -3,33027179988561e-08 -3,32352058762006e-08 -3,31124955178498e-08 -3,29356616059484e-08 -3,27057942117929e-08 -3,24239988523594e-08 -3,20913965468189e-08 -3,17091238730550e-08 -3,12783330241872e-08 -3,08001918650835e-08 -3,02758839888914e-08 -2,97066087735462e-08 -2,90935814382930e-08 -2,84380331002090e-08 -2,77412108307212e-08 -2,70043777121222e-08 -2,62288128940963e-08 -2,54158116502326e-08 -2,45666854345462e-08 -2,36827619380002e-08 -2,27653851450220e-08 -2,18159153900210e-08 -2,08357294139138e-08 -1,98262204206373e-08 -1,87887981336692e-08 -1,77248888525529e-08 -1,66359355094080e-08 -1,55233977254550e-08 -1,43887518675323e-08 -1,32334911046261e-08 -1,20591254643656e-08 -1,08671818895653e-08 -9,65920429473581e-09 -8,43675362260229e-09 -7,20140790062221e-09 -5,95476229750707e-09 -4,69842917974651e-09 -3,43403816812127e-09 -2,16323619421695e-09 -8,87687556956063e-10 3,90926020890712e-10 1,67090533617476e-09 2,95053364887635e-09 4,22807662555026e-09 5,50178228283311e-09 6,76988093091199e-09 8,03058511701101e-09 9,28208956886756e-09 1,05225711382110e-08 1,17501887442535e-08 1,29630833171593e-08 1,41593777415354e-08 1,53371767999032e-08 1,64945671161813e-08 1,76296170991781e-08 1,87403768860525e-08 1,98248782858086e-08 2,08811347227766e-08 2,19071411800839e-08 2,29008741431426e-08 2,38602915431329e-08 2,47833327004788e-08 2,56679182683270e-08 2,65119501760340e-08 2,73133115726445e-08 2,80698667703691e-08 2,87794611880696e-08 2,94399212947331e-08 3,00490545529623e-08 3,06046493624403e-08 3,11044750034474e-08 3,15462815802896e-08 3,19277999648139e-08 3,22467417398911e-08 3,25007991428757e-08 3,26876450091010e-08 3,28049327153576e-08 3,28502961233717e-08 3,28213495232890e-08 3,27156875771527e-08 3,25308852623844e-08 3,22644978152675e-08 3,19140606744252e-08 3,14770894243015e-08 3,09510797386437e-08 3,03335073239811e-08 2,96218278631074e-08 2,88134769585600e-08 2,79058700761017e-08 2,68964024882018e-08 2,57824492175149e-08 2,45613649803636e-08 2,32304841302189e-08 2,17871206011795e-08 2,02285678514559e-08 1,85520988068464e-08 1,67549658042214e-08 1,48344005350031e-08 1,27876139886454e-08 1,06117963961170e-08 8,30411717337864e-09 5,86172486488058e-09 3,28174708698806e-09 5,61290471549523e-10 -2,30255939070347e-09 -5,31273800662419e-09 -8,47220203718680e-09 -1,17839293540161e-08 -1,52509190958904e-08 -1,88761917252678e-08 -2,26627890848090e-08 -2,66137744538887e-08 -3,07322326051202e-08 -3,50212698608739e-08 -3,94840141497937e-08 -4,41236150633219e-08 -4,89432439122131e-08 -5,39460937830519e-08 -5,91353795947871e-08 -6,45143381552260e-08 -7,00862282175738e-08
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, new DefaultMatrixFormatProvider(CultureInfo.CreateSpecificCulture("fr-FR")));
Assert.IsTrue(jagged.IsEqual(expected, rtol: 1e-2));
}
// Evaluate t-SNE cost function (exactly)
internal static double evaluateError(double[][] P, double[][] Y, int N, int D)
{
// Compute the squared Euclidean distance matrix
double[][] DD = Jagged.Zeros(N, N);
double[][] Q = Jagged.Zeros(N, N);
computeSquaredEuclideanDistance(Y, N, D, DD);
// Compute Q-matrix and normalization sum
double sum_Q = DBL_MIN;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
if (n != m)
{
Q[n][m] = 1.0 / (1.0 + DD[n][m]);
sum_Q += Q[n][m];
}
else
{
Q[n][m] = DBL_MIN;
}
}
}
Q.Divide(sum_Q, result: Q);
// Sum t-SNE error
double C = 0.0;
for (int n = 0; n < P.Length; n++)
{
for (int j = 0; j < P[n].Length; j++)
{
C += P[n][j] * System.Math.Log((P[n][j] + FLT_MIN) / (Q[n][j] + FLT_MIN));
}
}
return(C);
}
public void FitTest()
{
double[] original = { 5, 5, 1, 4, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 3 };
var distribution = new MultivariateEmpiricalDistribution(original.ToJagged());
int[] weights = { 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 1 };
double[] sources = { 5, 1, 4, 1, 2, 3, 4, 3, 4, 3, 2, 3 };
double[][] samples = sources.ToJagged();
var target = new MultivariateEmpiricalDistribution(Jagged.Zeros(1, 1));
target.Fit(samples, weights);
Assert.AreEqual(distribution.Mean[0], target.Mean[0]);
Assert.AreEqual(distribution.Median[0], target.Median[0]);
Assert.AreEqual(distribution.Mode[0], target.Mode[0]);
Assert.AreEqual(distribution.Smoothing[0, 0], target.Smoothing[0, 0]);
Assert.AreEqual(distribution.Variance[0], target.Variance[0]);
Assert.IsTrue(target.Weights.IsEqual(weights.Divide(weights.Sum())));
Assert.AreEqual(target.Samples, samples);
for (double x = 0; x < 6; x += 0.1)
{
double actual, expected;
expected = distribution.ComplementaryDistributionFunction(x);
actual = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.DistributionFunction(x);
actual = target.DistributionFunction(x);
Assert.AreEqual(expected, actual);
expected = distribution.LogProbabilityDensityFunction(x);
actual = target.LogProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
expected = distribution.ProbabilityDensityFunction(x);
actual = target.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-15);
}
}
/// <summary>
/// Converts an image from one representation to another. When
/// converting to byte, the <see cref="Max"/> and <see cref="Min"/>
/// are ignored.
/// </summary>
///
/// <param name="input">The input image to be converted.</param>
/// <param name="output">The converted image.</param>
///
public void Convert(UnmanagedImage input, out byte[][] output)
{
int width = input.Width;
int height = input.Height;
int pixelSize = input.PixelSize;
int offset = input.Offset;
output = Jagged.Zeros <byte>(height, width);
unsafe
{
byte *src = (byte *)input.ImageData.ToPointer() + Channel;
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++, src += pixelSize)
{
output[y][x] = *src;
}
src += offset;
}
}
}
public void compute_squared_distance_1()
{
double[][] points =
{
new double[] { 2, 3, 2 },
new double[] { 5, 4, 5 },
new double[] { 9, 6, 4 },
new double[] { 4, 7, 5 },
new double[] { 8, 1, 1 },
new double[] { 1, 2, 4 },
};
var X = points.ToMatrix();
int N = X.Rows();
int D = X.Columns();
double[,] expected = new double[N, N];
TSNEWrapper.computeSquaredEuclideanDistance(X, expected);
double[][] actual = Jagged.Zeros(N, N);
TSNE.computeSquaredEuclideanDistance(points, N, D, actual);
Assert.IsTrue(actual.IsEqual(expected));
}
/// <summary>
/// Projects vectors from a sequence of vectors into
/// a hypersphere, augmenting their size in one unit
/// and normalizing them to be unit vectors.
/// </summary>
///
/// <param name="input">A sequence of vectors.</param>
///
/// <returns>A sequence of vector projections.</returns>
///
private double[][] snorm(double[][] input)
{
// Create the augmented sequence projection
double[][] projection = Jagged.Zeros(input.Length, input[0].Length + 1);
for (int i = 0; i < input.Length; i++)
{
double norm = alpha * alpha;
for (int j = 0; j < input[i].Length; j++)
{
norm += input[i][j] * input[i][j];
}
norm = Math.Sqrt(norm);
for (int j = 0; j < input[i].Length; j++)
{
projection[i][j] = input[i][j] / norm;
}
projection[i][input[i].Length] = alpha / norm;
}
return(projection); // return the projected sequence
}
private void init(double[][] inputs, int[] outputs, IDistance <double[]> distance)
{
this.distance = distance;
means = Jagged.Zeros(NumberOfOutputs, NumberOfInputs);
int[] counts = new int[NumberOfOutputs];
// Compute the average of the input vectors for each of
// the output classes. Afterwards, a decision can be cast
// by checking to which average a new sample is closer.
for (int i = 0; i < inputs.Length; i++)
{
int k = outputs[i];
double[] mean = means[k];
for (int j = 0; j < mean.Length; j++)
{
mean[j] += inputs[i][j];
}
counts[k]++;
}
means.Divide(counts, dimension: 0, result: means);
}
