This repository has been archived by the owner on Nov 19, 2020. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 2k
/
Linear.cs
491 lines (445 loc) · 16.7 KB
/
Linear.cs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
// Accord Statistics Library
// The Accord.NET Framework
// http://accord-framework.net
//
// Copyright © César Souza, 2009-2017
// cesarsouza at gmail.com
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
//
namespace Accord.Statistics.Kernels
{
using Accord.Math;
using Accord.Math.Distances;
using System;
using System.Runtime.CompilerServices;
using Accord.Compat;
/// <summary>
/// Linear Kernel.
/// </summary>
///
[Serializable]
public struct Linear : IKernel, IDistance, ILinear, ICloneable, IReverseDistance,
ITransform, IKernel<Sparse<double>>, ILinear<Sparse<double>>, IDistance<Sparse<double>>
{
private double constant;
/// <summary>
/// Constructs a new Linear kernel.
/// </summary>
///
/// <param name="constant">A constant intercept term. Default is 0.</param>
///
public Linear(double constant)
{
this.constant = constant;
}
/// <summary>
/// Gets or sets the kernel's intercept term. Default is 0.
/// </summary>
///
public double Constant
{
get { return constant; }
set { constant = value; }
}
/// <summary>
/// Linear kernel function.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
///
/// <returns>Dot product in feature (kernel) space.</returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Function(double[] x, double[] y)
{
double sum = constant;
for (int i = 0; i < y.Length; i++)
sum += x[i] * y[i];
return sum;
}
/// <summary>
/// Linear kernel function.
/// </summary>
///
/// <param name="z">Distance <c>z</c> in input space.</param>
///
/// <returns>Dot product in feature (kernel) space.</returns>
///
public double Function(double z)
{
return z + constant;
}
/// <summary>
/// Computes the squared distance in input space
/// between two points given in feature space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
///
/// <returns>Squared distance between <c>x</c> and <c>y</c> in input space.</returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(double[] x, double[] y)
{
if (x == y)
return 0.0;
double sum = 0;
for (int i = 0; i < x.Length; i++)
{
double u = x[i] - y[i];
sum += u * u;
}
return sum;
}
/// <summary>
/// Computes the squared distance in input space
/// between two points given in feature space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
///
/// <returns>Squared distance between <c>x</c> and <c>y</c> in input space.</returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Distance(Sparse<double> x, Sparse<double> y)
{
if (x == y)
return 0.0;
return Accord.Math.Distance.SquareEuclidean(x, y);
}
/// <summary>
/// Computes the squared distance in input space
/// between two points given in feature space.
/// </summary>
///
/// <param name="x">Vector <c>x</c> in feature (kernel) space.</param>
/// <param name="y">Vector <c>y</c> in feature (kernel) space.</param>
///
/// <returns>
/// Squared distance between <c>x</c> and <c>y</c> in input space.
/// </returns>
///
public double ReverseDistance(double[] x, double[] y)
{
double sumx = constant;
double sumy = constant;
double sum = constant;
for (int i = 0; i < x.Length; i++)
{
sumx += x[i] * x[i];
sumy += y[i] * y[i];
sum += x[i] * y[i];
}
return sumx + sumy - 2.0 * sum;
}
/// <summary>
/// Elementwise addition of a and b, storing in result.
/// </summary>
///
/// <param name="a">The first vector to add.</param>
/// <param name="b">The second vector to add.</param>
/// <param name="result">An array to store the result.</param>
/// <returns>The same vector passed as result.</returns>
///
public void Add(double[] a, double[] b, double[] result)
{
a.Add(b, result: result);
}
/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
///
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
///
public object Clone()
{
return MemberwiseClone();
}
/// <summary>
/// Elementwise multiplication of scalar a and vector b, storing in result.
/// </summary>
///
/// <param name="a">The scalar to be multiplied.</param>
/// <param name="b">The vector to be multiplied.</param>
/// <param name="accumulate">An array to store the result.</param>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public void Product(double a, double[] b, double[] accumulate)
{
if (a == 0)
return;
for (int j = 0; j < b.Length; j++)
accumulate[j] += a * b[j];
}
/// <summary>
/// Compress a set of support vectors and weights into a single
/// parameter vector.
/// </summary>
///
/// <param name="weights">The weights associated with each support vector.</param>
/// <param name="supportVectors">The support vectors.</param>
/// <param name="c">The constant (bias) value.</param>
///
/// <returns>A single parameter vector.</returns>
///
public double[] Compress(double[] weights, double[][] supportVectors, out double c)
{
double[] result = Matrix.Dot(weights, supportVectors);
c = -constant;
return result;
}
/// <summary>
/// Projects an input point into feature space.
/// </summary>
///
/// <param name="input">The input point to be projected into feature space.</param>
///
/// <returns>
/// The feature space representation of the given <paramref name="input"/> point.
/// </returns>
///
public double[] Transform(double[] input)
{
return Transform(input, constant);
}
/// <summary>
/// Projects a set of input points into feature space.
/// </summary>
///
/// <param name="inputs">The input points to be projected into feature space.</param>
///
/// <returns>
/// The feature space representation of the given <paramref name="inputs"/> points.
/// </returns>
///
public double[][] Transform(double[][] inputs)
{
double[][] r = new double[inputs.Length][];
for (int i = 0; i < inputs.Length; i++)
r[i] = Transform(inputs[i]);
return r;
}
/// <summary>
/// Projects an input point into feature space.
/// </summary>
///
/// <param name="input">The input point to be projected into feature space.</param>
/// <param name="constant">The <see cref="Constant"/> parameter of the kernel.</param>
///
/// <returns>
/// The feature space representation of the given <paramref name="input"/> point.
/// </returns>
///
public static double[] Transform(double[] input, double constant)
{
if (constant == 0)
return input;
var feature = new double[input.Length + 3];
for (int i = 0; i < input.Length; i++)
feature[i] = input[i];
feature[input.Length] = constant;
return feature;
}
/// <summary>
/// The kernel function.
/// </summary>
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>
/// Dot product in feature (kernel) space.
/// </returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Function(Sparse<double> x, Sparse<double> y)
{
return x.Dot(y) + constant;
}
/// <summary>
/// The kernel function.
/// </summary>
/// <param name="x">Vector <c>x</c> in input space.</param>
/// <param name="y">Vector <c>y</c> in input space.</param>
/// <returns>
/// Dot product in feature (kernel) space.
/// </returns>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public double Function(double[] y, Sparse<double> x)
{
return x.Dot(y) + constant;
}
/// <summary>
/// Elementwise addition of a and b, storing in result.
/// </summary>
///
/// <param name="a">The first vector to add.</param>
/// <param name="b">The second vector to add.</param>
/// <param name="result">An array to store the result.</param>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public void Add(Sparse<double> a, double[] b, double[] result)
{
a.Add(b, result);
}
/// <summary>
/// Elementwise multiplication of scalar a and vector b, storing in result.
/// </summary>
/// <param name="a">The scalar to be multiplied.</param>
/// <param name="b">The vector to be multiplied.</param>
/// <param name="accumulate">An array to store the result.</param>
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public void Product(double a, Sparse<double> b, double[] accumulate)
{
if (a == 0)
return;
for (int j = 0; j < b.Indices.Length; j++)
accumulate[b.Indices[j]] += a * b.Values[j];
}
///// <summary>
///// Elementwise multiplication of scalar a and vector b, storing in result.
///// </summary>
///// <param name="a">The scalar to be multiplied.</param>
///// <param name="b">The vector to be multiplied.</param>
///// <param name="accumulate">An array to store the result.</param>
//public void Product(double a, Sparse<double> b, Sparse<double> accumulate)
//{
// if (a == 0)
// return;
// for (int j = 0; j < b.Indices.Length; j++)
// accumulate.Values[b.Indices[j]] += a * b.Values[j];
//}
/// <summary>
/// Compress a set of support vectors and weights into a single
/// parameter vector.
/// </summary>
/// <param name="weights">The weights associated with each support vector.</param>
/// <param name="supportVectors">The support vectors.</param>
/// <param name="c">The constant (bias) value.</param>
/// <returns>
/// A single parameter vector.
/// </returns>
public Sparse<double> Compress(double[] weights, Sparse<double>[] supportVectors, out double c)
{
return Accord.Math.Sparse.FromDense(Compress(weights, supportVectors.ToDense(), out c));
}
/// <summary>
/// Gets the number of parameters in the input vectors.
/// </summary>
///
public int GetLength(double[][] inputs)
{
return inputs.Columns(max: true);
}
/// <summary>
/// Gets the number of parameters in the input vectors.
/// </summary>
///
public int GetLength(Sparse<double>[] inputs)
{
return inputs.Columns();
}
/// <summary>
/// Creates an input vector from the given double values.
/// </summary>
///
public double[] CreateVector(double[] values)
{
return Accord.Math.Vector.Create(values);
}
/// <summary>
/// Creates an input vector with the given dimensions.
/// </summary>
///
public double[] CreateVector(int dimensions)
{
return new double[dimensions];
}
Sparse<double> ILinear<Sparse<double>>.CreateVector(double[] values)
{
return Accord.Math.Sparse.FromDense(values);
}
//Sparse<double> ILinear<Sparse<double>>.CreateVector(int dimensions)
//{
// return Accord.Math.Sparse.FromDense(new double[dimensions], removeZeros: false);
//}
/// <summary>
/// Elementwise multiplication of vector a and vector b, accumulating in result.
/// </summary>
///
/// <param name="a">The vector to be multiplied.</param>
/// <param name="b">The vector to be multiplied.</param>
/// <param name="accumulate">An array to store the result.</param>
///
#if NET45 || NET46 || NET462 || NETSTANDARD2_0
[MethodImpl(MethodImplOptions.AggressiveInlining)]
#endif
public void Product(double[] a, Sparse<double> b, double[] accumulate)
{
for (int j = 0; j < b.Indices.Length; j++)
accumulate[b.Indices[j]] += a[b.Indices[j]] * b.Values[j];
}
/// <summary>
/// Elementwise multiplication of vector a and vector b, accumulating in result.
/// </summary>
///
/// <param name="a">The vector to be multiplied.</param>
/// <param name="b">The vector to be multiplied.</param>
/// <param name="accumulate">An array to store the result.</param>
///
public void Product(double[] a, double[] b, double[] accumulate)
{
for (int i = 0; i < a.Length; i++)
accumulate[i] += a[i] * b[i];
}
/// <summary>
/// Converts the input vectors to a double-precision representation.
/// </summary>
///
public double[][] ToDouble(double[][] input)
{
return input;
}
/// <summary>
/// Converts the input vectors to a double-precision representation.
/// </summary>
///
public double[][] ToDouble(Sparse<double>[] input)
{
return Accord.Math.Sparse.ToDense(input);
}
}
}