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Diffstat (limited to 'ml/dlib/dlib/statistics/cca_abstract.h')
| -rw-r--r-- | ml/dlib/dlib/statistics/cca_abstract.h | 191 |
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diff --git a/ml/dlib/dlib/statistics/cca_abstract.h b/ml/dlib/dlib/statistics/cca_abstract.h deleted file mode 100644 index 8e0b4e742..000000000 --- a/ml/dlib/dlib/statistics/cca_abstract.h +++ /dev/null @@ -1,191 +0,0 @@ -// Copyright (C) 2013 Davis E. King (davis@dlib.net) -// License: Boost Software License See LICENSE.txt for the full license. -#undef DLIB_CCA_AbSTRACT_Hh_ -#ifdef DLIB_CCA_AbSTRACT_Hh_ - -#include "../matrix/matrix_la_abstract.h" -#include "random_subset_selector_abstract.h" - -namespace dlib -{ - -// ---------------------------------------------------------------------------------------- - - template < - typename T - > - matrix<typename T::type,0,1> compute_correlations ( - const matrix_exp<T>& L, - const matrix_exp<T>& R - ); - /*! - requires - - L.size() > 0 - - R.size() > 0 - - L.nr() == R.nr() - ensures - - This function treats L and R as sequences of paired row vectors. It - then computes the correlation values between the elements of these - row vectors. In particular, we return a vector COR such that: - - COR.size() == L.nc() - - for all valid i: - - COR(i) == the correlation coefficient between the following sequence - of paired numbers: (L(k,i), R(k,i)) for k: 0 <= k < L.nr(). - Therefore, COR(i) is a value between -1 and 1 inclusive where 1 - indicates perfect correlation and -1 perfect anti-correlation. Note - that this function assumes the input data vectors have been centered - (i.e. made to have zero mean). If this is not the case then it will - report inaccurate results. - !*/ - -// ---------------------------------------------------------------------------------------- - - template < - typename T - > - matrix<T,0,1> cca ( - const matrix<T>& L, - const matrix<T>& R, - matrix<T>& Ltrans, - matrix<T>& Rtrans, - unsigned long num_correlations, - unsigned long extra_rank = 5, - unsigned long q = 2, - double regularization = 0 - ); - /*! - requires - - num_correlations > 0 - - L.size() > 0 - - R.size() > 0 - - L.nr() == R.nr() - - regularization >= 0 - ensures - - This function performs a canonical correlation analysis between the row - vectors in L and R. That is, it finds two transformation matrices, Ltrans - and Rtrans, such that row vectors in the transformed matrices L*Ltrans and - R*Rtrans are as correlated as possible. That is, we try to find two transforms - such that the correlation values returned by compute_correlations(L*Ltrans, R*Rtrans) - would be maximized. - - Let N == min(num_correlations, min(R.nr(),min(L.nc(),R.nc()))) - (This is the actual number of elements in the transformed vectors. - Therefore, note that you can't get more outputs than there are rows or - columns in the input matrices.) - - #Ltrans.nr() == L.nc() - - #Ltrans.nc() == N - - #Rtrans.nr() == R.nc() - - #Rtrans.nc() == N - - This function assumes the data vectors in L and R have already been centered - (i.e. we assume the vectors have zero means). However, in many cases it is - fine to use uncentered data with cca(). But if it is important for your - problem then you should center your data before passing it to cca(). - - This function works with reduced rank approximations of the L and R matrices. - This makes it fast when working with large matrices. In particular, we use - the svd_fast() routine to find reduced rank representations of the input - matrices by calling it as follows: svd_fast(L, U,D,V, num_correlations+extra_rank, q) - and similarly for R. This means that you can use the extra_rank and q - arguments to cca() to influence the accuracy of the reduced rank - approximation. However, the default values should work fine for most - problems. - - returns an estimate of compute_correlations(L*#Ltrans, R*#Rtrans). The - returned vector should exactly match the output of compute_correlations() - when the reduced rank approximation to L and R is accurate and regularization - is set to 0. However, if this is not the case then the return value of this - function will deviate from compute_correlations(L*#Ltrans, R*#Rtrans). This - deviation can be used to check if the reduced rank approximation is working - or you need to increase extra_rank. - - The dimensions of the output vectors produced by L*#Ltrans or R*#Rtrans are - ordered such that the dimensions with the highest correlations come first. - That is, after applying the transforms produced by cca() to a set of vectors - you will find that dimension 0 has the highest correlation, then dimension 1 - has the next highest, and so on. This also means that the list of numbers - returned from cca() will always be listed in decreasing order. - - This function performs the ridge regression version of Canonical Correlation - Analysis when regularization is set to a value > 0. In particular, larger - values indicate the solution should be more heavily regularized. This can be - useful when the dimensionality of the data is larger than the number of - samples. - - A good discussion of CCA can be found in the paper "Canonical Correlation - Analysis" by David Weenink. In particular, this function is implemented - using equations 29 and 30 from his paper. We also use the idea of doing CCA - on a reduced rank approximation of L and R as suggested by Paramveer S. - Dhillon in his paper "Two Step CCA: A new spectral method for estimating - vector models of words". - !*/ - -// ---------------------------------------------------------------------------------------- - - template < - typename sparse_vector_type, - typename T - > - matrix<T,0,1> cca ( - const std::vector<sparse_vector_type>& L, - const std::vector<sparse_vector_type>& R, - matrix<T>& Ltrans, - matrix<T>& Rtrans, - unsigned long num_correlations, - unsigned long extra_rank = 5, - unsigned long q = 2, - double regularization = 0 - ); - /*! - requires - - num_correlations > 0 - - L.size() == R.size() - - max_index_plus_one(L) > 0 && max_index_plus_one(R) > 0 - (i.e. L and R can't represent empty matrices) - - L and R must contain sparse vectors (see the top of dlib/svm/sparse_vector_abstract.h - for a definition of sparse vector) - - regularization >= 0 - ensures - - This is just an overload of the cca() function defined above. Except in this - case we take a sparse representation of the input L and R matrices rather than - dense matrices. Therefore, in this case, we interpret L and R as matrices - with L.size() rows, where each row is defined by a sparse vector. So this - function does exactly the same thing as the above cca(). - - Note that you can apply the output transforms to a sparse vector with the - following code: - sparse_matrix_vector_multiply(trans(Ltrans), your_sparse_vector) - !*/ - -// ---------------------------------------------------------------------------------------- - - template < - typename sparse_vector_type, - typename Rand_type, - typename T - > - matrix<T,0,1> cca ( - const random_subset_selector<sparse_vector_type,Rand_type>& L, - const random_subset_selector<sparse_vector_type,Rand_type>& R, - matrix<T>& Ltrans, - matrix<T>& Rtrans, - unsigned long num_correlations, - unsigned long extra_rank = 5, - unsigned long q = 2, - double regularization = 0 - ); - /*! - requires - - num_correlations > 0 - - L.size() == R.size() - - max_index_plus_one(L) > 0 && max_index_plus_one(R) > 0 - (i.e. L and R can't represent empty matrices) - - L and R must contain sparse vectors (see the top of dlib/svm/sparse_vector_abstract.h - for a definition of sparse vector) - - regularization >= 0 - ensures - - returns cca(L.to_std_vector(), R.to_std_vector(), Ltrans, Rtrans, num_correlations, extra_rank, q) - (i.e. this is just a convenience function for calling the cca() routine when - your sparse vectors are contained inside a random_subset_selector rather than - a std::vector) - !*/ - -// ---------------------------------------------------------------------------------------- - -} - -#endif // DLIB_CCA_AbSTRACT_Hh_ - - |