Beispiel #1
0
//[[Rcpp::export]]
Rcpp::List nnmf(const mat & A, const unsigned int k, mat W, mat H, umat Wm, umat Hm,
	const vec & alpha, const vec & beta, const unsigned int max_iter, const double rel_tol, 
	const int n_threads, const int verbose, const bool show_warning, const unsigned int inner_max_iter, 
	const double inner_rel_tol, const int method, unsigned int trace)
{
	/******************************************************************************************************
	 *              Non-negative Matrix Factorization(NNMF) using alternating scheme
	 *              ----------------------------------------------------------------
	 * Description:
	 * 	Decompose matrix A such that
	 * 		A = W H
	 * Arguments:
	 * 	A              : Matrix to be decomposed
	 * 	W, H           : Initial matrices of W and H, where ncol(W) = nrow(H) = k. # of rows/columns of W/H could be 0
	 * 	Wm, Hm         : Masks of W and H, s.t. masked entries are no-updated and fixed to initial values
	 * 	alpha          : [L2, angle, L1] regularization on W (non-masked entries)
	 * 	beta           : [L2, angle, L1] regularization on H (non-masked entries)
	 * 	max_iter       : Maximum number of iteration
	 * 	rel_tol        : Relative tolerance between two successive iterations, = |e2-e1|/avg(e1, e2)
	 * 	n_threads      : Number of threads (openMP)
	 * 	verbose        : Either 0 = no any tracking, 1 == progression bar, 2 == print iteration info
	 * 	show_warning   : If to show warning if targeted `tol` is not reached
	 * 	inner_max_iter : Maximum number of iterations passed to each inner W or H matrix updating loop
	 * 	inner_rel_tol  : Relative tolerance passed to inner W or H matrix updating loop, = |e2-e1|/avg(e1, e2)
	 * 	method         : Integer of 1, 2, 3 or 4, which encodes methods
	 * 	               : 1 = sequential coordinate-wise minimization using square loss
	 * 	               : 2 = Lee's multiplicative update with square loss, which is re-scaled gradient descent
	 * 	               : 3 = sequentially quadratic approximated minimization with KL-divergence
	 * 	               : 4 = Lee's multiplicative update with KL-divergence, which is re-scaled gradient descent
	 * 	trace          : A positive integer, error will be checked very 'trace' iterations. Computing WH can be very expansive,
	 * 	               : so one may not want to check error A-WH every single iteration
	 * Return:
	 * 	A list (Rcpp::List) of 
	 * 		W, H          : resulting W and H matrices
	 * 		mse_error     : a vector of mean square error (divided by number of non-missings)
	 * 		mkl_error     : a vector (length = number of iterations) of mean KL-distance
	 * 		target_error  : a vector of loss (0.5*mse or mkl), plus constraints
	 * 		average_epoch : a vector of average epochs (one complete swap over W and H)
	 * Author:
	 * 	Eric Xihui Lin <*****@*****.**>
	 * Version:
	 * 	2015-12-11
	 ******************************************************************************************************/

	unsigned int n = A.n_rows;
	unsigned int m = A.n_cols;
	//int k = H.n_rows; // decomposition rank k
	unsigned int N_non_missing = n*m;

	if (trace < 1) trace = 1;
	unsigned int err_len = (unsigned int)std::ceil(double(max_iter)/double(trace)) + 1;
	vec mse_err(err_len), mkl_err(err_len), terr(err_len), ave_epoch(err_len);

	// check progression
	bool show_progress = false;
	if (verbose == 1) show_progress = true;
	Progress prgrss(max_iter, show_progress);

	double rel_err = rel_tol + 1;
	double terr_last = 1e99;
	uvec non_missing;
	bool any_missing = !A.is_finite();
	if (any_missing) 
	{
		non_missing = find_finite(A);
		N_non_missing = non_missing.n_elem;
		mkl_err.fill(mean((A.elem(non_missing)+TINY_NUM) % log(A.elem(non_missing)+TINY_NUM) - A.elem(non_missing)));
	}
	else
		mkl_err.fill(mean(mean((A+TINY_NUM) % log(A+TINY_NUM) - A))); // fixed part in KL-dist, mean(A log(A) - A)

	if (Wm.empty())
		Wm.resize(0, n);
	else
		inplace_trans(Wm);
	if (Hm.empty())
		Hm.resize(0, m);

	if (W.empty())
	{
		W.randu(k, n);
		W *= 0.01;
		if (!Wm.empty())
			W.elem(find(Wm > 0)).fill(0.0);
	}
	else
		inplace_trans(W);

	if (H.empty())
	{
		H.randu(k, m);
		H *= 0.01;
		if (!Hm.empty())
			H.elem(find(Hm > 0)).fill(0.0);
	}

	if (verbose == 2)
	{
		Rprintf("\n%10s | %10s | %10s | %10s | %10s\n", "Iteration", "MSE", "MKL", "Target", "Rel. Err.");
		Rprintf("--------------------------------------------------------------\n");
	}

	int total_raw_iter = 0;
	unsigned int i = 0;
	unsigned int i_e = 0; // index for error checking
	for(; i < max_iter && std::abs(rel_err) > rel_tol; i++) 
	{
		Rcpp::checkUserInterrupt();
		prgrss.increment();

		if (any_missing)
		{
			// update W
			total_raw_iter += update_with_missing(W, H, A.t(), Wm, alpha, inner_max_iter, inner_rel_tol, n_threads, method);
			// update H
			total_raw_iter += update_with_missing(H, W, A, Hm, beta, inner_max_iter, inner_rel_tol, n_threads, method);

			if (i % trace == 0)
			{
				const mat & Ahat = W.t()*H;
				mse_err(i_e) = mean(square((A - Ahat).eval().elem(non_missing)));
				mkl_err(i_e) += mean((-(A+TINY_NUM) % log(Ahat+TINY_NUM) + Ahat).eval().elem(non_missing));
			}
		}
		else
		{
			// update W
			total_raw_iter += update(W, H, A.t(), Wm, alpha, inner_max_iter, inner_rel_tol, n_threads, method);
			// update H
			total_raw_iter += update(H, W, A, Hm, beta, inner_max_iter, inner_rel_tol, n_threads, method);

			if (i % trace == 0)
			{
				const mat & Ahat = W.t()*H;
				mse_err(i_e) = mean(mean(square((A - Ahat))));
				mkl_err(i_e) += mean(mean(-(A+TINY_NUM) % log(Ahat+TINY_NUM) + Ahat));
			}
		}

		if (i % trace == 0)
		{
			ave_epoch(i_e) = double(total_raw_iter)/(n+m);
			if (method < 3) // mse based
				terr(i_e) = 0.5*mse_err(i_e);
			else // KL based
				terr(i_e) = mkl_err(i_e);

			add_penalty(i_e, terr, W, H, N_non_missing, alpha, beta);

			rel_err = 2*(terr_last - terr(i_e)) / (terr_last + terr(i_e) + TINY_NUM );
			terr_last = terr(i_e);
			if (verbose == 2)
				Rprintf("%10d | %10.4f | %10.4f | %10.4f | %10.g\n", i+1, mse_err(i_e), mkl_err(i_e), terr(i_e), rel_err);

			total_raw_iter = 0; // reset to 0
			++i_e;
		}
	}

	// compute error of the last iteration
	if ((i-1) % trace != 0)
	{
		if (any_missing)
		{
			const mat & Ahat = W.t()*H;
			mse_err(i_e) = mean(square((A - Ahat).eval().elem(non_missing)));
			mkl_err(i_e) += mean((-(A+TINY_NUM) % log(Ahat+TINY_NUM) + Ahat).eval().elem(non_missing));
		}
		else
		{
			const mat & Ahat = W.t()*H;
			mse_err(i_e) = mean(mean(square((A - Ahat))));
			mkl_err(i_e) += mean(mean(-(A+TINY_NUM) % log(Ahat+TINY_NUM) + Ahat));
		}

		ave_epoch(i_e) = double(total_raw_iter)/(n+m);
		if (method < 3) // mse based
			terr(i_e) = 0.5*mse_err(i_e);
		else // KL based
			terr(i_e) = mkl_err(i_e);
		add_penalty(i_e, terr, W, H, N_non_missing, alpha, beta);

		rel_err = 2*(terr_last - terr(i_e)) / (terr_last + terr(i_e) + TINY_NUM );
		terr_last = terr(i_e);
		if (verbose == 2)
			Rprintf("%10d | %10.4f | %10.4f | %10.4f | %10.g\n", i+1, mse_err(i_e), mkl_err(i_e), terr(i_e), rel_err);

		++i_e;
	}

	if (verbose == 2)
	{
		Rprintf("--------------------------------------------------------------\n");
		Rprintf("%10s | %10s | %10s | %10s | %10s\n\n", "Iteration", "MSE", "MKL", "Target", "Rel. Err.");
	}

	if (i_e < err_len)
	{
		mse_err.resize(i_e);
		mkl_err.resize(i_e);
		terr.resize(i_e);
		ave_epoch.resize(i_e);
	}

	if (show_warning && rel_err > rel_tol)
		Rcpp::warning("Target tolerance not reached. Try a larger max.iter.");

	return Rcpp::List::create(
		Rcpp::Named("W") = W.t(),
		Rcpp::Named("H") = H,
		Rcpp::Named("mse_error") = mse_err,
		Rcpp::Named("mkl_error") = mkl_err,
		Rcpp::Named("target_error") = terr,
		Rcpp::Named("average_epoch") = ave_epoch,
		Rcpp::Named("n_iteration") = i
		);
}
Beispiel #2
0
//[[Rcpp::export]]
Rcpp::List nmf_brunet(const mat & A, int k, int max_iter , double rel_tol, int n_threads, bool show_progress, bool show_warning)
{
	/* 
	 * Description: 
	 * 	An implment of Brunet's multiplicative updates based on KL divergence for non-negative matrix factorization.
	 * Arguments:
	 * 	V: a matrix to be decomposed, such that V ~ W*H
	 * 	k: rank
	 * Return:
	 * 	A list of W, H, error, steps (= iteration until convergent or max_iter reached)
	 * Complexity:
	 * 	O(max_iter x k x V.n_row x V.n_col)
	 * Author:
	 * 	Eric Xihui Lin <*****@*****.**>
	 * Version:
	 * 	2015-10-31
	 */


	mat W = randu(A.n_rows, k), H = randu(k, A.n_cols);
	mat Abar = W*H; // current W*H
	rowvec w, ha; // W/h  = col/row sum of W/H
	colvec h, wa; // ha/wa = previous H.row/W.col for fast update of Abar
	vec err(max_iter), trgt_err(max_iter);
	trgt_err.fill(-1);

	// check progression
	Progress prgrss(max_iter, show_progress);

	int i = 0;
	for(; i < max_iter; i++) 
	{
		Rcpp::checkUserInterrupt();

		prgrss.increment();

		w = sum(W);
		h = sum(H, 1);
		for (int a = 0; a < k; a++)
		{
			wa = W.col(a);
			W.col(a) %= (A / Abar) * H.row(a).t() / h.at(a);
			Abar += (W.col(a) - wa) * H.row(a);

			ha = H.row(a);
			H.row(a) %= W.col(a).t() * (A / Abar) / w.at(a);
			Abar += W.col(a) * (H.row(a) - ha);
		}
		err.at(i) =  std::sqrt(mean(mean(square(A - Abar))));
		trgt_err.at(i) = accu(A % (arma::trunc_log(A) - arma::trunc_log(Abar)) - A - Abar);
		if (i > 0 && std::abs(trgt_err.at(i) - trgt_err.at(i-1))/(std::abs(trgt_err.at(i-1)) + 1e-6) < rel_tol)
			break;
	}

	if (show_warning && max_iter <= i)
		Rcpp::warning("Target tolerance not reached. Try a larger max.iter.");

	err.resize(i < max_iter ? i+1 : max_iter);
	trgt_err.resize(err.n_elem);

	return Rcpp::List::create(
		Rcpp::Named("W") = W,
		Rcpp::Named("H") = H,
		Rcpp::Named("error") = err,
		Rcpp::Named("target_error") = trgt_err
		);
}