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README for DBP-progs v2 ======================= Pauli Miettinen 16.5.2007 Introduction ------------ DBP-progs is a collection of software that can be used to solve the Discrete Basis Problem (DBP) and its variations. Broadly speaking, given a binary matrix, the goal of the Discrete Basis Problem is to represent it as a Boolean product of two smaller binary matrices. A Boolean product of two binary matrices is defined as is the standard matrix product, but with 1 + 1 = 1. This is version 2 of the package. It includes new applications and Matlab files to execute C programs within Matlab. The algorithms are described in [1, 3], and partly also in [2]. These are the algorithms that were used in [3]. There is a deprecated package (DBP-progs v1) that contains the exact algorithm used in [1] and [2], as there is a small difference between these two versions. The package contains one algorithm for DBP, several variations of it (explained in [3]), an algorithm for the Discrete Basis Partitioning Problem (DBPP) (defined in [1] and [3]), and some utility programs to generate data and ease the use of the algorithms. All programs are to be used at one's own peril. Changes to previous versions ---------------------------- There is a small change in the program `asso-solver': selecting the best basis vector among candidates did not fully agree with the explanations in [1, 2]. As the experiments in [1] and [2] were conducted using this version, the old package (named as DBP-progs-v1) is still available. Other major differences include programs `iter-postproc' and `iter-solver', and all m-files. The code for the other programs is cleaned, too, and the error reporting is upgraded. Contents of the package ----------------------- This package contains the following programs: o asso-solver - Implements the algorithm `DBP' from [3], or equivalently, the algorithm `Association' from [1] and [2]. Solves DBP. o k-medians-solver - Implements the algorithm `LocalSearch' described [1]. Solves DBPP. o create-decomp - Implements an exponential-time algorithm to create an optimal decomposition when both data and basis matrices are known. Described in [3]. o iter-postproc - Implements an iterative local search heuristic to improve the decomposition when dataset, basis vectors, and an initial usage matrix is given. Described in [3]. o iter-solver - Combines asso-solver and iter-postproc into a single program. Faster than running asso-solver and iter-postproc as separate programs. Same as `DBP+iter' in [3]. o comparer - Computes the quality of the decomposition with respect to the loss function described in [1-3]. o mod-matrix - Allows the user to modify the matrix representation between sparse and dense, and to transpose a matrix. o cdbp.m - A Matlab program that serves as an interface between Matlab and asso-solver. o cdbpiter.m - A Matlab program that serves as an interface between Matlab and iter-solver. o cdbpcluster.m - A Matlab program that solves DBP using clusters. Implements algorithm `DBP+clust' from [3]. o optmatch.m - A Matlab program that serves as an interface between Matlab and create-decomp. In addition, the package also contains two sample input files, one in dense and other in sparse format. Requirements ------------ This package is made for GNU Linux, and it should work in all platforms having GNU LibC (glibc, tested with version 2.5), GNU C compiler (gcc, tested with version 4.1.1), and GNU make (tested with version 3.80). The package is also reported to work with Solaris (details unknown), but it will need `libiberty.so' to provide `getopt_long()' (see below). To unpack this package, one also needs tar and gzip. Using the m-files naturally requires Matlab (tested with version 7.3.0.298, but should work with older versions, too). Also, program `cdbpcluster.m' uses k-means clustering from SOM Toolbox (version 2, available from <http://www.cis.hut.fi/projects/somtoolbox/>). All programs should compile also in 64-bit environment, but only `asso-solver' is tested to work. Usage in non-GNU environments ----------------------------- In general, the applications should be portable with small changes to all platforms supporting ANSI C. If you do not have gcc or GNU make, you probably have to edit the Makefiles (there is one in each subdirectory, also). If you do not have GNU libc, you have to edit the main Makefile: remove text `-D_GNU_SOURCE' from CFLAGS. As a result, the utility functions from `util.c.' do not write program name before the error functions, but otherwise everything should work fine. The function `getopt_long()' from glibc is rarely available in other platforms. However, all important command-line options have short alternatives, so you should be able to replace `getopt_long()' by `getopt()' without much of troubles (in some cases you need to remove optional arguments, though). Finally, all programs that need randomness use `/dev/urandom' as a default source of random bits. If your platform does not support this, you can manually define the random seed (`-d' command-line option) to make the programs use standard `rand()' pseudo-RNG. Installation ------------ To install this package, you must at first unpack it. Command tar xvfz DBP-progs.tar.gz creates a new directory, `DBP-progs', and unpacks package's contents there. To compile the programs, issue `cd DBP-progs && make'. Binaries are located under their respective subdirectories (both `iter-solver' and `iter-postproc' are in `iter-solver/'). If you use some other C compiler than gcc, or you want to change compiler flags, you can change appropriate rows at main Makefile, located under `DBP-progs/'. Input data formats ------------------ All programs accept input in two different formats, namely dense and sparse format. For testing purposes, and for human eyes, dense format is more convenient, while for real usage, sparse format probably saves a considerable amount of disk space. Example inputs in both formats are located under `samples' subdirectory. In what follows, spaces and newlines can be replaced by any number of blank characters as defined in C standard library (blank characters are space, tab, newline, vertical tab, form feed, and carriage return). Rules for the formats are simple: All files are in ASCII format. In both formats, first two lines contain one integer denoting the number of rows and columns in the matrix, respectively. In dense format, the elements of the matrix are then given in row-major format (that is, at first uppermost row, then second row from up etc.). Elements are either 0 or 1 and are separated from each other by a space. In sparse format, only the 1s in the matrix are listed. At first, in each row there is an integer expressing the number of 1s in that row. Directly after that (separated by space, of course) there are the indices of columns in which matrix has 1s. First column is column number 1. Sample files of both formats are included under `samples/' directory. The m-files assume standard Matlab matrices. They write dense matrices in the disk, even if the input matrix is of sparse type. Limitations ----------- Program `asso-solver' should not have any limitations except those set by the platform (e.g., the amount of free memory). Programs `iter-solver' and `iter-postproc' can only handle cases where the basis size is at most the number of bits in C's `long int' type (that is, 32 with 32-bit machines and (usually) 64 with 64-bit machines). This is an implementation detail, and should you need larger bases, it should not require too much work to change the necessary parts of the code. However, that will probably yield to a slower program. Program `create-decomp' takes exponential time with respect to the basis size, being in practice feasible only with moderate basis sizes (less than 20 or so). Usage ----- A complete list of program's command line arguments is printed when program is executed with `--help' command-line argument. This applies to all programs in this package. A sample session might go as follows (outputs omitted). ~$ cd DBP-progs ~/DBP-progs$ asso-solver/asso-solver -ssamples/dense-matrix.txt \ -basso-basis.txt \ -Dasso-decomp.txt -t0.9 -k4 ~/DBP-progs$ mod-matrix/mod-matrix -iasso-decomp.txt -oasso-decomp-t.txt -t ~/DBP-progs$ k-medians-solver/k-medians-solver -ssamples/dense-matrix.txt \ -bmed-basis.txt \ -omed-decomp.txt -k4 ~/DBP-progs$ iter-solver/iter-postproc -ssamples/dense-matrix.txt \ -basso-basis.txt\ -Oasso-decomp-t.txt \ -Diter-asso-decomp.txt ~/DBP-progs$ create-decomp/create-decomp -ssamples/dense-matrix.txt \ -basso-basis.txt \ -Dopti-asso-decomp.txt ~/DBP-progs$ comparer/comparer -ssamples/dense-matrix.txt \ -basso-basis.txt \ -Dasso-decomp-t.txt ~/DBP-progs$ comparer/comparer -ssamples/dense-matrix.txt \ -basso-basis.txt \ -Diter-asso-decomp.txt ~/DBP-progs$ comparer/comparer -ssamples/dense-matrix.txt \ -basso-basis.txt \ -Dopti-asso-decomp.txt ~/DBP-progs$ comparer/comparer -ssamples/dense-matrix.txt \ -bmed-basis.txt \ -Dmed-decomp.txt Program `mod-matrix' has to be used since `asso-solver' returns the decomposition matrix as a transpose. You can also use `mod-matrix' to reformat a matrix from dense to sparse format, or vice versa. Both basis and decomposition matrix are printed in dense format. References ---------- [1] Pauli Miettinen: The Discrete Basis Problem. Report C-2006-010, Department of Computer Science, University of Helsinki 2006 (M.Sc. Thesis). [2] Pauli Miettinen, Taneli Mielikäinen, Aristides Gionis, Gautam Das, and Heikki Mannila: The Discrete Basis Problem. In J. Fürnkranz, T. Scheffer, and M. Spiliopoulou (eds.), Knowledge discovery in databases: PKDD 2006 -- 10th European conference on principles and practice of knowledge discovery in databases, Berlin, Germany, September 2006, Lecture Notes in Artificial Intelligence, 4213, Springer 2006, pages 335-346. [3] Pauli Miettinen, Taneli Mielikäinen, Aristides Gionis, Gautam Das, and Heikki Mannila: The Discrete Basis Problem. Submitted to IEEE Transactions on Knowledge and Data Engineering (extended version of [2]).