#!/usr/bin/env python # -*- coding: utf-8 -*- # # Copyright (C) 2010 Radim Rehurek # Licensed under the GNU LGPL v2.1 - http://www.gnu.org/licenses/lgpl.html """Module for `Latent Semantic Analysis (aka Latent Semantic Indexing) `_. Implements fast truncated SVD (Singular Value Decomposition). The SVD decomposition can be updated with new observations at any time, for an online, incremental, memory-efficient training. This module actually contains several algorithms for decomposition of large corpora, a combination of which effectively and transparently allows building LSI models for: * corpora much larger than RAM: only constant memory is needed, independent of the corpus size * corpora that are streamed: documents are only accessed sequentially, no random access * corpora that cannot be even temporarily stored: each document can only be seen once and must be processed immediately (one-pass algorithm) * distributed computing for very large corpora, making use of a cluster of machines Wall-clock `performance on the English Wikipedia `_ (2G corpus positions, 3.2M documents, 100K features, 0.5G non-zero entries in the final TF-IDF matrix), requesting the top 400 LSI factors: ====================================================== ============ ================== algorithm serial distributed ====================================================== ============ ================== one-pass merge algorithm 5h14m 1h41m multi-pass stochastic algo (with 2 power iterations) 5h39m N/A [1]_ ====================================================== ============ ================== *serial* = Core 2 Duo MacBook Pro 2.53Ghz, 4GB RAM, libVec *distributed* = cluster of four logical nodes on three physical machines, each with dual core Xeon 2.0GHz, 4GB RAM, ATLAS Examples -------- >>> from gensim.test.utils import common_dictionary, common_corpus >>> from gensim.models import LsiModel >>> >>> model = LsiModel(common_corpus, id2word=common_dictionary) >>> vectorized_corpus = model[common_corpus] # vectorize input copus in BoW format .. [1] The stochastic algo could be distributed too, but most time is already spent reading/decompressing the input from disk in its 4 passes. The extra network traffic due to data distribution across cluster nodes would likely make it *slower*. """ import logging import sys import numpy as np import scipy.linalg import scipy.sparse from scipy.sparse import sparsetools from six import iterkeys from six.moves import xrange from gensim import interfaces, matutils, utils from gensim.models import basemodel logger = logging.getLogger(__name__) # accuracy defaults for the multi-pass stochastic algo P2_EXTRA_DIMS = 100 # set to `None` for dynamic P2_EXTRA_DIMS=k P2_EXTRA_ITERS = 2 def clip_spectrum(s, k, discard=0.001): """Find how many factors should be kept to avoid storing spurious (tiny, numerically unstable) values. Parameters ---------- s : list of float Eigenvalues of the original matrix. k : int Maximum desired rank (number of factors) discard: float Percentage of the spectrum's energy to be discarded. Returns ------- int Rank (number of factors) of the reduced matrix. """ # compute relative contribution of eigenvalues towards the energy spectrum rel_spectrum = np.abs(1.0 - np.cumsum(s / np.sum(s))) # ignore the last `discard` mass (or 1/k, whichever is smaller) of the spectrum small = 1 + len(np.where(rel_spectrum > min(discard, 1.0 / k))[0]) k = min(k, small) # clip against k logger.info("keeping %i factors (discarding %.3f%% of energy spectrum)", k, 100 * rel_spectrum[k - 1]) return k def asfarray(a, name=''): """Get an array laid out in Fortran order in memory. Parameters ---------- a : numpy.ndarray Input array. name : str, optional Array name, used only for logging purposes. Returns ------- np.ndarray The input `a` in Fortran, or column-major order. """ if not a.flags.f_contiguous: logger.debug("converting %s array %s to FORTRAN order", a.shape, name) a = np.asfortranarray(a) return a def ascarray(a, name=''): """Return a contiguous array in memory (C order). Parameters ---------- a : numpy.ndarray Input array. name : str, optional Array name, used for logging purposes. Returns ------- np.ndarray Contiguous array (row-major order) of same shape and content as `a`. """ if not a.flags.contiguous: logger.debug("converting %s array %s to C order", a.shape, name) a = np.ascontiguousarray(a) return a class Projection(utils.SaveLoad): """Low dimensional projection of a term-document matrix. This is the class taking care of the 'core math': interfacing with corpora, splitting large corpora into chunks and merging them etc. This done through the higher-level :class:`~gensim.models.lsimodel.LsiModel` class. Notes ----- The projection can be later updated by merging it with another :class:`~gensim.models.lsimodel.Projection` via :meth:`~gensim.models.lsimodel.Projection.merge`. This is how incremental training actually happens. """ def __init__(self, m, k, docs=None, use_svdlibc=False, power_iters=P2_EXTRA_ITERS, extra_dims=P2_EXTRA_DIMS, dtype=np.float64): """Construct the (U, S) projection from a corpus. Parameters ---------- m : int Number of features (terms) in the corpus. k : int Desired rank of the decomposed matrix. docs : {iterable of list of (int, float), scipy.sparse.csc} Corpus in BoW format or as sparse matrix. use_svdlibc : bool, optional If True - will use `sparsesvd library `_, otherwise - our own version will be used. power_iters: int, optional Number of power iteration steps to be used. Tune to improve accuracy. extra_dims : int, optional Extra samples to be used besides the rank `k`. Tune to improve accuracy. dtype : numpy.dtype, optional Enforces a type for elements of the decomposed matrix. """ self.m, self.k = m, k self.power_iters = power_iters self.extra_dims = extra_dims if docs is not None: # base case decomposition: given a job `docs`, compute its decomposition, # *in-core*. if not use_svdlibc: u, s = stochastic_svd( docs, k, chunksize=sys.maxsize, num_terms=m, power_iters=self.power_iters, extra_dims=self.extra_dims, dtype=dtype) else: try: import sparsesvd except ImportError: raise ImportError("`sparsesvd` module requested but not found; run `easy_install sparsesvd`") logger.info("computing sparse SVD of %s matrix", str(docs.shape)) if not scipy.sparse.issparse(docs): docs = matutils.corpus2csc(docs) # ask for extra factors, because for some reason SVDLIBC sometimes returns fewer factors than requested ut, s, vt = sparsesvd.sparsesvd(docs, k + 30) u = ut.T del ut, vt k = clip_spectrum(s ** 2, self.k) self.u = u[:, :k].copy() self.s = s[:k].copy() else: self.u, self.s = None, None def empty_like(self): """Get an empty Projection with the same parameters as the current object. Returns ------- :class:`~gensim.models.lsimodel.Projection` An empty copy (without corpus) of the current projection. """ return Projection(self.m, self.k, power_iters=self.power_iters, extra_dims=self.extra_dims) def merge(self, other, decay=1.0): """Merge current :class:`~gensim.models.lsimodel.Projection` instance with another. Warnings -------- The content of `other` is destroyed in the process, so pass this function a copy of `other` if you need it further. The `other` :class:`~gensim.models.lsimodel.Projection` is expected to contain the same number of features. Parameters ---------- other : :class:`~gensim.models.lsimodel.Projection` The Projection object to be merged into the current one. It will be destroyed after merging. decay : float, optional Weight of existing observations relatively to new ones. Setting `decay` < 1.0 causes re-orientation towards new data trends in the input document stream, by giving less emphasis to old observations. This allows LSA to gradually "forget" old observations (documents) and give more preference to new ones. """ if other.u is None: # the other projection is empty => do nothing return if self.u is None: # we are empty => result of merge is the other projection, whatever it is self.u = other.u.copy() self.s = other.s.copy() return if self.m != other.m: raise ValueError( "vector space mismatch: update is using %s features, expected %s" % (other.m, self.m) ) logger.info("merging projections: %s + %s", str(self.u.shape), str(other.u.shape)) m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1] # TODO Maybe keep the bases as elementary reflectors, without # forming explicit matrices with ORGQR. # The only operation we ever need is basis^T*basis ond basis*component. # But how to do that in scipy? And is it fast(er)? # find component of u2 orthogonal to u1 logger.debug("constructing orthogonal component") self.u = asfarray(self.u, 'self.u') c = np.dot(self.u.T, other.u) self.u = ascarray(self.u, 'self.u') other.u -= np.dot(self.u, c) other.u = [other.u] # do some reference magic and call qr_destroy, to save RAM q, r = matutils.qr_destroy(other.u) # q, r = QR(component) assert not other.u # find the rotation that diagonalizes r k = np.bmat([ [np.diag(decay * self.s), np.multiply(c, other.s)], [matutils.pad(np.array([]).reshape(0, 0), min(m, n2), n1), np.multiply(r, other.s)] ]) logger.debug("computing SVD of %s dense matrix", k.shape) try: # in np < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'. # for these early versions of np, catch the error and try to compute # SVD again, but over k*k^T. # see http://www.mail-archive.com/np-discussion@scipy.org/msg07224.html and # bug ticket http://projects.scipy.org/np/ticket/706 # sdoering: replaced np's linalg.svd with scipy's linalg.svd: # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper # for partial svd/eigendecomp in np :( //sdoering: maybe there is one in scipy? u_k, s_k, _ = scipy.linalg.svd(k, full_matrices=False) except scipy.linalg.LinAlgError: logger.error("SVD(A) failed; trying SVD(A * A^T)") # if this fails too, give up with an exception u_k, s_k, _ = scipy.linalg.svd(np.dot(k, k.T), full_matrices=False) s_k = np.sqrt(s_k) # go back from eigen values to singular values k = clip_spectrum(s_k ** 2, self.k) u1_k, u2_k, s_k = np.array(u_k[:n1, :k]), np.array(u_k[n1:, :k]), s_k[:k] # update & rotate current basis U = [U, U']*[U1_k, U2_k] logger.debug("updating orthonormal basis U") self.s = s_k self.u = ascarray(self.u, 'self.u') self.u = np.dot(self.u, u1_k) q = ascarray(q, 'q') q = np.dot(q, u2_k) self.u += q # make each column of U start with a non-negative number (to force canonical decomposition) if self.u.shape[0] > 0: for i in xrange(self.u.shape[1]): if self.u[0, i] < 0.0: self.u[:, i] *= -1.0 class LsiModel(interfaces.TransformationABC, basemodel.BaseTopicModel): """Model for `Latent Semantic Indexing `_. The decomposition algorithm is described in `"Fast and Faster: A Comparison of Two Streamed Matrix Decomposition Algorithms" `_. Notes ----- * :attr:`gensim.models.lsimodel.LsiModel.projection.u` - left singular vectors, * :attr:`gensim.models.lsimodel.LsiModel.projection.s` - singular values, * ``model[training_corpus]`` - right singular vectors (can be reconstructed if needed). See Also -------- `FAQ about LSI matrices `_. Examples -------- >>> from gensim.test.utils import common_corpus, common_dictionary, get_tmpfile >>> from gensim.models import LsiModel >>> >>> model = LsiModel(common_corpus[:3], id2word=common_dictionary) # train model >>> vector = model[common_corpus[4]] # apply model to BoW document >>> model.add_documents(common_corpus[4:]) # update model with new documents >>> tmp_fname = get_tmpfile("lsi.model") >>> model.save(tmp_fname) # save model >>> loaded_model = LsiModel.load(tmp_fname) # load model """ def __init__(self, corpus=None, num_topics=200, id2word=None, chunksize=20000, decay=1.0, distributed=False, onepass=True, power_iters=P2_EXTRA_ITERS, extra_samples=P2_EXTRA_DIMS, dtype=np.float64): """Construct an `LsiModel` object. Either `corpus` or `id2word` must be supplied in order to train the model. Parameters ---------- corpus : {iterable of list of (int, float), scipy.sparse.csc}, optional Stream of document vectors or sparse matrix of shape (`num_terms`, `num_documents`). num_topics : int, optional Number of requested factors (latent dimensions) id2word : dict of {int: str}, optional ID to word mapping, optional. chunksize : int, optional Number of documents to be used in each training chunk. decay : float, optional Weight of existing observations relatively to new ones. distributed : bool, optional If True - distributed mode (parallel execution on several machines) will be used. onepass : bool, optional Whether the one-pass algorithm should be used for training. Pass `False` to force a multi-pass stochastic algorithm. power_iters: int, optional Number of power iteration steps to be used. Increasing the number of power iterations improves accuracy, but lowers performance extra_samples : int, optional Extra samples to be used besides the rank `k`. Can improve accuracy. dtype : type, optional Enforces a type for elements of the decomposed matrix. """ self.id2word = id2word self.num_topics = int(num_topics) self.chunksize = int(chunksize) self.decay = float(decay) if distributed: if not onepass: logger.warning("forcing the one-pass algorithm for distributed LSA") onepass = True self.onepass = onepass self.extra_samples, self.power_iters = extra_samples, power_iters self.dtype = dtype if corpus is None and self.id2word is None: raise ValueError( 'at least one of corpus/id2word must be specified, to establish input space dimensionality' ) if self.id2word is None: logger.warning("no word id mapping provided; initializing from corpus, assuming identity") self.id2word = utils.dict_from_corpus(corpus) self.num_terms = len(self.id2word) else: self.num_terms = 1 + (max(self.id2word.keys()) if self.id2word else -1) self.docs_processed = 0 self.projection = Projection( self.num_terms, self.num_topics, power_iters=self.power_iters, extra_dims=self.extra_samples, dtype=dtype ) self.numworkers = 1 if not distributed: logger.info("using serial LSI version on this node") self.dispatcher = None else: if not onepass: raise NotImplementedError( "distributed stochastic LSA not implemented yet; " "run either distributed one-pass, or serial randomized." ) try: import Pyro4 dispatcher = Pyro4.Proxy('PYRONAME:gensim.lsi_dispatcher') logger.debug("looking for dispatcher at %s", str(dispatcher._pyroUri)) dispatcher.initialize( id2word=self.id2word, num_topics=num_topics, chunksize=chunksize, decay=decay, power_iters=self.power_iters, extra_samples=self.extra_samples, distributed=False, onepass=onepass ) self.dispatcher = dispatcher self.numworkers = len(dispatcher.getworkers()) logger.info("using distributed version with %i workers", self.numworkers) except Exception as err: # distributed version was specifically requested, so this is an error state logger.error("failed to initialize distributed LSI (%s)", err) raise RuntimeError("failed to initialize distributed LSI (%s)" % err) if corpus is not None: self.add_documents(corpus) def add_documents(self, corpus, chunksize=None, decay=None): """Update model with new `corpus`. Parameters ---------- corpus : {iterable of list of (int, float), scipy.sparse.csc} Stream of document vectors or sparse matrix of shape (`num_terms`, num_documents). chunksize : int, optional Number of documents to be used in each training chunk, will use `self.chunksize` if not specified. decay : float, optional Weight of existing observations relatively to new ones, will use `self.decay` if not specified. Notes ----- Training proceeds in chunks of `chunksize` documents at a time. The size of `chunksize` is a tradeoff between increased speed (bigger `chunksize`) vs. lower memory footprint (smaller `chunksize`). If the distributed mode is on, each chunk is sent to a different worker/computer. """ logger.info("updating model with new documents") # get computation parameters; if not specified, use the ones from constructor if chunksize is None: chunksize = self.chunksize if decay is None: decay = self.decay if not scipy.sparse.issparse(corpus): if not self.onepass: # we are allowed multiple passes over the input => use a faster, randomized two-pass algo update = Projection(self.num_terms, self.num_topics, None, dtype=self.dtype) update.u, update.s = stochastic_svd( corpus, self.num_topics, num_terms=self.num_terms, chunksize=chunksize, extra_dims=self.extra_samples, power_iters=self.power_iters, dtype=self.dtype ) self.projection.merge(update, decay=decay) self.docs_processed += len(corpus) if hasattr(corpus, '__len__') else 0 else: # the one-pass algo doc_no = 0 if self.dispatcher: logger.info('initializing %s workers', self.numworkers) self.dispatcher.reset() for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)): logger.info("preparing a new chunk of documents") nnz = sum(len(doc) for doc in chunk) # construct the job as a sparse matrix, to minimize memory overhead # definitely avoid materializing it as a dense matrix! logger.debug("converting corpus to csc format") job = matutils.corpus2csc( chunk, num_docs=len(chunk), num_terms=self.num_terms, num_nnz=nnz, dtype=self.dtype) del chunk doc_no += job.shape[1] if self.dispatcher: # distributed version: add this job to the job queue, so workers can work on it logger.debug("creating job #%i", chunk_no) # put job into queue; this will eventually block, because the queue has a small finite size self.dispatcher.putjob(job) del job logger.info("dispatched documents up to #%s", doc_no) else: # serial version, there is only one "worker" (myself) => process the job directly update = Projection( self.num_terms, self.num_topics, job, extra_dims=self.extra_samples, power_iters=self.power_iters, dtype=self.dtype ) del job self.projection.merge(update, decay=decay) del update logger.info("processed documents up to #%s", doc_no) self.print_topics(5) # wait for all workers to finish (distributed version only) if self.dispatcher: logger.info("reached the end of input; now waiting for all remaining jobs to finish") self.projection = self.dispatcher.getstate() self.docs_processed += doc_no else: assert not self.dispatcher, "must be in serial mode to receive jobs" update = Projection( self.num_terms, self.num_topics, corpus.tocsc(), extra_dims=self.extra_samples, power_iters=self.power_iters, dtype=self.dtype ) self.projection.merge(update, decay=decay) logger.info("processed sparse job of %i documents", corpus.shape[1]) self.docs_processed += corpus.shape[1] def __str__(self): """Get a human readable representation of model. Returns ------- str A human readable string of the current objects parameters. """ return "LsiModel(num_terms=%s, num_topics=%s, decay=%s, chunksize=%s)" % ( self.num_terms, self.num_topics, self.decay, self.chunksize ) def __getitem__(self, bow, scaled=False, chunksize=512): """Get the latent representation for `bow`. Parameters ---------- bow : {list of (int, int), iterable of list of (int, int)} Document or corpus in BoW representation. scaled : bool, optional If True - topics will be scaled by the inverse of singular values. chunksize : int, optional Number of documents to be used in each applying chunk. Returns ------- list of (int, float) Latent representation of topics in BoW format for document **OR** :class:`gensim.matutils.Dense2Corpus` Latent representation of corpus in BoW format if `bow` is corpus. """ assert self.projection.u is not None, "decomposition not initialized yet" # if the input vector is in fact a corpus, return a transformed corpus as a result is_corpus, bow = utils.is_corpus(bow) if is_corpus and chunksize: # by default, transform `chunksize` documents at once, when called as `lsi[corpus]`. # this chunking is completely transparent to the user, but it speeds # up internal computations (one mat * mat multiplication, instead of # `chunksize` smaller mat * vec multiplications). return self._apply(bow, chunksize=chunksize) if not is_corpus: bow = [bow] # convert input to scipy.sparse CSC, then do "sparse * dense = dense" multiplication vec = matutils.corpus2csc(bow, num_terms=self.num_terms, dtype=self.projection.u.dtype) topic_dist = (vec.T * self.projection.u[:, :self.num_topics]).T # (x^T * u).T = u^-1 * x # # convert input to dense, then do dense * dense multiplication # # ± same performance as above (BLAS dense * dense is better optimized than scipy.sparse), # but consumes more memory # vec = matutils.corpus2dense(bow, num_terms=self.num_terms, num_docs=len(bow)) # topic_dist = np.dot(self.projection.u[:, :self.num_topics].T, vec) # # use np's advanced indexing to simulate sparse * dense # # ± same speed again # u = self.projection.u[:, :self.num_topics] # topic_dist = np.empty((u.shape[1], len(bow)), dtype=u.dtype) # for vecno, vec in enumerate(bow): # indices, data = zip(*vec) if vec else ([], []) # topic_dist[:, vecno] = np.dot(u.take(indices, axis=0).T, np.array(data, dtype=u.dtype)) if not is_corpus: # convert back from matrix into a 1d vec topic_dist = topic_dist.reshape(-1) if scaled: topic_dist = (1.0 / self.projection.s[:self.num_topics]) * topic_dist # s^-1 * u^-1 * x # convert a np array to gensim sparse vector = tuples of (feature_id, feature_weight), # with no zero weights. if not is_corpus: # lsi[single_document] result = matutils.full2sparse(topic_dist) else: # lsi[chunk of documents] result = matutils.Dense2Corpus(topic_dist) return result def get_topics(self): """Get the topic vectors. Notes ----- The number of topics can actually be smaller than `self.num_topics`, if there were not enough factors in the matrix (real rank of input matrix smaller than `self.num_topics`). Returns ------- np.ndarray The term topic matrix with shape (`num_topics`, `vocabulary_size`) """ projections = self.projection.u.T num_topics = len(projections) topics = [] for i in range(num_topics): c = np.asarray(projections[i, :]).flatten() norm = np.sqrt(np.sum(np.dot(c, c))) topics.append(1.0 * c / norm) return np.array(topics) def show_topic(self, topicno, topn=10): """Get the words that define a topic along with their contribution. This is actually the left singular vector of the specified topic. The most important words in defining the topic (greatest absolute value) are included in the output, along with their contribution to the topic. Parameters ---------- topicno : int The topics id number. topn : int Number of words to be included to the result. Returns ------- list of (str, float) Topic representation in BoW format. """ # size of the projection matrix can actually be smaller than `self.num_topics`, # if there were not enough factors (real rank of input matrix smaller than # `self.num_topics`). in that case, return an empty string if topicno >= len(self.projection.u.T): return '' c = np.asarray(self.projection.u.T[topicno, :]).flatten() norm = np.sqrt(np.sum(np.dot(c, c))) most = matutils.argsort(np.abs(c), topn, reverse=True) return [(self.id2word[val], 1.0 * c[val] / norm) for val in most] def show_topics(self, num_topics=-1, num_words=10, log=False, formatted=True): """Get the most significant topics. Parameters ---------- num_topics : int, optional The number of topics to be selected, if -1 - all topics will be in result (ordered by significance). num_words : int, optional The number of words to be included per topics (ordered by significance). log : bool, optional If True - log topics with logger. formatted : bool, optional If True - each topic represented as string, otherwise - in BoW format. Returns ------- list of (int, str) If `formatted=True`, return sequence with (topic_id, string representation of topics) **OR** list of (int, list of (str, float)) Otherwise, return sequence with (topic_id, [(word, value), ... ]). """ shown = [] if num_topics < 0: num_topics = self.num_topics for i in xrange(min(num_topics, self.num_topics)): if i < len(self.projection.s): if formatted: topic = self.print_topic(i, topn=num_words) else: topic = self.show_topic(i, topn=num_words) shown.append((i, topic)) if log: logger.info("topic #%i(%.3f): %s", i, self.projection.s[i], topic) return shown def print_debug(self, num_topics=5, num_words=10): """Print (to log) the most salient words of the first `num_topics` topics. Unlike :meth:`~gensim.models.lsimodel.LsiModel.print_topics`, this looks for words that are significant for a particular topic *and* not for others. This *should* result in a more human-interpretable description of topics. Alias for :func:`~gensim.models.lsimodel.print_debug`. Parameters ---------- num_topics : int, optional The number of topics to be selected (ordered by significance). num_words : int, optional The number of words to be included per topics (ordered by significance). """ # only wrap the module-level fnc print_debug( self.id2word, self.projection.u, self.projection.s, range(min(num_topics, len(self.projection.u.T))), num_words=num_words ) def save(self, fname, *args, **kwargs): """Save the model to a file. Notes ----- Large internal arrays may be stored into separate files, with `fname` as prefix. Warnings -------- Do not save as a compressed file if you intend to load the file back with `mmap`. Parameters ---------- fname : str Path to output file. *args Variable length argument list, see :meth:`gensim.utils.SaveLoad.save`. **kwargs Arbitrary keyword arguments, see :meth:`gensim.utils.SaveLoad.save`. See Also -------- :meth:`~gensim.models.lsimodel.LsiModel.load` """ if self.projection is not None: self.projection.save(utils.smart_extension(fname, '.projection'), *args, **kwargs) super(LsiModel, self).save(fname, *args, ignore=['projection', 'dispatcher'], **kwargs) @classmethod def load(cls, fname, *args, **kwargs): """Load a previously saved object using :meth:`~gensim.models.lsimodel.LsiModel.save` from file. Notes ----- Large arrays can be memmap'ed back as read-only (shared memory) by setting the `mmap='r'` parameter. Parameters ---------- fname : str Path to file that contains LsiModel. *args Variable length argument list, see :meth:`gensim.utils.SaveLoad.load`. **kwargs Arbitrary keyword arguments, see :meth:`gensim.utils.SaveLoad.load`. See Also -------- :meth:`~gensim.models.lsimodel.LsiModel.save` Returns ------- :class:`~gensim.models.lsimodel.LsiModel` Loaded instance. Raises ------ IOError When methods are called on instance (should be called from class). """ kwargs['mmap'] = kwargs.get('mmap', None) result = super(LsiModel, cls).load(fname, *args, **kwargs) projection_fname = utils.smart_extension(fname, '.projection') try: result.projection = super(LsiModel, cls).load(projection_fname, *args, **kwargs) except Exception as e: logging.warning("failed to load projection from %s: %s", projection_fname, e) return result def print_debug(id2token, u, s, topics, num_words=10, num_neg=None): """Log the most salient words per topic. Parameters ---------- id2token : :class:`~gensim.corpora.dictionary.Dictionary` Mapping from ID to word in the Dictionary. u : np.ndarray The 2D U decomposition matrix. s : np.ndarray The 1D reduced array of eigenvalues used for decomposition. topics : list of int Sequence of topic IDs to be printed num_words : int, optional Number of words to be included for each topic. num_neg : int, optional Number of words with a negative contribution to a topic that should be included. """ if num_neg is None: # by default, print half as many salient negative words as positive num_neg = num_words / 2 logger.info('computing word-topic salience for %i topics', len(topics)) topics, result = set(topics), {} # TODO speed up by block computation for uvecno, uvec in enumerate(u): uvec = np.abs(np.asarray(uvec).flatten()) udiff = uvec / np.sqrt(np.sum(np.dot(uvec, uvec))) for topic in topics: result.setdefault(topic, []).append((udiff[topic], uvecno)) logger.debug("printing %i+%i salient words", num_words, num_neg) for topic in sorted(iterkeys(result)): weights = sorted(result[topic], key=lambda x: -abs(x[0])) _, most = weights[0] if u[most, topic] < 0.0: # the most significant word has a negative sign => flip sign of u[most] normalize = -1.0 else: normalize = 1.0 # order features according to salience; ignore near-zero entries in u pos, neg = [], [] for weight, uvecno in weights: if normalize * u[uvecno, topic] > 0.0001: pos.append('%s(%.3f)' % (id2token[uvecno], u[uvecno, topic])) if len(pos) >= num_words: break for weight, uvecno in weights: if normalize * u[uvecno, topic] < -0.0001: neg.append('%s(%.3f)' % (id2token[uvecno], u[uvecno, topic])) if len(neg) >= num_neg: break logger.info('topic #%s(%.3f): %s, ..., %s', topic, s[topic], ', '.join(pos), ', '.join(neg)) def stochastic_svd(corpus, rank, num_terms, chunksize=20000, extra_dims=None, power_iters=0, dtype=np.float64, eps=1e-6): """Run truncated Singular Value Decomposition (SVD) on a sparse input. Parameters ---------- corpus : {iterable of list of (int, float), scipy.sparse} Input corpus as a stream (does not have to fit in RAM) or a sparse matrix of shape (`num_terms`, num_documents). rank : int Desired number of factors to be retained after decomposition. num_terms : int The number of features (terms) in `corpus`. chunksize : int, optional Number of documents to be used in each training chunk. extra_dims : int, optional Extra samples to be used besides the rank `k`. Can improve accuracy. power_iters: int, optional Number of power iteration steps to be used. Increasing the number of power iterations improves accuracy, but lowers performance. dtype : numpy.dtype, optional Enforces a type for elements of the decomposed matrix. eps: float, optional Percentage of the spectrum's energy to be discarded. Notes ----- The corpus may be larger than RAM (iterator of vectors), if `corpus` is a `scipy.sparse.csc` instead, it is assumed the whole corpus fits into core memory and a different (more efficient) code path is chosen. This may return less than the requested number of top `rank` factors, in case the input itself is of lower rank. The `extra_dims` (oversampling) and especially `power_iters` (power iterations) parameters affect accuracy of the decomposition. This algorithm uses `2 + power_iters` passes over the input data. In case you can only afford a single pass, set `onepass=True` in :class:`~gensim.models.lsimodel.LsiModel` and avoid using this function directly. The decomposition algorithm is based on `"Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions" `_. Returns ------- (np.ndarray 2D, np.ndarray 1D) The left singular vectors and the singular values of the `corpus`. """ rank = int(rank) if extra_dims is None: samples = max(10, 2 * rank) # use more samples than requested factors, to improve accuracy else: samples = rank + int(extra_dims) logger.info("using %i extra samples and %i power iterations", samples - rank, power_iters) num_terms = int(num_terms) # first phase: construct the orthonormal action matrix Q = orth(Y) = orth((A * A.T)^q * A * O) # build Y in blocks of `chunksize` documents (much faster than going one-by-one # and more memory friendly than processing all documents at once) y = np.zeros(dtype=dtype, shape=(num_terms, samples)) logger.info("1st phase: constructing %s action matrix", str(y.shape)) if scipy.sparse.issparse(corpus): m, n = corpus.shape assert num_terms == m, "mismatch in number of features: %i in sparse matrix vs. %i parameter" % (m, num_terms) o = np.random.normal(0.0, 1.0, (n, samples)).astype(y.dtype) # draw a random gaussian matrix sparsetools.csc_matvecs(m, n, samples, corpus.indptr, corpus.indices, corpus.data, o.ravel(), y.ravel()) # y = corpus * o del o # unlike np, scipy.sparse `astype()` copies everything, even if there is no change to dtype! # so check for equal dtype explicitly, to avoid the extra memory footprint if possible if y.dtype != dtype: y = y.astype(dtype) logger.info("orthonormalizing %s action matrix", str(y.shape)) y = [y] q, _ = matutils.qr_destroy(y) # orthonormalize the range logger.debug("running %i power iterations", power_iters) for _ in xrange(power_iters): q = corpus.T * q q = [corpus * q] q, _ = matutils.qr_destroy(q) # orthonormalize the range after each power iteration step else: num_docs = 0 for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)): logger.info('PROGRESS: at document #%i', (chunk_no * chunksize)) # construct the chunk as a sparse matrix, to minimize memory overhead # definitely avoid materializing it as a dense (num_terms x chunksize) matrix! s = sum(len(doc) for doc in chunk) chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype) # documents = columns of sparse CSC m, n = chunk.shape assert m == num_terms assert n <= chunksize # the very last chunk of A is allowed to be smaller in size num_docs += n logger.debug("multiplying chunk * gauss") o = np.random.normal(0.0, 1.0, (n, samples)).astype(dtype) # draw a random gaussian matrix sparsetools.csc_matvecs( m, n, samples, chunk.indptr, chunk.indices, # y = y + chunk * o chunk.data, o.ravel(), y.ravel() ) del chunk, o y = [y] q, _ = matutils.qr_destroy(y) # orthonormalize the range for power_iter in xrange(power_iters): logger.info("running power iteration #%i", power_iter + 1) yold = q.copy() q[:] = 0.0 for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)): logger.info('PROGRESS: at document #%i/%i', chunk_no * chunksize, num_docs) # documents = columns of sparse CSC chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=dtype) tmp = chunk.T * yold tmp = chunk * tmp del chunk q += tmp del yold q = [q] q, _ = matutils.qr_destroy(q) # orthonormalize the range qt = q[:, :samples].T.copy() del q if scipy.sparse.issparse(corpus): b = qt * corpus logger.info("2nd phase: running dense svd on %s matrix", str(b.shape)) u, s, vt = scipy.linalg.svd(b, full_matrices=False) del b, vt else: # second phase: construct the covariance matrix X = B * B.T, where B = Q.T * A # again, construct X incrementally, in chunks of `chunksize` documents from the streaming # input corpus A, to avoid using O(number of documents) memory x = np.zeros(shape=(qt.shape[0], qt.shape[0]), dtype=dtype) logger.info("2nd phase: constructing %s covariance matrix", str(x.shape)) for chunk_no, chunk in enumerate(utils.grouper(corpus, chunksize)): logger.info('PROGRESS: at document #%i/%i', chunk_no * chunksize, num_docs) chunk = matutils.corpus2csc(chunk, num_terms=num_terms, dtype=qt.dtype) b = qt * chunk # dense * sparse matrix multiply del chunk x += np.dot(b, b.T) # TODO should call the BLAS routine SYRK, but there is no SYRK wrapper in scipy :( del b # now we're ready to compute decomposition of the small matrix X logger.info("running dense decomposition on %s covariance matrix", str(x.shape)) # could use linalg.eigh, but who cares... and svd returns the factors already sorted :) u, s, vt = scipy.linalg.svd(x) # sqrt to go back from singular values of X to singular values of B = singular values of the corpus s = np.sqrt(s) q = qt.T.copy() del qt logger.info("computing the final decomposition") keep = clip_spectrum(s ** 2, rank, discard=eps) u = u[:, :keep].copy() s = s[:keep] u = np.dot(q, u) return u.astype(dtype), s.astype(dtype)