33,683 research outputs found
Clustering and Latent Semantic Indexing Aspects of the Nonnegative Matrix Factorization
This paper provides a theoretical support for clustering aspect of the
nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker
optimality conditions, we show that NMF objective is equivalent to graph
clustering objective, so clustering aspect of the NMF has a solid
justification. Different from previous approaches which usually discard the
nonnegativity constraints, our approach guarantees the stationary point being
used in deriving the equivalence is located on the feasible region in the
nonnegative orthant. Additionally, since clustering capability of a matrix
decomposition technique can sometimes imply its latent semantic indexing (LSI)
aspect, we will also evaluate LSI aspect of the NMF by showing its capability
in solving the synonymy and polysemy problems in synthetic datasets. And more
extensive evaluation will be conducted by comparing LSI performances of the NMF
and the singular value decomposition (SVD), the standard LSI method, using some
standard datasets.Comment: 28 pages, 5 figure
Learning Topic Models and Latent Bayesian Networks Under Expansion Constraints
Unsupervised estimation of latent variable models is a fundamental problem
central to numerous applications of machine learning and statistics. This work
presents a principled approach for estimating broad classes of such models,
including probabilistic topic models and latent linear Bayesian networks, using
only second-order observed moments. The sufficient conditions for
identifiability of these models are primarily based on weak expansion
constraints on the topic-word matrix, for topic models, and on the directed
acyclic graph, for Bayesian networks. Because no assumptions are made on the
distribution among the latent variables, the approach can handle arbitrary
correlations among the topics or latent factors. In addition, a tractable
learning method via optimization is proposed and studied in numerical
experiments.Comment: 38 pages, 6 figures, 2 tables, applications in topic models and
Bayesian networks are studied. Simulation section is adde
Implementation of a Combined OFDM-Demodulation and WCDMA-Equalization Module
For a dual-mode baseband receiver for the OFDMWireless LAN andWCDMA standards, integration of the demodulation and equalization tasks on a dedicated hardware module has been investigated. For OFDM demodulation, an FFT algorithm based on cascaded twiddle factor decomposition has been selected. This type of algorithm combines high spatial and temporal regularity in the FFT data-flow graphs with a minimal number of computations. A frequency-domain algorithm based on a circulant channel approximation has been selected for WCDMA equalization. It has good performance, low hardware complexity and a low number of computations. Its main advantage is the reuse of the FFT kernel, which contributes to the integration of both tasks. The demodulation and equalization module has been described at the register transfer level with the in-house developed Arx language. The core of the module is a pipelined radix-23 butterfly combined with a complex multiplier and complex divider. The module has an area of 0.447 mm2 in 0.18 Āæm technology and a power consumption of 10.6 mW. The proposed module compares favorably with solutions reported in literature
A Scalable Asynchronous Distributed Algorithm for Topic Modeling
Learning meaningful topic models with massive document collections which
contain millions of documents and billions of tokens is challenging because of
two reasons: First, one needs to deal with a large number of topics (typically
in the order of thousands). Second, one needs a scalable and efficient way of
distributing the computation across multiple machines. In this paper we present
a novel algorithm F+Nomad LDA which simultaneously tackles both these problems.
In order to handle large number of topics we use an appropriately modified
Fenwick tree. This data structure allows us to sample from a multinomial
distribution over items in time. Moreover, when topic counts
change the data structure can be updated in time. In order to
distribute the computation across multiple processor we present a novel
asynchronous framework inspired by the Nomad algorithm of
\cite{YunYuHsietal13}. We show that F+Nomad LDA significantly outperform
state-of-the-art on massive problems which involve millions of documents,
billions of words, and thousands of topics
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