2,853 research outputs found
Optimal Kullback-Leibler Aggregation via Information Bottleneck
In this paper, we present a method for reducing a regular, discrete-time
Markov chain (DTMC) to another DTMC with a given, typically much smaller number
of states. The cost of reduction is defined as the Kullback-Leibler divergence
rate between a projection of the original process through a partition function
and a DTMC on the correspondingly partitioned state space. Finding the reduced
model with minimal cost is computationally expensive, as it requires an
exhaustive search among all state space partitions, and an exact evaluation of
the reduction cost for each candidate partition. Our approach deals with the
latter problem by minimizing an upper bound on the reduction cost instead of
minimizing the exact cost; The proposed upper bound is easy to compute and it
is tight if the original chain is lumpable with respect to the partition. Then,
we express the problem in the form of information bottleneck optimization, and
propose using the agglomerative information bottleneck algorithm for searching
a sub-optimal partition greedily, rather than exhaustively. The theory is
illustrated with examples and one application scenario in the context of
modeling bio-molecular interactions.Comment: 13 pages, 4 figure
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
Learning Hybrid Neuro-Fuzzy Classifier Models From Data: To Combine or Not to Combine?
To combine or not to combine? Though not a question of the same gravity as the Shakespeare’s to be or not
to be, it is examined in this paper in the context of a hybrid neuro-fuzzy pattern classifier design process. A general fuzzy
min-max neural network with its basic learning procedure is used within six different algorithm independent learning
schemes. Various versions of cross-validation, resampling techniques and data editing approaches, leading to a generation
of a single classifier or a multiple classifier system, are scrutinised and compared. The classification performance on
unseen data, commonly used as a criterion for comparing different competing designs, is augmented by further four
criteria attempting to capture various additional characteristics of classifier generation schemes. These include: the ability
to estimate the true classification error rate, the classifier transparency, the computational complexity of the learning
scheme and the potential for adaptation to changing environments and new classes of data. One of the main questions
examined is whether and when to use a single classifier or a combination of a number of component classifiers within a
multiple classifier system
Splitting hybrid Make-To-Order and Make-To-Stock demand profiles
In this paper a demand time series is analysed to support Make-To-Stock (MTS)
and Make-To-Order (MTO) production decisions. Using a purely MTS production
strategy based on the given demand can lead to unnecessarily high inventory
levels thus it is necessary to identify likely MTO episodes.
This research proposes a novel outlier detection algorithm based on special
density measures. We divide the time series' histogram into three clusters. One
with frequent-low volume covers MTS items whilst a second accounts for high
volumes which is dedicated to MTO items. The third cluster resides between the
previous two with its elements being assigned to either the MTO or MTS class.
The algorithm can be applied to a variety of time series such as stationary and
non-stationary ones.
We use empirical data from manufacturing to study the extent of inventory
savings. The percentage of MTO items is reflected in the inventory savings
which were shown to be an average of 18.1%.Comment: demand analysis; time series; outlier detection; production strategy;
Make-To-Order(MTO); Make-To-Stock(MTS); 15 pages, 9 figure
- …