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A niching memetic algorithm for simultaneous clustering and feature selection
Clustering is inherently a difficult task, and is made even more difficult when the selection of relevant features is also an issue. In this paper we propose an approach for simultaneous clustering and feature selection using a niching memetic algorithm. Our approach (which we call NMA_CFS) makes feature selection an integral part of the global clustering search procedure and attempts to overcome the problem of identifying less promising locally optimal solutions in both clustering and feature selection, without making any a priori assumption about the number of clusters. Within the NMA_CFS procedure, a variable composite representation is devised to encode both feature selection and cluster centers with different numbers of clusters. Further, local search operations are introduced to refine feature selection and cluster centers encoded in the chromosomes. Finally, a niching method is integrated to preserve the population diversity and prevent premature convergence. In an experimental evaluation we demonstrate the effectiveness of the proposed approach and compare it with other related approaches, using both synthetic and real data
Fractional norms and quasinorms do not help to overcome the curse of dimensionality
The curse of dimensionality causes the well-known and widely discussed
problems for machine learning methods. There is a hypothesis that using of the
Manhattan distance and even fractional quasinorms lp (for p less than 1) can
help to overcome the curse of dimensionality in classification problems. In
this study, we systematically test this hypothesis. We confirm that fractional
quasinorms have a greater relative contrast or coefficient of variation than
the Euclidean norm l2, but we also demonstrate that the distance concentration
shows qualitatively the same behaviour for all tested norms and quasinorms and
the difference between them decays as dimension tends to infinity. Estimation
of classification quality for kNN based on different norms and quasinorms shows
that a greater relative contrast does not mean better classifier performance
and the worst performance for different databases was shown by different norms
(quasinorms). A systematic comparison shows that the difference of the
performance of kNN based on lp for p=2, 1, and 0.5 is statistically
insignificant
DCSI -- An improved measure of cluster separability based on separation and connectedness
Whether class labels in a given data set correspond to meaningful clusters is
crucial for the evaluation of clustering algorithms using real-world data sets.
This property can be quantified by separability measures. A review of the
existing literature shows that neither classification-based complexity measures
nor cluster validity indices (CVIs) adequately incorporate the central aspects
of separability for density-based clustering: between-class separation and
within-class connectedness. A newly developed measure (density cluster
separability index, DCSI) aims to quantify these two characteristics and can
also be used as a CVI. Extensive experiments on synthetic data indicate that
DCSI correlates strongly with the performance of DBSCAN measured via the
adjusted rand index (ARI) but lacks robustness when it comes to multi-class
data sets with overlapping classes that are ill-suited for density-based hard
clustering. Detailed evaluation on frequently used real-world data sets shows
that DCSI can correctly identify touching or overlapping classes that do not
form meaningful clusters
-softmax: Improving Intra-class Compactness and Inter-class Separability of Features
Intra-class compactness and inter-class separability are crucial indicators
to measure the effectiveness of a model to produce discriminative features,
where intra-class compactness indicates how close the features with the same
label are to each other and inter-class separability indicates how far away the
features with different labels are. In this work, we investigate intra-class
compactness and inter-class separability of features learned by convolutional
networks and propose a Gaussian-based softmax (-softmax) function
that can effectively improve intra-class compactness and inter-class
separability. The proposed function is simple to implement and can easily
replace the softmax function. We evaluate the proposed -softmax
function on classification datasets (i.e., CIFAR-10, CIFAR-100, and Tiny
ImageNet) and on multi-label classification datasets (i.e., MS COCO and
NUS-WIDE). The experimental results show that the proposed
-softmax function improves the state-of-the-art models across all
evaluated datasets. In addition, analysis of the intra-class compactness and
inter-class separability demonstrates the advantages of the proposed function
over the softmax function, which is consistent with the performance
improvement. More importantly, we observe that high intra-class compactness and
inter-class separability are linearly correlated to average precision on MS
COCO and NUS-WIDE. This implies that improvement of intra-class compactness and
inter-class separability would lead to improvement of average precision.Comment: 15 pages, published in TNNL
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