Parametric Embedding for Class Visualization

Iwata, Tomoharu; Saito, Kazumi; Ueda, Naonori; Stromsten, Sean; Griffiths, Thomas L.; Tenenbaum, Joshua B.

doi:10.1162/neco.2007.19.9.2536

Cited by 57 publications

(61 citation statements)

References 11 publications

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“…The idea of representing points in the space of the clusters was discussed in (Gupta and Ghosh, 2001) and in (Iwata et al, 2007). In (Gupta and Ghosh, 2001) the authors propose a Cluster Space model in order to analyze the similarity between a customer and a cluster in the transactional application area.…”

Section: Related Workmentioning

confidence: 99%

Unsupervised Discriminant Embedding in Cluster Spaces

Szekely

Bruno

Marchand-Maillet

2009

Proceedings of the International Conference on Knowledge Discovery and Information Retrieval

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Abstract:This paper proposes a new representation space, called the cluster space, for data points that originate from high dimensions. Whereas existing dedicated methods concentrate on revealing manifolds from within the data, we consider here the context of clustered data and derive the dimension reduction process from cluster information. Points are represented in the cluster space by means of their a posteriori probability values estimated using Gaussian Mixture Models. The cluster space obtained is the optimal space for discrimination in terms of the Quadratic Discriminant Analysis (QDA). Moreover, it is shown to alleviate the negative impact of the curse of dimensionality on the quality of cluster discrimination and is a useful preprocessing tool for other dimension reduction methods. Various experiments illustrate the effectiveness of the cluster space both on synthetic and real data.

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Section: Related Workmentioning

confidence: 99%

Unsupervised Discriminant Embedding in Cluster Spaces

Szekely

Bruno

Marchand-Maillet

2009

Proceedings of the International Conference on Knowledge Discovery and Information Retrieval

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“…This is also known as joint embedding or co-embedding [23,16,24]. The goal is to generate co-embeddings, where both groups of objects are embedded in a joint space.…”

Section: Introductionmentioning

confidence: 99%

“…The goal is to generate co-embeddings, where both groups of objects are embedded in a joint space. Various stochastic methods have been previously proposed to achieve this, such as Parametric Embedding [23], Co-occurrence Data Embedding [25], Bayesian Co-occurrence Data Embedding [16], as well as a dynamic embedding model that processes a sequence of co-occurrence data changing over time [26]. These algorithms treat the co-occurrence object pairs as being generated by a Gaussian mixture in the embedding space, and then recover the embedding that maximizes the likelihood of the observed data.…”

Section: Introductionmentioning

confidence: 99%

Computation of heterogeneous object co-embeddings from relational measurements

Liatsis

et al. 2017

Pattern Recognition

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Dimensionality reduction and data embedding methods generate low dimensional representations of a single type of homogeneous data objects. In this work, we examine the problem of generating co-embeddings or pattern representations from two different types of objects within a joint common space of controlled dimensionality, where the only available information is assumed to be a set of pairwise relations or similarities between instances of the two groups. We propose a new method that models the embedding of each object type symmetrically to the other type, subject to flexible scale constraints and weighting parameters. The embedding generation relies on an efficient optimization despatched using matrix decomposition, that is also extended to support multidimensional co-embeddings. We also propose a scheme of heuristically reducing the parameters of the model, and a simple way of measuring the conformity between the original object relations and the ones re-estimated from the co-embeddings, in order to achieve model selection by identifying the optimal model parameters with a simple search procedure. The capabilities of the proposed method are demonstrated with multiple synthetic and real-world datasets from the text mining domain. The experimental results and comparative analyses indicate that the proposed algorithm outperforms existing methods for co-embedding generation.

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“…An ad hoc metric adaptation is used in Geng, Zhan, and Zhou (2005) to extend Isomap (Tenenbaum, Silva, & Langford, 2000) to class labels. Alternative approaches change the cost function of dimensionality reduction, for instance by using conditional probabilities, class-wise similarity matrices or introducing a covariancebased coloring matrix for the side information as proposed in Iwata et al (2007), Memisevic and Hinton (2005), and Song, Smola, Borgwardt, and Gretton (2008).…”

Section: Introductionmentioning

confidence: 99%

Limited Rank Matrix Learning, discriminative dimension reduction and visualization

et al. 2012

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a b s t r a c tWe present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-dimensional representations of the data. This allows to incorporate prior knowledge of the intrinsic dimension and to reduce the number of adaptive parameters efficiently.In particular, for very large dimensional data, the limitation of the rank can reduce computation time and memory requirements significantly. Furthermore, two-or three-dimensional representations constitute an efficient visualization method for labeled data sets. The identification of a suitable projection is not treated as a pre-processing step but as an integral part of the supervised training. Several real world data sets serve as an illustration and demonstrate the usefulness of the suggested method.

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Parametric Embedding for Class Visualization

Cited by 57 publications

References 11 publications

Unsupervised Discriminant Embedding in Cluster Spaces

Unsupervised Discriminant Embedding in Cluster Spaces

Computation of heterogeneous object co-embeddings from relational measurements

Limited Rank Matrix Learning, discriminative dimension reduction and visualization

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