143,377 research outputs found
Random Feature Maps for Dot Product Kernels
Approximating non-linear kernels using feature maps has gained a lot of
interest in recent years due to applications in reducing training and testing
times of SVM classifiers and other kernel based learning algorithms. We extend
this line of work and present low distortion embeddings for dot product kernels
into linear Euclidean spaces. We base our results on a classical result in
harmonic analysis characterizing all dot product kernels and use it to define
randomized feature maps into explicit low dimensional Euclidean spaces in which
the native dot product provides an approximation to the dot product kernel with
high confidence.Comment: To appear in the proceedings of the 15th International Conference on
Artificial Intelligence and Statistics (AISTATS 2012). This version corrects
a minor error with Lemma 10. Acknowledgements : Devanshu Bhimwa
Asymmetric Feature Maps with Application to Sketch Based Retrieval
We propose a novel concept of asymmetric feature maps (AFM), which allows to
evaluate multiple kernels between a query and database entries without
increasing the memory requirements. To demonstrate the advantages of the AFM
method, we derive a short vector image representation that, due to asymmetric
feature maps, supports efficient scale and translation invariant sketch-based
image retrieval. Unlike most of the short-code based retrieval systems, the
proposed method provides the query localization in the retrieved image. The
efficiency of the search is boosted by approximating a 2D translation search
via trigonometric polynomial of scores by 1D projections. The projections are a
special case of AFM. An order of magnitude speed-up is achieved compared to
traditional trigonometric polynomials. The results are boosted by an
image-based average query expansion, exceeding significantly the state of the
art on standard benchmarks.Comment: CVPR 201
Compact Random Feature Maps
Kernel approximation using randomized feature maps has recently gained a lot
of interest. In this work, we identify that previous approaches for polynomial
kernel approximation create maps that are rank deficient, and therefore do not
utilize the capacity of the projected feature space effectively. To address
this challenge, we propose compact random feature maps (CRAFTMaps) to
approximate polynomial kernels more concisely and accurately. We prove the
error bounds of CRAFTMaps demonstrating their superior kernel reconstruction
performance compared to the previous approximation schemes. We show how
structured random matrices can be used to efficiently generate CRAFTMaps, and
present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class
classifiers. We present experiments on multiple standard data-sets with
performance competitive with state-of-the-art results.Comment: 9 page
Rules for the Cortical Map of Ocular Dominance and Orientation Columns
Three computational rules are sufficient to generate model cortical maps that simulate the interrelated structure of cortical ocular dominance and orientation columns: a noise input, a spatial band pass filter, and competitive normalization across all feature dimensions. The data of Blasdel from optical imaging experiments reveal cortical map fractures, singularities, and linear zones that are fit by the model. In particular, singularities in orientation preference tend to occur in the centers of ocular dominance columns, and orientation contours tend to intersect ocular dominance columns at right angles. The model embodies a universal computational substrate that all models of cortical map development and adult function need to realize in some form.Air Force Office of Scientific Research (F49620-92-J- 0499, F49620-92-J-0334); Office of Naval Research (N00014-92-J-4015, N00014-91-J-4100); National Science Foundation (IRI-90-24877); British Petroleum (BP 89A-1204
Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification
The approximation of nonlinear kernels via linear feature maps has recently
gained interest due to their applications in reducing the training and testing
time of kernel-based learning algorithms. Current random projection methods
avoid the curse of dimensionality by embedding the nonlinear feature space into
a low dimensional Euclidean space to create nonlinear kernels. We introduce a
Layered Random Projection (LaRP) framework, where we model the linear kernels
and nonlinearity separately for increased training efficiency. The proposed
LaRP framework was assessed using the MNIST hand-written digits database and
the COIL-100 object database, and showed notable improvement in object
classification performance relative to other state-of-the-art random projection
methods.Comment: 5 page
Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions
The key idea of variational auto-encoders (VAEs) resembles that of
traditional auto-encoder models in which spatial information is supposed to be
explicitly encoded in the latent space. However, the latent variables in VAEs
are vectors, which can be interpreted as multiple feature maps of size 1x1.
Such representations can only convey spatial information implicitly when
coupled with powerful decoders. In this work, we propose spatial VAEs that use
feature maps of larger size as latent variables to explicitly capture spatial
information. This is achieved by allowing the latent variables to be sampled
from matrix-variate normal (MVN) distributions whose parameters are computed
from the encoder network. To increase dependencies among locations on latent
feature maps and reduce the number of parameters, we further propose spatial
VAEs via low-rank MVN distributions. Experimental results show that the
proposed spatial VAEs outperform original VAEs in capturing rich structural and
spatial information.Comment: Accepted by SDM2019. Code is publicly available at
https://github.com/divelab/sva
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