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- Cristina Garcia-Cardona, Ekaterina Merkurjev, Andrea L. Bertozzi, Arjuna Flenner, Allon G. Percus
- IEEE Transactions on Pattern Analysis and Machine…
- 2014

We present two graph-based algorithms for multiclass segmentation of high-dimensional data on graphs. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the… (More)

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional’s double-well potential… (More)

- Ekaterina Merkurjev, Cristina Garcia-Cardona, Andrea L. Bertozzi, Arjuna Flenner, Allon G. Percus
- Appl. Math. Lett.
- 2014

We present two graph-based algorithms for multiclass segmentation of high-dimensional data,motivated by the binary diffuse interfacemodel. One algorithmgeneralizesGinzburg– Landau (GL) functional minimization on graphs to the Gibbs simplex. The other algorithm uses a reduction of GLminimization, based on theMerriman–Bence–Osher scheme formotion by mean… (More)

- Cristina Garcia-Cardona, Arjuna Flenner, Allon G. Percus
- ICPRAM
- 2013

We present a graph-based variational algorithm for multiclass classification of high-dimensional data, motivated by total variation techniques. The energy functional is based on a diffuse interface model with a periodic potential. We augment the model by introducing an alternative measure of smoothness that preserves symmetry among the class labels. Through… (More)

- Diletta Giuntini, Eugene A. Olevsky, +5 authors Deepak Kapoor
- Materials
- 2013

The present paper shows the application of a three-dimensional coupled electrical, thermal, mechanical finite element macro-scale modeling framework of Spark Plasma Sintering (SPS) to an actual problem of SPS tooling overheating, encountered during SPS experimentation. The overheating phenomenon is analyzed by varying the geometry of the tooling that… (More)

- Jialin Liu, Cristina Garcia-Cardona, Brendt Wohlberg, Wotao Yin
- ArXiv
- 2017

While a number of different algorithms have recently been proposed for convolutional dictionary learning, this remains an expensive problem. The single biggest impediment to learning from large training sets is the memory requirements, which grow at least linearly with the size of the training set since all existing methods are batch algorithms. The work… (More)

- Laura M. Smith, Kristina Lerman, Cristina Garcia-Cardona, Allon G. Percus, Rumi Ghosh
- Physical review. E, Statistical, nonlinear, and…
- 2013

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a spectral partitioning method that exploits the properties of epidemic diffusion. An… (More)

- Cristina Garcia-Cardona, Arjuna Flenner, Allon G. Percus
- ICPRAM
- 2013

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification… (More)

- Cristina Garcia-Cardona, Brendt Wohlberg
- ArXiv
- 2017

Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the convolutional sparse coding problem, the corresponding dictionary learning problem is substantially more challenging.… (More)

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