| <Poster Width="1734" Height="1227"> |
| <Panel left="31" right="156" width="408" height="237"> |
| <Text>1. C ONTRIBUTIONS</Text> |
| <Text>The key contributions of our work are:</Text> |
| <Text>• Analysis of the spatial receptive field (RF) designs for</Text> |
| <Text>pooled features.</Text> |
| <Text>• Evidence that spatial pyramids may be suboptimal in</Text> |
| <Text>feature generation.</Text> |
| <Text>• An algorithm that jointly learns adaptive RF and</Text> |
| <Text>the classifiers, with an efficient implementation using</Text> |
| <Text>over-completeness and structured sparsity.</Text> |
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| <Panel left="451" right="157" width="828" height="238"> |
| <Text>2. T HE P IPELINE</Text> |
| <Figure left="532" right="194" width="667" height="137" no="1" OriWidth="0.555491" OriHeight="0.0848972 |
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| <Text>State-of-the-art classification algorithms take a two-layer pipeline: the coding layer learns activations from local</Text> |
| <Text>image patches, and the pooling layer aggregates activations in multiple spatial regions. Linear classifiers are learned</Text> |
| <Text>from the pooled features.</Text> |
| </Panel> |
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| <Panel left="1293" right="156" width="407" height="239"> |
| <Text>3. N EUROSCIENCE I NSPIRATION</Text> |
| <Figure left="1347" right="199" width="314" height="178" no="2" OriWidth="0" OriHeight="0 |
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| <Panel left="30" right="408" width="409" height="408"> |
| <Text>4. S PATIAL P OOLING R EVISITED</Text> |
| <Text>• Much work has been done on the coding part, while</Text> |
| <Text>the spatial pooling methods are often hand-crafted.</Text> |
| <Text>• Sample performances on CIFAR-10 with different re-</Text> |
| <Text>ceptive field designs:</Text> |
| <Figure left="102" right="553" width="280" height="132" no="3" OriWidth="0" OriHeight="0 |
| " /> |
| <Text>Note the suboptimality of SPM - random selection</Text> |
| <Text>from an overcomplete set of spatially pooled features</Text> |
| <Text>consistently outperforms SPM.</Text> |
| <Text>• We propose to learn the spatial receptive fields as well</Text> |
| <Text>as the codes and the classifier.</Text> |
| </Panel> |
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| <Panel left="31" right="830" width="406" height="364"> |
| <Text>5. N OTATIONS</Text> |
| <Text>• I: image input.</Text> |
| <Text>• A1 , · · · , AK : code activation as matrices, with Akij : ac-</Text> |
| <Text>tivation of code k at position (i, j).</Text> |
| <Text>• Ri : RF of the i-th pooled feature.</Text> |
| <Text>• op(·): pooling operator, such as max(·).</Text> |
| <Text>• f (x, θ): the classifier based on pooled features x.</Text> |
| <Text>• A pooled feature xi is defined by choosing a code in-</Text> |
| <Text>dexed by ci and a spatial RF Ri :</Text> |
| <Text>The vector of pooled features x is then determined</Text> |
| <Text>by the set of parameters C = {c1 , · · · , cM } and R =</Text> |
| <Text>{R1 , · · · , RM }.</Text> |
| </Panel> |
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| <Panel left="452" right="410" width="406" height="361"> |
| <Text>6. T HE L EARNING P ROBLEM</Text> |
| <Text>N{(In , yn )}n=1 ,• Given a set of training datawe jointly</Text> |
| <Text>learn the classifier and the pooled features as (assum-</Text> |
| <Text>ing that coding is done in an unsupervised way):</Text> |
| <Text>• Advantage: pooled features are tailored towards the</Text> |
| <Text>classification task (also reduces redundancy).</Text> |
| <Text>• Disadvantage: may be intractable - an exponential</Text> |
| <Text>number of possible receptive fields.</Text> |
| <Text>• Solution: reasonably overcomplete receptive field</Text> |
| <Text>candidates + sparsity constraints to control the num-</Text> |
| <Text>ber of final features.</Text> |
| </Panel> |
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| <Panel left="452" right="785" width="406" height="411"> |
| <Text>7. O VERCOMPLETE RF</Text> |
| <Text>• We propose to use overcomplete receptive field can-</Text> |
| <Text>didates based on regular grids:</Text> |
| <Figure left="487" right="879" width="102" height="100" no="4" OriWidth="0.104624" OriHeight="0.0817694 |
| " /> |
| <Text> (a) Base</Text> |
| <Figure left="606" right="878" width="102" height="101" no="5" OriWidth="0.104624" OriHeight="0.080429 |
| " /> |
| <Text> (b) SPM</Text> |
| <Figure left="725" right="878" width="102" height="101" no="6" OriWidth="0.103468" OriHeight="0.0808758 |
| " /> |
| <Text> (c) Ours</Text> |
| <Text>• The structured sparsity regularization is adopted to</Text> |
| <Text>select only a subset of features for classification:</Text> |
| </Panel> |
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| <Panel left="871" right="409" width="407" height="787"> |
| <Text>8. G REEDY F EATURE S ELECTION</Text> |
| <Text>• Directly perform optimization is still time and mem-</Text> |
| <Text>ory consuming.</Text> |
| <Text>• Following [Perkins JMLR03], We adopted an incre-</Text> |
| <Text>mental, greedy approach to select features based on</Text> |
| <Text>their scores:</Text> |
| <Text>• After each increment, the model is retrained only with</Text> |
| <Text>respect to an active subset of selected features to en-</Text> |
| <Text>sure fast re-training:</Text> |
| <Figure left="983" right="753" width="193" height="160" no="7" OriWidth="0.212717" OriHeight="0.139857 |
| " /> |
| <Text>• Benefit of overcompleteness in spatial pooling + fea-</Text> |
| <Text>ture selection: higher performance with smaller code-</Text> |
| <Text>books and lower feature dimensions.</Text> |
| <Figure left="981" right="1008" width="222" height="169" no="8" OriWidth="0.244509" OriHeight="0.150134 |
| " /> |
| </Panel> |
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| <Panel left="1293" right="410" width="405" height="540"> |
| <Text>9. R ESULTS</Text> |
| <Text>• Performance comparison on CIFAR-10 with state-of-</Text> |
| <Text>the-art approaches:</Text> |
| <Figure left="1332" right="506" width="354" height="213" no="9" OriWidth="0.343353" OriHeight="0.152368 |
| " /> |
| <Text>• Result on MNIST and the 1-vs-1 saliency map ob-</Text> |
| <Text>tained from our algorithm:</Text> |
| <Figure left="1327" right="790" width="359" height="155" no="10" OriWidth="0.358382" OriHeight="0.120197 |
| " /> |
| </Panel> |
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| <Panel left="1294" right="964" width="404" height="230"> |
| <Text>10. R EFERENCES</Text> |
| <Text>• A Coates and AY Ng. The importance of encoding</Text> |
| <Text>versus training with sparse coding and vector quanti-</Text> |
| <Text>zation. ICML 2011.</Text> |
| <Text>• S Perkins, K Lacker, and J Theiler. Grafting: fast, incre-</Text> |
| <Text>mental feature selection by gradient descent in func-</Text> |
| <Text>tion space. JMLR, 3:1333–1356, 2003.</Text> |
| <Text>• DH Hubel and TN Wiesel. Receptive fields, binocu-</Text> |
| <Text>lar interaction and functional architecture in the cat’s</Text> |
| <Text>visual cortex. J. of Physiology, 160(1):106–154, 1962.</Text> |
| </Panel> |
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| </Poster> |
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