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Fig. 5. Average efficiency for the three different classification methods with 1 o tolerance versus the size of the training set. These are learning techniques for object recognition and catego- rization and, therefore, they should be further compared with classic methodologies capable to solve similar problems. Consequently, a single SVM classifier was used as a reference against the HTM learn- ing framework applied to the same configuration of the dataset. The only modification was a dimensionality reduction of the dataset, uti- lizing principal component analysis (PCA). The resulting dimensions retained more than 95% of the initial information, simplifying the

Figure 5 Average efficiency for the three different classification methods with 1 o tolerance versus the size of the training set. These are learning techniques for object recognition and catego- rization and, therefore, they should be further compared with classic methodologies capable to solve similar problems. Consequently, a single SVM classifier was used as a reference against the HTM learn- ing framework applied to the same configuration of the dataset. The only modification was a dimensionality reduction of the dataset, uti- lizing principal component analysis (PCA). The resulting dimensions retained more than 95% of the initial information, simplifying the

Related Figures (6)

Fig. 1. The proposed HTM network structure for supervised learning.
Fig. 1. The proposed HTM network structure for supervised learning.
Fig. 2. (a) The circular input space presented in the receptive field of the node, (b) the rate of adding new quantization centers, (c) a mapping of the learned quantization centers using Numenta’s Inc. method and (d) a mapping of the learned quantization centers according to the proposed method. where E is the expected value operator and @g is the standard devi- ation of the respective quantization center. The R(qi,q) is a diagonal The approximation, as introduced in Section 2.2, is very suitable in applications where the input corresponds to a time-based se- quence of images, e.g. video, where the successive images share a great amount of common information. Thus, the input vectors pre- sented in the receptive field of a node over time mostly represent the same content shifted by a small portion of pixels. Therefore, it
Fig. 2. (a) The circular input space presented in the receptive field of the node, (b) the rate of adding new quantization centers, (c) a mapping of the learned quantization centers using Numenta’s Inc. method and (d) a mapping of the learned quantization centers according to the proposed method. where E is the expected value operator and @g is the standard devi- ation of the respective quantization center. The R(qi,q) is a diagonal The approximation, as introduced in Section 2.2, is very suitable in applications where the input corresponds to a time-based se- quence of images, e.g. video, where the successive images share a great amount of common information. Thus, the input vectors pre- sented in the receptive field of a node over time mostly represent the same content shifted by a small portion of pixels. Therefore, it
Fig. 3. (a) The correlation matrix between the quantization centers in a node and (b) the thresholded correlation matrix with a threshold of 0.8 corresponding to statistical significance greater than 95%.
Fig. 3. (a) The correlation matrix between the quantization centers in a node and (b) the thresholded correlation matrix with a threshold of 0.8 corresponding to statistical significance greater than 95%.
Fig. 4. The average efficiency for all the classes based on the distance threshold of the spatial module (a) for the original implementation and (b) for the proposed method. In this section the proposed method is evaluated. The network described by George and Jaros (2007) has been implemented for benchmarking against the optimized HTM. The two different net- works complied to the same tree-shaped structure, ensuring thus the comparability of the experimental results. In both versions of the HTM, respective 4-level networks were implemented (v= 4). The node placed on the top of the hierarchy is the classification one with input images of size 32 by 32 pixels. Thus, each node in level 0 receives patches of 4 by 4 pixels, which are then reshaped to the input vectors. For the experimental validation the ETH-80
Fig. 4. The average efficiency for all the classes based on the distance threshold of the spatial module (a) for the original implementation and (b) for the proposed method. In this section the proposed method is evaluated. The network described by George and Jaros (2007) has been implemented for benchmarking against the optimized HTM. The two different net- works complied to the same tree-shaped structure, ensuring thus the comparability of the experimental results. In both versions of the HTM, respective 4-level networks were implemented (v= 4). The node placed on the top of the hierarchy is the classification one with input images of size 32 by 32 pixels. Thus, each node in level 0 receives patches of 4 by 4 pixels, which are then reshaped to the input vectors. For the experimental validation the ETH-80
Classification rate for the original and the proposed HTM using k-nn. Table 1 Table 2 Classification rate for the original and the proposed HTM using SVM.
Classification rate for the original and the proposed HTM using k-nn. Table 1 Table 2 Classification rate for the original and the proposed HTM using SVM.
classifier, yet the one versus all methodology was utilized for the testing procedure. The selected library for the implementation was the LIBSVM, proposed by Chang and Lin (2011). Linear, poly- nomial and Gaussian kernels have been tested, although the linear kernel proved capable enough to distinguish efficiently the differ- ent classes. The model regularization parameter C, which penalizes large errors, is chosen equal to 1000, in order to optimize data sep- aration. The utilization of SVM in the top node of the hierarchy yielded greater classification accuracy for both methods, as shown in Table 2. 5. Conclusions
classifier, yet the one versus all methodology was utilized for the testing procedure. The selected library for the implementation was the LIBSVM, proposed by Chang and Lin (2011). Linear, poly- nomial and Gaussian kernels have been tested, although the linear kernel proved capable enough to distinguish efficiently the differ- ent classes. The model regularization parameter C, which penalizes large errors, is chosen equal to 1000, in order to optimize data sep- aration. The utilization of SVM in the top node of the hierarchy yielded greater classification accuracy for both methods, as shown in Table 2. 5. Conclusions
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