Artificial neural networks (ANNs) have become the driving force behind recent artificial intelligence (AI) research. An important problem with implementing a neural network is the design of its architecture. Typically, such an architecture is obtained manually by exploring its hyperparameter space and kept fixed during training. This approach is both time-consuming and inefficient. Furthermore, modern neural networks often contain millions of parameters, whereas many applications require small inference models. Also, while ANNs have found great success in big-data applications, there is also significant interest in using ANNs for medium- and small-data applications that can be run on energy-constrained edge devices. To address these challenges, we propose a neural network synthesis methodology (SCANN) that can generate very compact neural networks without loss in accuracy for small and medium-size datasets. We also use dimensionality reduction methods to reduce the feature size of the datasets, so as to alleviate the curse of dimensionality. Our final synthesis methodology consists of three steps: dataset dimensionality reduction, neural network compression in each layer, and neural network compression with SCANN. We evaluate SCANN on the medium-size MNIST dataset by comparing our synthesized neural networks to the well-known LeNet-5 baseline. Without any loss in accuracy, SCANN generates a @math smaller network than the LeNet-5 Caffe model. We also evaluate the efficiency of using dimensionality reduction alongside SCANN on nine small to medium-size datasets. Using this methodology enables us to reduce the number of connections in the network by up to @math (geometric mean: @math ), with little to no drop in accuracy. We also show that our synthesis methodology yields neural networks that are much better at navigating the accuracy vs. energy efficiency space.
The high dimensionality of many datasets used in various applications of machine learning leads to the curse of dimensionality problem. Therefore, researchers have explored dimensionality reduction methods to improve the performance of machine learning models by decreasing the number of features. Traditional dimensionality reduction methods include Principal Component Analysis (PCA), Kernel PCA, Factor Analysis (FA), Independent Component Analysis (ICA), as well as Spectral Embedding methods. Some graph-based methods include Isomap @cite_29 and Maximum Variance Unfolding @cite_25 . FeatureNet @cite_13 uses community detection in small sample size datasets to map high-dimensional data to lower dimensions. Other dimensionality reduction methods include stochastic proximity embedding (SPE) @cite_14 , Linear Discriminant Analysis (LDA), and t-distributed Stochastic Neighbor Embedding (t-SNE) @cite_7 . A detailed survey of dimensionality reduction methods can be found in @cite_40 .
@cite_14 @cite_7 @cite_29 @cite_40 @cite_13 @cite_25
16346066 2109531142 2161041254 2807933484
Over the past few years, some embedding methods have been proposed for feature extraction and dimensionality reduction in various machine learning and pattern classification tasks. Among the methods proposed are Neighborhood Preserving Embedding (NPE), Locality Preserving Projection (LPP) and Local Discriminant Embedding (LDE) which have been used in such applications as face recognition and image video retrieval. However, although the data in these applications are more naturally represented as higher-order tensors, the embedding methods can only work with vectorized data representations which may not capture well some useful information in the original data. Moreover, high-dimensional vectorized representations also suffer from the curse of dimensionality and the high computational demand. In this paper, we propose some novel tensor embedding methods which, unlike previous methods, take data directly in the form of tensors of arbitrary order as input. These methods allow the relationships between dimensions of a tensor representation to be efficiently characterized. Moreover, they also allow the intrinsic local geometric and topological properties of the manifold embedded in a tensor space to be naturally estimated. Furthermore, they do not suffer from the curse of dimensionality and the high computational demand. We demonstrate the effectiveness of the proposed tensor embedding methods on a face recognition application and compare them with some previous methods. Extensive experiments show that our methods are not only more effective but also more efficient. Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high-dimensional data analysis. Fisher discriminant analysis (FDA) is a traditional technique for supervised dimensionality reduction, but it tends to give undesired results if samples in a class are multimodal. An unsupervised dimensionality reduction method called locality-preserving projection (LPP) can work well with multimodal data due to its locality preserving property. However, since LPP does not take the label information into account, it is not necessarily useful in supervised learning scenarios. In this paper, we propose a new linear supervised dimensionality reduction method called local Fisher discriminant analysis (LFDA), which effectively combines the ideas of FDA and LPP. LFDA has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem. We demonstrate the practical usefulness and high scalability of the LFDA method in data visualization and classification tasks through extensive simulation studies. We also show that LFDA can be extended to non-linear dimensionality reduction scenarios by applying the kernel trick. Mining useful clusters from high dimensional data have received significant attention of the computer vision and pattern recognition community in the recent years. Linear and nonlinear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), nonconvexity (for matrix factorization methods), and susceptibility to gross corruptions in the data. In this paper, we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient, and scalable for huge datasets with O(n log(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data. Real world networks constructed from raw data are often characterized by complex community structures. Existing dimensionality reduction techniques, however, do not take such characteristics into account. This is especially important for problems with low number of samples where the curse of dimensionality is particularly significant. Therefore, in this paper, we propose FeatureNet, a novel community-based dimensionality reduction framework targeting small sample problems. To this end, we propose a new method to directly construct a network from high-dimensional raw data while explicitly revealing its hidden community structure; these communities are then used to learn low-dimensional features using a representation learning framework. We show the effectiveness of our approach on eight datasets covering application areas as diverse as handwritten digits, biology, physical sciences, NLP, and computational sustainability. Extensive experiments on the above datasets (with sizes mostly between 100 and 1500 samples) demonstrate that FeatureNet significantly outperforms (i.e., up to 40 improvement in classification accuracy) ten well-known dimensionality reduction methods like PCA, Kernel PCA, Isomap, SNE, t-SNE, etc.