Many modern applications deal with multi-label data, such as functional categorizations of genes, image labeling and text categorization. Classification of such data with a large number of labels and latent dependencies among them is a challenging task, and it becomes even more challenging when the data is received online and in chunks. Many of the current multi-label classification methods require a lot of time and memory, which make them infeasible for practical real-world applications. In this paper, we propose a fast linear label space dimension reduction method that transforms the labels into a reduced encoded space and trains models on the obtained pseudo labels. Additionally, it provides an analytical method to update the decoding matrix which maps the labels into the original space and is used during the test phase. Experimental results show the effectiveness of this approach in terms of running times and the prediction performance over different measures.
To make our method efficient, we select the encoding matrix randomly. Choosing random features or projections has been an active topic in machine learning. Random features have been reasonably successful in scaling kernel methods when dealing with large data sets @cite_11 @cite_36 @cite_37 . Training neural networks with random weights has also been elaborated in the literature @cite_7 @cite_2 . Studies show that there is significant redundancy in the parametrization of several deep learning methods and many of them even need not be learned at all @cite_3 . Subsequent studies propose using random features to reduce the number of parameters for deep convolutional neural networks without sacrificing predictive performance @cite_18 . Another study shows that features from a one-layer convolutional pooling architecture with completely random filters could achieve an average recognition rate that is just slightly worse than unsupervised pre-trained and fine-tuned filters @cite_13 . Further investigations show that a surprising fraction of the performance can be attributed to the architecture alone @cite_14 .
@cite_37 @cite_18 @cite_14 @cite_7 @cite_36 @cite_3 @cite_2 @cite_13 @cite_11
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In the field of neural network research a number of experiments described seem to be in contradiction with the classical pattern recognition or statistical estimation theory. The authors attempt to give some experimental understanding why this could be possible by showing that a large fraction of the parameters (the weights of neural networks) are of less importance and do not need to be measured with high accuracy. The remaining part is capable to implement the desired classifier and because this is only a small fraction of the total number of weights, the reported experiments seem to be more realistic from a classical point of view. > Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such computation significantly. Key to Fastfood is the observation that Hadamard matrices when combined with diagonal Gaussian matrices exhibit properties similar to dense Gaussian random matrices. Yet unlike the latter, Hadamard and diagonal matrices are inexpensive to multiply and store. These two matrices can be used in lieu of Gaussian matrices in Random Kitchen Sinks (Rahimi & Recht, 2007) and thereby speeding up the computation for a large range of kernel functions. Specifically, Fastfood requires O(n log d) time and O(n) storage to compute n non-linear basis functions in d dimensions, a significant improvement from O(nd) computation and storage, without sacrificing accuracy. We prove that the approximation is unbiased and has low variance. Extensive experiments show that we achieve similar accuracy to full kernel expansions and Random Kitchen Sinks while being 100x faster and using 1000x less memory. These improvements, especially in terms of memory usage, make kernel methods more practical for applications that have large training sets and or require real-time prediction. A new learning algorithm for multilayer neural networks that we have named No-Propagation (No-Prop) is hereby introduced. With this algorithm, the weights of the hidden-layer neurons are set and fixed with random values. Only the weights of the output-layer neurons are trained, using steepest descent to minimize mean square error, with the LMS algorithm of Widrow and Hoff. The purpose of introducing nonlinearity with the hidden layers is examined from the point of view of Least Mean Square Error Capacity (LMS Capacity), which is defined as the maximum number of distinct patterns that can be trained into the network with zero error. This is shown to be equal to the number of weights of each of the output-layer neurons. The No-Prop algorithm and the Back-Prop algorithm are compared. Our experience with No-Prop is limited, but from the several examples presented here, it seems that the performance regarding training and generalization of both algorithms is essentially the same when the number of training patterns is less than or equal to LMS Capacity. When the number of training patterns exceeds Capacity, Back-Prop is generally the better performer. But equivalent performance can be obtained with No-Prop by increasing the network Capacity by increasing the number of neurons in the hidden layer that drives the output layer. The No-Prop algorithm is much simpler and easier to implement than Back-Prop. Also, it converges much faster. It is too early to definitively say where to use one or the other of these algorithms. This is still a work in progress. In many recent object recognition systems, feature extraction stages are generally composed of a filter bank, a non-linear transformation, and some sort of feature pooling layer. Most systems use only one stage of feature extraction in which the filters are hard-wired, or two stages where the filters in one or both stages are learned in supervised or unsupervised mode. This paper addresses three questions: 1. How does the non-linearities that follow the filter banks influence the recognition accuracy? 2. does learning the filter banks in an unsupervised or supervised manner improve the performance over random filters or hardwired filters? 3. Is there any advantage to using an architecture with two stages of feature extraction, rather than one? We show that using non-linearities that include rectification and local contrast normalization is the single most important ingredient for good accuracy on object recognition benchmarks. We show that two stages of feature extraction yield better accuracy than one. Most surprisingly, we show that a two-stage system with random filters can yield almost 63 recognition rate on Caltech-101, provided that the proper non-linearities and pooling layers are used. Finally, we show that with supervised refinement, the system achieves state-of-the-art performance on NORB dataset (5.6 ) and unsupervised pre-training followed by supervised refinement produces good accuracy on Caltech-101 (≫ 65 ), and the lowest known error rate on the undistorted, unprocessed MNIST dataset (0.53 ). To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user specified shift-invariant kernel. We explore two sets of random features, provide convergence bounds on their ability to approximate various radial basis kernels, and show that in large-scale classification and regression tasks linear machine learning algorithms applied to these features outperform state-of-the-art large-scale kernel machines.