Ternary Residual Networks
Sub-8-bit representation of DNNs incur some noticeable loss of accuracy despite rigorous (re)training at low-precision. Such loss of accuracy essentially makes them equivalent to a much shallower counterpart, diminishing the power of being deep networks. To address this problem of accuracy drop we introduce the notion of \textit{residual networks} where we add more low-precision edges to sensitive branches of the sub-8-bit network to compensate for the lost accuracy. Further, we present a perturbation theory to identify such sensitive edges. Aided by such an elegant trade-off between accuracy and model size, the 8-2 architecture (8-bit activations, ternary weights), enhanced by residual ternary edges, turns out to be sophisticated enough to achieve similar accuracy as 8-8 representation ($\sim 1\%$ drop from our FP-32 baseline), despite $\sim 1.6\times$ reduction in model size, $\sim 26\times$ reduction in number of multiplications , and potentially $\sim 2\times$ inference speed up comparing to 8-8 representation, on the state-of-the-art deep network ResNet-101 pre-trained on ImageNet dataset. Moreover, depending on the varying accuracy requirements in a dynamic environment, the deployed low-precision model can be upgraded/downgraded on-the-fly by partially enabling/disabling residual connections. For example, disabling the least important residual connections in the above enhanced network, the accuracy drop is $\sim 2\%$ (from our FP-32 baseline), despite $\sim 1.9\times$ reduction in model size, $\sim 32\times$ reduction in number of multiplications, and potentially $\sim 2.3\times$ inference speed up comparing to 8-8 representation. Finally, all the ternary connections are sparse in nature, and the residual ternary conversion can be done in a resource-constraint setting without any low-precision (re)training and without accessing the data. …

Sequence and Set Similarity Measure (S3M)
In many data mining applications, both classification and clustering algorithms require a distance/similarity measure. The central problem in similarity based clustering/classification comprising sequential data is deciding an appropriate similarity metric. The existing metrics like Euclidean, Jaccard, Cosine, and so forth do not exploit the sequential nature of data explicitly. In this paper, the authors propose a similarity preserving function called Sequence and Set Similarity Measure (S3M) that captures both the order of occurrence of items in sequences and the constituent items of sequences. …

Flat Clustering and Topic Modeling based on Fast Rank-2 NMF (FlatNMF2)
The importance of unsupervised clustering and topic modeling is well recognized with ever-increasing volumes of text data. In this paper, we propose a fast method for hierarchical clustering and topic modeling called HierNMF2. Our method is based on fast Rank-2 nonnegative matrix factorization (NMF) that performs binary clustering and an efficient node splitting rule. Further utilizing the final leaf nodes generated in HierNMF2 and the idea of nonnegative least squares fitting, we propose a new clustering/topic modeling method called FlatNMF2 that recovers a flat clustering/topic modeling result in a very simple yet significantly more effective way than any other existing methods. We describe highly optimized open source software in C++ for both HierNMF2 and FlatNMF2 for hierarchical and partitional clustering/topic modeling of document data sets. Substantial experimental tests are presented that illustrate significant improvements both in computational time as well as quality of solutions. We compare our methods to other clustering methods including K-means, standard NMF, and CLUTO, and also topic modeling methods including latent Dirichlet allocation (LDA) and recently proposed algorithms for NMF with separability constraints. Overall, we present efficient tools for analyzing large-scale data sets, and techniques that can be generalized to many other data analytics problem domains. …