In this month’s column, we discuss the solutions to some of the questions we discussed in last month’s column.

As you know, it is our practice to feature computer science interview questions in the column regularly, for our student readers to prepare for interviews. A few of our student readers have requested me to provide the answers to the questions as well. Given that this column is meant to kindle the reader’s curiosity and seek out solutions instead of providing canned answers to questions, I generally do not provide solutions to the questions featured here. So, instead of providing the complete solutions, as requested, it may help the readers to discuss the high level solutions in more detail, while they work out the concrete answers. Hence, in this month’s column, we will discuss some of the topics that the featured questions are based on.

One of the questions from last month’s column was on the difference between virtual machines and containers. Virtual machines are intended to facilitate server virtualisation, wherein the physical hardware resources are virtualised by a special piece of software known as the virtual machine monitor or hypervisor. This controls the virtual machines that run on top of it. Each virtual machine has its own copy of its operating system. Typically, a VMM or hypervisor runs on top of the host operating system (though it is possible to have a bare metal hypervisor which runs on top of the firmware itself). Each VM runs its own operating system, which is known as the guest operating system. These guest operating systems can be different from each other. On the other hand, containers run on top of a single host operating system, which is why they are sometimes referred to as supporting operating system virtualisation, whereas virtual machines are referred to as supporting server virtualisation. Typically, multiple containers sit on top of a single host operating system, which itself runs on top of a physical server. All the containers share the same host operating system kernel and the libraries.

Now, let us consider the case in which we have a bug in an operating system. If this operating system version was running as a guest OS in a VM environment, the impact of the OS bug would be confined only to that VM running the guest OS. On the other hand, assume that this OS was the host OS on top of which all containers were hosted. All the containers would be impacted by the same bug, since there is no OS isolation in a container environment. In that case, what then is the advantage of containers? The very fact that containers share the same OS components makes them very lightweight and easy to deploy. The container density is much higher than the VM density, given the same physical configuration. A detailed discussion of the security issues of containers can be found in the blog post

Question (3) from last month’s column was about information retrieval. Readers were asked why we need to use inverse document frequency as a measure for relevant documents retrieval, given a query. As we know, TF-IDF is primarily used as the measure for information retrieval. TF stands for term frequency. This is a measure of how frequently a term occurs in a single document. If T1 is a query term and it occurs with a high frequency in document D1, it seems obvious that D1 may be a relevant document when a user is searching for query T1. However, let us consider that our document collection is a set of documents associated with cricket, and our query is ‘wisden player’. Now, it is possible that many documents contain the query term ‘player’ and so its TF will be high for many documents. Hence, this term ‘player’ may not help us to discriminate the set of documents that are more relevant to the user’s query. However, the term ‘wisden’ is a more significant term as it is likely to be present only in the relevant documents. So we need to get those documents that contain the discriminating term ‘wisden’ and not include all those documents which contain the non-discriminating term ‘player’.

This is where the inverse document frequency comes into play. Inverse document frequency (IDF) is an inverse of the measure of the number of documents that contain the term. Hence, for a discriminating term, since it would be present in fewer documents, its inverse document frequency would be much higher; hence, it can help offset the effect of non-discriminating terms for which the IDF will be much lower. Typically, both TF and IDF are scaled and normalised appropriately. Hence, IDF is typically defined as IDF (term t) = Log (N/Nt), where N is the total number of documents in the corpus and Nt is the total number of documents in which term ‘t’ is present. I leave it to the reader to figure out whether IDF helps to improve precision, recall, or both.
Question (4) in last month’s column was about predicting the results of election polls in states. This problem can be analysed in multiple different ways. Let’s assume that we want to predict the winning party for a particular state, given that there are multiple parties contesting the election. We also know the past history of elections in that state, as well as various other features collected from past data. This can be modelled as a multi-label classification, where the winner is one of N parties contesting the elections.

On the other hand, if we are considering all the constituencies of the state, can we cluster the constituencies into different clusters such that each cluster represents the set of constituencies won by a specific party. We opt for clustering if we don’t have labelled data for the winners in previous elections. In that case, we just want to use the features/attributes of different constituencies and cluster them. However, note that though we get a set of clusters, we don’t know what these clusters represent. Hence, a human expert needs to label these clusters. Once these clusters are labelled, an unlabelled constituency can be labelled by assigning the cluster label that is closest to it. So this question can be modelled in multiple ways — either as a classification problem or as a clustering problem, depending on available data for analysis.

Question (8) was about word embeddings, which is the hottest topic currently in natural language processing. Frequency or count based approaches have earlier been widely used in natural language processing. For instance, latent semantic analysis or latent semantic indexing is one of the major approaches in this direction. These approaches have typically been based on global counts, wherein for each word, we consider all the words that have co-occurred with it, to construct its representation. Hence, the entire corpus has to be processed before we get a representation for each word based on co-occurrence counts.

On the other hand, word embeddings are based on a small local context window which is moved over all the contexts in the corpus and, at any point in time, a continuous vector representation is available for each word which gets updated as we examine more contexts. Note that co-occurrence based counts are typically sparse representations since a word will not co-occur with many other words in the vocabulary. On the other hand, embeddings are dense representations since they are of much lower dimensions.

A detailed discussion on the relation between embeddings and global count based representations can be found in the paper ‘GloVe: Global Vectors for Word Representation’ by Pennington et al available at It would be good for the readers to experiment with both Google word2vec embeddings available online (this includes word vectors for a vocabulary of three million words trained on a Google News dataset) as well as the Glove vectors available at Word embeddings and, subsequently, paragraph and document embeddings are widely used as inputs in various natural language processing tasks. In fact, they are used as input representation for many of the deep learning based text processing systems. There are a number of word2vec implementations available, the popular ones being from the Gensim package (, which is widely used. It would be useful for the readers to understand how word embeddings are learnt using neural networks without requiring any labelled data. While word embeddings are typically used in deep neural networks, the word2vec model for generating the word embeddings is not a deep architecture, but a shallow neural network architecture. More details can be found in the word2vec paper

If you have any favourite programming questions/software topics that you would like to discuss on this forum, please send them to me, along with your solutions and feedback, at sandyasm_AT_yahoo_DOT_com. Till we meet again next month, here’s wishing all our readers a wonderful and productive year ahead!


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