Introduction

Ricardo Vigário

As this book celebrates some great scientific avenues inspired by visionary researchers of the likes of Erkki Oja, I believe it is of particular relevance to remember the person, his career, and the shoulders from where several such amazing prospects sprung forth.

Many are the topics of research where Erkki has brought a marked contribution. Many more are the researchers, young and older, who shared and shaped paths of their working careers with him. For the sake of conciseness and a certain focus, I took the liberty to invite only a few of Erkki’s distinguished friends and colleagues to contribute with some words describing their relation to him. We will see in all of them the same admiration and recognition for a true scholar, but also some echoes of the person and the communicator, who often transcends the limits of the “work rules,” and ventures into the friendship realm.

This chapter is admittedly “the” nonscientific contribution in the book. Therefore, instead of thoroughly editing its text, in search for a rather cohesive structure, I will opt for a more platonic approach: reality will always exceed all finite projections we may find for it. In the cave wall that is this book, I will therefore let each of the participants voice their own views about Erkki. Those projections will certainly not be uncorrelated, let alone independent, as they address and characterize a common multi-dimensional source. Yet, the subspace spanned by the following words will hopefully draw an impressionist sketch of the person, the scholar, and the friend.

Using the liberty that assists the convener of such a delightful forum, I will take the opportunity to open with my own, short contribution.

A Student and a Co-Worker

In the early 1990s, I contacted a professor in Portugal on the subject of finding a suitable supervisor for a postgraduate research work. I thought I knew exactly what I wanted to do, but was rather uncertain where to go, and whom to work with. That professor, also in this chapter (LBA), suggested two names he knew who were leading researchers in the area I wanted to study – unsupervised learning, with biologically plausible computer vision goals. One worked in a remote city in Finland, far away from its capital. The other, Ralph Linsker, had a research group at IBM Thomas J. Watson Res. Center, in New York, USA. I thought: “maybe I can spend this year in Finland, and then move to IBM for the doctoral degree.” This decision was made even easier because Erkki Oja had just moved to Otaniemi, a campus in the thriving capital region.

Over 20 years later, after experiencing research at several other leading machine learning groups, I find myself still working in the same department, idealized by academician Teuvo Kohonen, and developed by Erkki Oja to very high international standards. One could wrongfully mistake this persistence for inertia. None could be farther from the truth. It was very clear, from my very first encounter with Erkki and his research group, that his department was a perfect place to germinate new ideas, and even propose new research directions. At the time, it had a recognized group of experts in Neural Networks, carrying out leading research in unsupervised learning. Equally important in my decision was the fact that the university campus comprised, among many other excellent research areas, an internationally recognized brain research unit, led by the expert hands of researchers, such as the academicians Olli V. Lounasmaa and Riitta Hari.

One cannot say that neuroinformatics was then at the core of Erkki’s research interests. Yet, he had always a finger on the pulse of science, and saw that a bridge between the aforementioned areas of research excellence was a valuable asset in the development of his own research endeavors. As one example, under his mentoring, pioneering research on biomedical applications of independent component analysis (ICA) was proposed. This is still, to date, one of the most accomplished areas of applied research for ICA.

The two anecdotal stories above reflect well Erkki’s nature: an acute scholar, with an amiable nature; a visionary in science, as well as a true mentor, empowering his junior colleagues, leading and supporting them to take independent responsibility in science; and with a door always open, and a word of guidance at all times.

With permission, I will end these lines with the words of academician Riitta Hari: “over the years, I have had the privilege of interacting with Erkki at a scientific, academic, and personal level, and the interaction has always been smooth and effective. I highly appreciate Erkki as a scientist and a colleague. I am sure that his outstanding research and pedagogical mentoring will continue to promote science in multiple disciplines.”

Prof. Simon Haykin

A novel property of Neural Networks and Learning Machines is their inherent ability to learn from the environment; and through learning, improve their performance in some statistical sense. Work in such research fields, right from their inception, has been motivated by the recognition that the human brain is a powerful information processing machine, which distinguishes itself, in a remarkable manner, from the digital computer.

Professor Erkki Oja’s influential scientific work spans over four highly prolific decades, from early research on associative memories in the late 1970s and early 1980s. To elaborate, Hebbian learning and principles of subspace analysis are basic to pattern recognition and machine vision, as well as blind source separation (BSS) and ICA, fields in which Prof. Oja researched throughout the 1990s and early 2000s. More recently, nonnegative matrix factorization and computational inference came into prominence. Throughout all that time, the points made herein apply to an insatiable thirst for knowledge, and an exceptional ability to detect and discover new trends in Neural Computation. Simply put, all of the above are the hallmark of a distinguished academic, namely, Prof. Erkki Oja.

A highly remarkable learning rule, known as Oja’s rule, so-called in recognition of the work done by Prof. Oja, was published in 1982. The rule was motivated by Hebb’s postulate of learning, which was first described in a book written by the neuropsychologist Donald Hebb in 1949. For the record, Oja’s rule may be described as follows:

The rule is simple to state, yet it is very rich in its mathematical exposé.

Furthermore, Prof. Oja and his research teams, over the years, went on to expand his learning rule for the identification of eigensubspaces, nonlinear principal component decompositions, and ICA algorithms. In addition to very elegant and efficient theoretical advances in Neural Computation and related topics, Prof. Oja always sought their use in practice, supporting pioneering research in many ambitious application areas: computer vision and pattern recognition; neuroinformatics and biomedical engineering applications; as well as proactive information retrieval and inference.

To conclude, Prof. Oja is an innovator par excellence. Knowing him as I do, he will continue to impact the world of Neural Computation through his pioneering contributions in years to come.

Prof. José Príncipe

In the 1970s, Erkki Oja opened up roads to many discoveries in the late portion of the twentieth century and beyond. His first works on PCA provided the tone which blended a very solid grounding in mathematics with the amazing power of online adaptation that we still are grasping to fully understand. They require imagination, intuition, and transcend the aseptic world of mathematics. Erkki predicted and solidified many important applications of his simple adaptation rule (now with his name), and the applications of FastICA to imaging will always be connoted with him and his group in Finland.

His leadership in adaptive informatics, and more recently in computational inference, has propelled many young scientists in Finland, and all around the world to this exciting domain so important for big data. But on top of it all, Erkki’s legacy transcends science and engineering. He is a true scholar, a gentleman, a wonderful person, and I am very fortunate to call him my friend.

Prof. Tülay Adali

Erkki Oja has been a true leader in the field, and paved the way to much of the exciting work going on today in the machine learning field, particularly in nonlinear adaptive processing. He has provided the essential bridge between neural computation and adaptive optimization theory, and has not only provided the tools to address many of today’s challenging problems but also offered different and fruitful ways to visualize them, making his impact particularly long lasting. The continuing strong rate in citations to his work from all periods, including those from the early 1980s, is a simple testament to the influence of his work and its continuing importance.

Beyond all this, he does inspire those around him, not only to achieve their best technically but also to enjoy life. It has been always a pleasure to be in his company, which might include sharing a fine meal with a nice glass of wine, or following the rhythm of the music, as he...